Multi-cycle distribution method for gas station with small capacity-sales ratio in active distribution mode

Abstract

The invention provides a multi-cycle distribution method for a gas station with a small capacity-sales ratio in an active distribution mode. The method comprises the following steps: aiming at a gas station with a small capacity-to-sales ratio in an active distribution mode, constructing a mixed integer programming model with a demand segmentation inventory path problem IRPSD-SC problem by considering the storage capacity limitation of a plurality of periods and the gas station; setting an objective function and a constraint condition of a mixed integer programming model of the IRPSD-SC problem, and taking the minimum transportation cost, the minimum stockout cost of a gas station and the minimum inventory holding cost as the objective function; taking a node access constraint, a vehicle loading constraint, a time constraint and a multi-cycle inventory holding level constraint as constraint conditions; and based on a greedy thought, constructing an initial solution of the mixed integer programming model by taking stockout avoidance as a principle, inputting a mixed variable neighborhood search algorithm, and outputting a multi-cycle distribution result of the gas station with the small capacity-sales ratio. The method can effectively solve the problem of gas station distribution in an active distribution mode, realizes cost reduction, efficiency improvement, energy conservation and emission reduction, and promotes high-quality development of the petrochemical industry in China.

Description

Technical Field

[0001] The present invention relates to the technical field of secondary distribution of refined oil products, and in particular to a multi-cycle distribution method for a gas station with a small volume-to-sales ratio in an active distribution mode. Background Art

[0002] Theoretically, IRPSD (Inventory Routing Problem with Split Delivery) is a combination of the two research fields of IRP (Inventory Routing Problem) and SDVRP (Split Delivery Vehicle Routing Problem). SDVRP emphasizes the segmentation of customer demand, that is, vehicles are allowed to visit customers multiple times. The number of deliveries and the amount of each delivery are decision variables when solving the problem, which increases the complexity of the research. However, the total delivery volume of customers in SDVRP is known, and generally does not involve inventory capacity restrictions, nor does it consider the customer's consumption or sales of products. Therefore, there is no constraint relationship between the various deliveries in SDVRP, and the conditions for delivery are also flexible, and delivery can even be made at any time in the delivery cycle. IRP emphasizes the joint decision of inventory and transportation in the supply chain. The objective function generally includes both inventory holding costs and transportation costs, but a customer is generally delivered only once in a cycle.

[0003] In the IRPSD problem, the demand of each customer in each cycle is known and must be met without out-of-stock. Customers are allowed to be delivered multiple times in one cycle. Considering the complexity of the problem, some scholars have designed a solution method based on the approximate model of the problem and the Lagrangian relaxation method. The relaxation problem is decomposed into an inventory problem and a path problem by the Lagrangian relaxation method, and then solved by the linear programming algorithm and the minimum cost flow algorithm respectively. Some scholars have carried out research on IRPSD in the active delivery mode with the background of gas station delivery, considering multiple cycles and tank capacity constraints, while allowing users to be replenished multiple times in each cycle and not allowing out-of-stock. In his model, the delivery volume and delivery frequency of the oil tank are both decision variables, and each vehicle only runs one trip. However, both studies did not consider customers with small capacity-to-sales ratios (oil tanks). Their common shortcoming is that they both assume that the customer's replenishment in a cycle must not exceed the remaining storage capacity at the beginning of the cycle, that is, the customer can accommodate the total replenishment of the cycle at the beginning of the period (the customer's demand in a cycle is much smaller than the storage capacity). Therefore, whether it is a one-time delivery or multiple deliveries, the vehicle will not violate the storage capacity constraints when visiting the customer at any time, so there is no need to consider the customer's accommodation time.

[0004] The path optimization problem in the secondary distribution scenario of refined oil has experienced a development from no compartments to compartments, from single oil products to multiple oil products, from single trip to multiple trips, and from not considering time windows to considering time windows. The research trend is that the scenarios are becoming more and more complex and closer to reality, but there are still many gaps between them and the actual situation. First, most of the literature is aimed at the pull distribution model, that is, the distribution demand is known. Secondly, there are very few studies on the active distribution model, and most of the literature does not consider the scenario of multiple continuous deliveries to the same customer. However, in practice, for some gas stations with small tank capacity and fast sales speed, it is necessary to replenish a single oil product multiple times within a day. The present invention takes this scenario into consideration, and takes into account details such as vehicles with compartments, multiple products, multiple trips, time windows, and customer storage capacity restrictions, so it is more in line with reality.

[0005] In the active distribution model, the inventory of the demander is determined by the supplier. The supplier needs to decide when to transport what product, what quantity, and what kind of product to which customer. This is a complex decision problem. In addition, there may be some "small capacity-to-sales ratio customers" with small storage capacity and large demand in the supply chain network. The supplier needs to frequently replenish their inventory and make reasonable distribution plans. Due to the inventory constraints of customers, the delivery time of the supplier's vehicle is subject to the hard constraints of the customer's storage time point and the soft constraints of the out-of-stock time point. If the vehicle arrives earlier than the storage time point, it needs to wait. If it arrives later than the out-of-stock time point, it needs to pay the out-of-stock cost. The time window formed by these two time points is closely related to the decision of the distribution volume, making this decision problem more complicated.

[0006] At present, oil companies that adopt the active distribution model basically adopt the method of manually preparing distribution plans based on experience. The main disadvantages of manually preparing distribution plans in the existing technology are: first, it takes a long time to prepare the plan, and the labor cost of dispatchers in large national oil companies is huge; second, when the scale of the distribution network is large, it is difficult to find a reasonable distribution plan that guarantees oil supply, meets constraints and has low costs.

[0007] At present, most of the existing technologies for secondary distribution of refined oil products are based on the premise of passive distribution mode, that is, the demand for various oil products at each gas station is known. There is still a lack of research on the secondary distribution of refined oil products under the active distribution mode, and the distribution optimization problem for customers with small volume-to-sales ratio has not been solved. Summary of the invention

[0008] An embodiment of the present invention provides a multi-cycle distribution method for a gas station with a small volume-to-sales ratio under an active distribution mode, so as to effectively implement active distribution of refined oil to the gas station with a small volume-to-sales ratio.

[0009] In order to achieve the above object, the present invention adopts the following technical scheme.

[0010] A multi-cycle distribution method for a gas station with a small capacity-to-sales ratio under an active distribution mode, comprising:

[0011] For gas stations with small capacity-to-sales ratio under active distribution mode, a mixed integer programming model for the inventory routing problem with demand splitting (IRPSD-SC) is constructed considering multiple cycles and the storage capacity constraints of gas stations.

[0012] The objective function and constraint conditions of the mixed integer programming model of the IRPSD-SC problem are set, with the transportation cost, the out-of-stock cost of the gas station and the inventory holding cost being minimized as the objective function; the node access constraint, the vehicle loading constraint, the time constraint and the multi-period inventory holding level constraint being used as the constraint conditions;

[0013] Based on the greedy idea and the principle of avoiding stockouts, an initial solution of the mixed integer programming model of the IRPSD-SC problem is constructed, and the initial solution is used as the input of a hybrid variable neighborhood search algorithm. The hybrid variable neighborhood search algorithm outputs a multi-period distribution result of the gas station with a small capacity-to-sales ratio, which includes which vehicle delivers which grade of refined oil and how much quantity to which gas station at which time in which period.

[0014] Preferably, for the gas station with small capacity-to-sales ratio in the active distribution mode, a mixed integer programming model for the IRPSD-SC problem is constructed by considering multiple cycles and the storage capacity constraints of the gas station, including:

[0015] For gas stations with small capacity-to-sales ratio under active distribution mode, the minimum sum of transportation cost, out-of-stock cost and inventory holding cost is taken as the objective function, and a mixed integer mathematical programming model for the IRPSD-SC problem with multiple consecutive deliveries, multiple cycles, multiple oil products and compartments is established.

[0016] The basic assumptions of the mixed integer mathematical programming model are as follows:

[0017] (1) The oil depot and gas station remain in operation during each cycle;

[0018] (2) Any fuel product at a gas station is allowed to be delivered multiple times within one cycle;

[0019] (3) In the IRPSD-SC problem, the inventory holding cost of the gas station in each period is calculated based on the initial inventory holding level, and the inventory holding cost per unit time is known;

[0020] (4) Allowing for stockouts, the cost of which is related to the duration of the stockout and the speed at which the oil product is sold;

[0021] (5) Each compartment of the vehicle can only carry one type of oil, and all oil products in a compartment can only be delivered to one gas station, that is, the vehicle compartments are indivisible;

[0022] (6) Each vehicle is only allowed to run once in a cycle. A vehicle departs from the oil depot, delivers the products it carries to the relevant gas station, and then returns to the oil depot. This is called a trip. Each trip of the vehicle must be within the same cycle and is not allowed to run across cycles.

[0023] (7) The delivery volume of a vehicle to a gas station is an integer multiple of a fixed volume, and the volume delivered by a vehicle to a single gas station at a time cannot exceed its total onboard capacity;

[0024] (8) When a vehicle is in motion, it incurs transportation costs, which are related to mileage;

[0025] (9) Ignoring the time and cost of loading and unloading vehicles;

[0026] (10) The vehicle’s unit distance traveled cost, travel speed, number of compartments, and compartment capacity are known.

[0027] Preferably, the objective function and constraint conditions of the mixed integer programming model for setting the IRPSD-SC problem are to minimize the transportation cost, the out-of-stock cost of the gas station and the inventory holding cost as the objective function; and to use the node access constraint, the vehicle loading constraint, the time constraint and the multi-period inventory holding level constraint as the constraint conditions, including:

[0028] In the mixed integer programming model of the IRPSD-SC problem, a directed graph G = (V, E) is used to represent the distribution network of the supply chain system, where V is a vertex set, V = C∪{0}∪{n+1}, {0} and {n+1} both represent the same distribution center oil depot, and each oil tank of each oil product at each gas station is regarded as a customer, and each customer is represented as a node. C = {1, ..., n} represents the customer node set. After loading from the distribution center, the vehicle departs, delivers the loaded goods to the relevant customers, and returns to the distribution center. The vehicle only delivers once in each cycle. A pair of virtual start nodes and end nodes are set for each vehicle. The vehicle departs from {0} and returns to {n+1} after delivery. E represents the edge set, E = {(i, j)|i, j∈V, i≠j}. The specific parameters and variable settings are shown in Table 2:

[0029] Table 2 Model collection

[0030]

[0031] Table 3 Model parameters

[0032]

[0033] Table 4 Model decision variables

[0034]

[0035] The total cost is composed of vehicle transportation cost, out-of-stock cost and inventory holding cost. The objective function of the mixed integer programming model of the IRPSD-SC problem is set to minimize the total cost:

[0036] min(f1+f2+f3)

[0037]

[0038] The constraints of the mixed integer programming model for setting the IRPSD-SC problem include node access constraints, vehicle loading constraints, time constraints, and multi-period inventory holding level constraints, as follows:

[0039] Node access constraints include:

[0040]

[0041]

[0042] The above formulas indicate that the oil tank node needs to satisfy the flow balance, that is, the vehicle must leave after arriving at the customer node to ensure the flow balance of the node; the access order constraint between nodes ensures that the vehicle starts from the starting distribution center, visits several customers, and then returns to the distribution center; the vehicle cannot visit the distribution center continuously and multiple times; in a certain delivery of any customer node, the node can only be visited once at most; it is guaranteed that the vehicle only runs once at most; the r+1th delivery must occur under the premise of the existence of the rth delivery, which guarantees the order of the number of times the customer is visited multiple times, reflecting the characteristics of demand segmentation;

[0043] Vehicle loading constraints include:

[0044]

[0045] Among them, formulas 1 to 3 are used to track the changes in the number of available compartments of the vehicle during driving. Among them, formula 1 indicates that the available compartments of the vehicle when it departs from the distribution center yard are all c; formulas 2 and 3 represent the changing trend of the number of compartments of the vehicle when the vehicle visits between nodes, that is, the number of available compartments at the rear node is equal to the available compartments at the front node minus the used compartments; formula 4 indicates that the delivery volume is limited by the vehicle capacity; formula 5 establishes the decision variable and The relationship between indicates that if there is a visit to a customer, the compartment required for its delivery volume must be no less than 1, otherwise it is 0, that is, if there is a visit, it must be delivered;

[0046] Time-related constraints include:

[0047]

[0048] Among them, formula 1 describes the order The out-of-stock situation during the period, when the arrival time is later than the out-of-stock time point, there is an out-of-stock situation, and its value is the difference between the order arrival time and the out-of-stock time point, otherwise the out-of-stock duration is 0; Formulas 2 and 3 are used to determine the relationship between the starting service time of the vehicle serving each node. Specifically, the vehicle journey starts from the distribution center, and the time to serve the next node should be greater than the customer's accommodation time point and the time required to reach the node. If the vehicle arrives earlier than the accommodation time point, it is necessary to wait for the arrival of the accommodation time point at the node before starting the service; Formula 4 represents the time sequence of the start service time between the previous and next visits to the same node, and ensures that if the r+1th visit exists, the r+1th visit is after the rth visit; Formula 5 indicates that the vehicle must work within the scheduling period, that is, it starts from the distribution center after the start of the scheduling period and must return to the distribution center before the end of the scheduling period; Formula 6 represents the time relationship between the visits between cycles, that is, the visit of the t+1 cycle must be after the visit of the t cycle; Formula 7 indicates that the customer may also be out of stock from the last delivery to the end of this cycle, and the out-of-stock duration of this part is recorded as This can be obtained by comparing the out-of-stock time point after the last delivery to customer i with the beginning and end time of the next cycle;

[0049] Multi-period inventory level constraints include:

[0050]

[0051] is a non-negative integer

[0052] Formula 1 represents the relationship between customer inventory levels between adjacent cycles. The beginning inventory level of customer i at the beginning of the next cycle is equal to the beginning inventory level of the current cycle plus the total delivery volume of the customer in this cycle, minus the sales volume of customer i in this cycle; Formula 2 indicates that the customer inventory level must not exceed the storage capacity; Formula 3 is a constraint on the decision variables.

[0053] Preferably, the initial solution of the mixed integer programming model of the IRPSD-SC problem is constructed based on the greedy idea and the principle of avoiding stock-outs, including:

[0054] The parallel path strategy is used to construct the vehicle path. The parallel path construction strategy means that for a fleet of m vehicles, K vehicles select the access node in turn and perform state transfer. After traversing all vehicles, traverse each vehicle in K again to perform the second state transfer, and repeat until a feasible solution is formed.

[0055] Based on the greedy idea, the initial solution is constructed based on the principle of avoiding stockouts. That is, each time the vehicle selects the tank node with the shortest stockout time based on the current distribution network status, and delivers the maximum amount of oil to the node to ensure that it does not run out of oil within the cycle while meeting the vehicle's remaining capacity limit. If the vehicle's remaining capacity is insufficient to accommodate the demand of any tank, or the vehicle cannot return to the oil depot within the cycle after delivering to the next node, the vehicle is ordered to return to the oil depot immediately. After all vehicles return to the oil depot, the distribution plan for the next cycle is generated until the distribution plan for all cycles is generated.

[0056] The specific steps for generating the initial solution are as follows:

[0057] Step 1: Initialize all parameters, set T = 1;

[0058] Step 2: Calculate the list of tank nodes in this cycle at the time of out-of-stock based on the inventory at the beginning of the cycle and the sales speed of each tank. T , list T This is the set of orders that may be out of stock during this period;

[0059]

[0060] Step 3: Judge, if list T If not empty, execute Step 4, otherwise execute Step 12;

[0061] Step 4: Select list T The customer tank with the smallest out-of-stock time a , traverse each car from i=1 and execute step5;

[0062] Step 5: Determine k i Has it been returned to the library? If k i If not returned, execute step 6, otherwise execute step 10;

[0063] Step 6: Determine k i Are there any remaining compartments? If yes, execute step 7, otherwise execute step 9;

[0064] Step 7: Determine k i Is to visit the tank a After that, check whether it can return to the oil depot within the cycle. If yes, execute step 8, otherwise execute step 9;

[0065] Step 8: k i Move to tank a And confirm the order quantity Q=min(Q i_MIN ,Q k-remain ), where Qi_MIN It indicates the minimum oil quantity to ensure that customer i does not run out of oil during this cycle, Q k―remain Indicates the remaining capacity of vehicle k, updates all customer and vehicle status information, and updates the list T , execute step 10;

[0066] Step 9: Let k i Return to the oil depot immediately, z=z+1;

[0067] Step 10: Let i = i + 1, and repeat steps 5-8 until i>m, that is, traverse every car in the fleet;

[0068] Step 11: Determine whether all vehicles have returned to the oil depot. If so, proceed to step 12; otherwise, return to step 4.

[0069] Step 12: Let T = T + 1, update all vehicle information and oil depot information, where the oil depot inventory holding level inherits the inventory of the previous cycle, and determine whether all cycle distribution plans have been generated. If T>T max , output the initial solution, otherwise return to step 2.

[0070] Preferably, the initial solution is used as an input of a hybrid variable neighborhood search algorithm, and the hybrid variable neighborhood search algorithm outputs a multi-period distribution result of the gas station with a small volume-to-sales ratio, wherein the multi-period distribution result includes which vehicle distributes which grade of refined oil and how much quantity to which gas station at which time in which period, including:

[0071] It is set that there are two types of entities in the hybrid variable neighborhood search algorithm: vehicles and nodes. Nodes include oil tanks and oil depots. From the dimensions of vehicles, orders and periodic inventory, the single-vehicle order exchange neighborhood structure, the same-cycle multi-vehicle order exchange neighborhood structure, the inter-week order exchange neighborhood structure, the random oil tank adjustment neighborhood structure, the carpooling optimization neighborhood structure, the vehicle addition optimization neighborhood structure, the minimum vehicle removal optimization neighborhood structure, the out-of-stock order optimization neighborhood structure within the trip, the multi-vehicle out-of-stock order optimization neighborhood structure in the same cycle, the out-of-stock order optimization neighborhood structure between weeks, the order delivery volume optimization neighborhood structure, the order removal neighborhood structure, the order addition neighborhood structure and the service time optimization neighborhood structure are designed, and a total of 14 neighborhood structures are provided;

[0072] The hybrid variable neighborhood search algorithm is based on the initial solution and uses the 14 neighborhood structures to generate the distribution plan of the gas station with a small capacity-to-sales ratio. The event scheduling algorithm is used to update all node states and vehicle states after each new distribution plan of the gas station is generated, and the cost is recalculated. The start service time of each customer node is determined by the FIFO rule. After multiple iterative calculations, the multi-cycle distribution results of the gas station with a small capacity-to-sales ratio are obtained. The multi-cycle distribution results include which vehicle distributes which grade of refined oil and how much quantity to which gas station at which time in which cycle.

[0073] Preferably, the hybrid variable neighborhood search algorithm generates a distribution plan for the gas station with a small capacity-to-sales ratio based on the initial solution using the 14 neighborhood structures, including:

[0074] In addition to accepting improved new solutions, the hybrid variable neighborhood search algorithm also accepts poor new solutions with a certain probability, and uses the new solution as the current solution, returns to the first neighborhood to continue searching. The probability depends on the target value difference between the new solution and the current solution and the cooling temperature, and the calculation formula is as follows:

[0075]

[0076] in is the current temperature, and its initial temperature is Whenever VNS enters external circulation, it enters the cooling process;

[0077] Use the half-decay method to control the temperature, that is, set the temperature half-decay position to control the temperature at σ n The temperature decays to half of the cooling process at the first VNS iteration, controlling the relationship between temperature and the number of iterations.

[0078]

[0079] The search order of the local search operator in the hybrid variable neighborhood search algorithm is:

[0080] Order delivery quantity optimization → Access sequence optimization operators (random oil tank adjustment, order exchange between weeks, order exchange of multiple vehicles in the same cycle, single vehicle order exchange) → Order increase and decrease operators (vehicle increase optimization) → Out-of-stock order optimization operators (out-of-stock order optimization within the trip, out-of-stock order optimization of multiple vehicles in the same cycle, out-of-stock order optimization between weeks) → Carpooling optimization → Vehicle number adjustment operators (minimum vehicle removal optimization) → Service time optimization;

[0081] The pseudo code of the hybrid variable neighborhood search algorithm is as follows:

[0082]

[0083] It can be seen from the technical solutions provided by the above embodiments of the present invention that the present invention establishes a mathematical programming model and designs a solution algorithm for the problem of manually compiling distribution plans, generates a reasonable actual distribution plan for refined oil products in a short time, reduces the cost of manual input, and provides decision support for the automatic and intelligent formulation of distribution plans for oil companies. The method can generate a replenishment distribution plan for a small capacity-to-sales ratio gas station with a small tank capacity and a large sales volume under the active distribution mode.

[0084] Additional aspects and advantages of the present invention will be given in part in the following description, which will become obvious from the following description, or may be learned through practice of the present invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0085] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings required for use in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other accompanying drawings can be obtained based on these accompanying drawings without paying creative work.

[0086] Figure 1 A processing flow chart of a multi-cycle distribution method for a gas station with a small capacity-to-sales ratio in an active distribution mode provided by an embodiment of the present invention;

[0087] Figure 2 A schematic diagram of a vehicle driving route and loading scheme for a certain refined oil distribution problem provided by an embodiment of the present invention;

[0088] Figure 3 A schematic diagram of the relationship between gas stations and oil tanks in a distribution network provided by an embodiment of the present invention.

[0089] Figure 4 A schematic diagram of a solution to an IRPSD-SC problem provided by an embodiment of the present invention;

[0090] Figure 5 An initial solution generation flow chart provided by an embodiment of the present invention;

[0091] Figure 6 A schematic diagram of a neighborhood structure for a bicycle order exchange provided by an embodiment of the present invention;

[0092] Figure 7 A neighborhood structure diagram of a same-cycle multi-vehicle order exchange provided by an embodiment of the present invention;

[0093] Figure 8 A neighborhood structure diagram of an inter-period order exchange provided by an embodiment of the present invention;

[0094] Fig. 9 A schematic diagram of a random oil tank adjustment neighborhood structure provided in an embodiment of the present invention.

[0095] Fig.10 A schematic diagram of applying an event scheduling method provided by an embodiment of the present invention to the IRPSD-SC problem;

[0096] Fig.11 A schematic diagram of the impact analysis of customers with a small capacity-to-sales ratio provided in an embodiment of the present invention. DETAILED DESCRIPTION

[0097] The embodiments of the present invention are described in detail below, examples of which are shown in the accompanying drawings, wherein the same or similar reference numerals throughout represent the same or similar elements or elements having the same or similar functions. The embodiments described below with reference to the accompanying drawings are exemplary and are only used to explain the present invention, and cannot be interpreted as limiting the present invention.

[0098] It will be understood by those skilled in the art that, unless expressly stated, the singular forms "one", "said", and "the" used herein may also include plural forms. It should be further understood that the term "comprising" used in the specification of the present invention refers to the presence of the features, integers, steps, operations, elements and / or components, but does not exclude the presence or addition of one or more other features, integers, steps, operations, elements, components and / or groups thereof. It should be understood that when we refer to an element as being "connected" or "coupled" to another element, it may be directly connected or coupled to the other element, or there may be intermediate elements. In addition, the "connection" or "coupling" used herein may include wireless connection or coupling. The term "and / or" used herein includes any unit and all combinations of one or more associated listed items.

[0099] It will be understood by those skilled in the art that, unless otherwise defined, all terms (including technical and scientific terms) used herein have the same meaning as those generally understood by those skilled in the art in the art to which the present invention belongs. It should also be understood that terms such as those defined in common dictionaries should be understood to have meanings consistent with the meanings in the context of the prior art, and will not be interpreted with idealized or overly formal meanings unless defined as herein.

[0100] To facilitate understanding of the embodiments of the present invention, several specific embodiments will be further explained below with reference to the accompanying drawings, and each embodiment does not constitute a limitation on the embodiments of the present invention.

[0101] Active distribution mode: The supplier (oil depot) determines the replenishment quantity and replenishment frequency of the gas station in each distribution cycle (shift) and organizes vehicles for distribution; the same customer may need multiple deliveries in a cycle, and due to storage capacity constraints, the time window of each delivery is a decision variable.

[0102] Gas station with small capacity-to-sales ratio: a gas station with large sales volume but small tank capacity. For this type of gas station, multiple deliveries are required within a delivery cycle (shift) to meet sales demand. Gas stations need to maintain a certain amount of inventory at the end of the period to meet sales needs at the beginning of the next day, but the problems with the single-cycle delivery method often make the end-of-period inventory very low or even zero, making it difficult to guarantee sales at the beginning of the next day. This solution can generate delivery plans for multiple cycles at one time, and actually execute the plan for the first cycle, and then generate multiple cycle delivery plans again in the next cycle, and keep rolling forward, so that the inventory can meet sales needs at the beginning of the next day.

[0103] According to the actual distribution demand of gas stations under the active distribution mode, the present invention abstracts the distribution problem of customers with small capacity-to-sales ratio into a multi-period (Multi-Period), multi-product (Multi-Product), vehicle with compartment (Multi-Compartment Vehicle) inventory routing problem with demand segmentation (IRPSD-SC) for customers with small capacity-to-sales ratio, and establishes a mathematical programming model.

[0104] The IRPSD-SC problem is a new type of inventory routing problem with demand segmentation. It considers multiple cycles and multiple products, and uses vehicles with compartments for distribution. Customers with a small volume-to-sales ratio (such as a gas station's 92-grade oil tank) need multiple replenishment and delivery in one cycle. The difference in each delivery volume will affect the time window for subsequent deliveries. The delivery volume and number of deliveries for each replenishment are both decision variables.

[0105] The specific description is as follows:

[0106] In a supply chain system consisting of one supplier (distribution center) and multiple demanders, the distribution center delivers a variety of products to the demanders, using vehicles with compartments for transportation, and the supplier is responsible for formulating a replenishment plan. The distribution center has sufficient inventory of each product and a full range of products. The distribution center has a parking lot and an unlimited number of vehicles. The vehicle model is single, and the compartment information (number of compartments, compartment volume) of each vehicle is known. The fleet needs to operate in shifts, and the length of each shift is one cycle. Each delivery by the vehicle must depart from the distribution center and return in the same cycle.

[0107] Each demander sells several products, and each product has a maximum inventory level limit. For example, various oil products at a gas station are stored separately in tanks with limited capacity. Each product of each demander is regarded as a customer. For example, the tank of No. 92 gasoline at a gas station is regarded as a customer. Given the inventory capacity, initial inventory and sales speed of each customer, it is required that when the delivery vehicle arrives at the customer, the remaining storage capacity of the customer can accommodate the delivery volume of the vehicle this time. If the customer is sold out, it will cause out-of-stock costs and economic losses. There are a certain number of customers with small capacity-to-sales ratios among the customers. They have a large sales speed and a small storage capacity, and they all need to be delivered multiple times in a cycle. Considering multiple cycles, the inventory level of each customer at the end of a cycle is equal to the inventory level at the beginning of the next cycle. It should be emphasized that considering multiple cycles will greatly increase the complexity of the problem and require more time to solve, but its advantage is that if only a single cycle is considered, the inventory at the end of the period may be insufficient, and it is difficult to guarantee the supply at the beginning of the second cycle, resulting in a large number of out-of-stocks at the beginning of the next cycle, which is intolerable for enterprises. Considering multiple cycles can ensure that there will not be a large number of out-of-stocks at the beginning of the previous cycles. Although there may still be a problem of insufficient inventory at the end of the last cycle, this problem can be solved through rolling scheduling.

[0108] Aiming at the actual needs of gas stations of enterprises such as Sinopec, the present invention studies the optimization problem of secondary distribution scheduling of refined oil products, takes into account the actual characteristics of oil tank capacity limitation, continuous multiple distribution of oil tanks, multiple products, multiple compartments, multiple cycles, etc., designs a hybrid variable neighborhood search algorithm (VNSA, Variable Neighborhood Search based Approach) that combines a variable neighborhood search algorithm (VNS) with a simulated annealing algorithm (SA), designs 14 neighborhood structures, and verifies the feasibility and practicability of the algorithm through a large number of examples and case experiments.

[0109] The present invention first gives basic assumptions based on the characteristics of the research problem, considers the common node access constraints of the traditional vehicle routing problem (VRP) and the vehicle loading constraints, time-related constraints and multi-period inventory holding level constraints that are unique to this problem, takes the minimum sum of transportation cost, out-of-stock cost and inventory holding cost as the objective function, and establishes a mixed integer mathematical programming model for the vehicle routing problem with multiple consecutive deliveries, multiple cycles, multiple products and compartments (IRPSD-SC). Aiming at the problem, three variable neighborhood search algorithms are designed and implemented with simulated annealing algorithm and variable neighborhood search algorithm as the theoretical basis for algorithm design. According to the characteristics of the IRPSD-SC problem, 14 neighborhood structures are designed. On this basis, a hybrid variable neighborhood search algorithm (VNSA) integrating simulated annealing is designed and implemented. The VNSA algorithm introduces the idea of ​​accepting a more inferior solution with a certain probability in the simulated annealing algorithm into the variable neighborhood search algorithm to enhance the global search capability of the algorithm. A greedy-based heuristic initial solution generation algorithm and 14 neighborhood search operators that integrate the characteristics of the IRPSD-SC problem are designed, and various neighborhood search operators are applied to the variable neighborhood search algorithm (VNSA) that integrates simulated annealing.

[0110] The processing flow chart of a multi-cycle distribution method for a gas station with a small volume-to-sales ratio in an active distribution mode provided by an embodiment of the present invention is as follows: Figure 1 As shown, the process includes the following steps:

[0111] Step S10: The present invention innovatively considers customers with small capacity-to-sales ratios in the IRPSD problem, and proposes the IRPSD-SC problem for the first time. A mixed integer programming model for the IRPSD-SC problem is constructed based on the background of small capacity-to-sales ratio gas stations and divisible demand in the active distribution mode. Under the active distribution mode, this mixed integer programming model combines the IRP (Inventory Routing Problem) problem with the SDVRP (Split Delivery Vehicle Routing Problem) problem for a supply chain network of one supplier and multiple customers; it considers multiple cycles, customer capacity constraints, and customers with small capacity-to-sales ratios, and allows multiple deliveries and out-of-stock situations for each customer within one cycle.

[0112] Step S20: Establish the objective function and constraints of the mixed integer programming model of the IRPSD-SC problem. The objective function is to minimize the transportation cost, the customer's out-of-stock cost and the inventory holding cost; the four types of constraints are node access constraints, vehicle loading constraints, time constraints and multi-period inventory holding level constraints.

[0113] Step S30: The present invention adopts the VNSA algorithm which is a hybrid variable neighborhood search algorithm and simulated annealing algorithm to solve the mathematical model of the IRPSD-SC problem. The initial solution is iteratively optimized using perturbations and local searches. In combination with the characteristics of the IRPSD-SC problem, 14 optimization operators for local search and perturbation processes are designed from the dimensions of vehicles, orders, inventory, etc. In order to enhance the global search capability of the algorithm, the variable neighborhood search algorithm is combined with the simulated annealing algorithm, and the acceptance criteria based on simulated annealing are adopted in the local search. In addition to accepting improved new solutions, poorer new solutions are also accepted with a certain probability.

[0114] Based on the greedy idea, the initial solution of the mixed integer programming model of the IRPSD-SC problem is constructed in the principle of avoiding stockouts. The initial solution is used as the input of the VNSA (hybrid variable neighborhood search algorithm). The VNSA algorithm outputs the multi-cycle distribution results of gas stations with small capacity-to-sales ratios. The multi-cycle distribution results mainly include the following information: in which cycle, which vehicle delivers which grade of refined oil to which gas station and how much, the distribution tasks of each vehicle in each cycle, the order of completing these tasks, the time of arrival at the gas station, etc.

[0115] Specifically, the above step S10 includes:

[0116] It is required to formulate a reasonable replenishment plan to replenish each customer by orderly arranging the number of deliveries to each customer, the delivery quantity and delivery time of each delivery, as well as the transportation routes of the vehicles, so as to minimize the sum of transportation costs, customer inventory holding costs and out-of-stock costs.

[0117] Aiming at gas stations with small capacity-to-sales ratio under active distribution mode, the minimization of the sum of transportation cost, out-of-stock cost and inventory holding cost is taken as the objective function, and a mixed integer mathematical programming model for the IRPSD-SC problem with multiple continuous deliveries, multiple cycles, multiple products and compartments is established.

[0118] The basic assumptions of the mixed integer mathematical programming model are as follows:

[0119] (1) The distribution center and customers remain operational during each cycle;

[0120] (2) Customers are allowed to receive multiple deliveries within one cycle;

[0121] (3) In the IRPSD-SC problem, the inventory holding cost of the customer in each period is calculated based on the initial inventory holding level. The inventory holding cost per unit time is known;

[0122] (4) Out-of-stock conditions are allowed. The cost of out-of-stock conditions is related to the duration of the out-of-stock situation and the speed at which the product is sold;

[0123] (5) Each compartment of the vehicle can only carry one type of product, and all products in a compartment can only be delivered to one customer, i.e., the vehicle compartments are indivisible;

[0124] (6) Each vehicle is only allowed to operate once in a cycle (a vehicle departs from the distribution center, delivers the products it carries to the relevant customers, and then returns to the distribution center, which is called a trip or a journey), and each trip of the vehicle must be within the same cycle and is not allowed to operate across cycles;

[0125] (7) The delivery volume of a vehicle to a customer is an integer multiple of a fixed amount (e.g., 500 liters), and the volume delivered to a single customer at a time cannot exceed the vehicle's total capacity;

[0126] (8) When a vehicle is in motion, it incurs transportation costs, which are related to mileage;

[0127] (9) Ignoring the time and cost of loading and unloading vehicles;

[0128] (10) The vehicle’s unit distance traveled cost, travel speed, number of compartments, and compartment capacity are known.

[0129] The distribution plans that gas stations need to determine in each cycle include:

[0130] (1) The orders for each gas station's tanks in each cycle, and the delivery volume of each order;

[0131] (2) The order of delivery of multiple orders for the same tank;

[0132] (3) Which vehicle will deliver each order?

[0133] (4) the order in which vehicles access the order;

[0134] (5) The time when the vehicle is delivered to each order.

[0135] In the example part, small-scale and large-scale example sets of the IRPSD-SC problem are respectively produced. Each example is taken from the Solomon example set and appropriately adapted. The business data of each oil tank is taken from the actual data of Sinopec gas stations. The multi-period distribution results finally obtained include the initial value of each example, the best value of VNSA and the average value. The following uses the actual data of the enterprise's refined oil distribution network as an example to illustrate the solution to the IRPSD-SC problem of the embodiment of the present invention. Figure 2 The diagram shows the vehicle route and loading scheme for a refined oil distribution problem. Table 2 shows the detailed distribution scheme for two cycles. The refined oil distribution network includes 1 oil depot, 4 gas stations, and 8 oil tanks. Each gas station has 1 to 3 oil tanks, which store 92, 95 and 98 gasoline products (in Figure 2In the first and second cycles, two homogeneous vehicles with compartments were used, each with three compartments of 10,000 liters. In each cycle, the vehicle departed from the oil depot, made one trip, and returned to the depot before the end of the cycle. Each cycle lasted 24 hours.

[0136] Table 3 IRPSD-SC solution example

[0137]

[0138] The solution is explained by taking the trip of vehicle d in the second cycle as an example, and the rest of the trips are similar: vehicle d departs from the oil depot yard at 34h, loaded with 2 compartments of 92# gasoline products and 1 compartment of 95# gasoline products. After 0.8h of driving, vehicle d arrives at gas station C and unloads 1 compartment of 8,000 liters of 92# gasoline products and then leaves immediately. After 0.48h, it drives to gas station A and unloads 2 compartments of 16,000 liters of 95# products to replenish the 95# gasoline tank in gas station A, and then returns to the oil depot yard at 40.1h. During this week, vehicle c replenished 10,000 liters of 95# oil tank at gas station A at 25.3h. Therefore, this replenishment of vehicle d is the second replenishment of the oil tank in this cycle.

[0139] Specifically, the above step S20 includes: constructing a mathematical model of the IRPSD-SC problem according to the problem. Use a directed graph G = (V, E) to represent the distribution network of the supply chain system, where V is a vertex set, V = C∪{0}∪{n+1}, and {0} and {n+1} both represent the same distribution center. Each customer is represented as a node, and C = {1,…,n} represents the customer node set. After loading from the distribution center, the vehicle departs, delivers the loaded goods to the relevant customers, and then returns to the distribution center. The vehicle only delivers once in each cycle, and a pair of virtual starting nodes and terminal nodes are set for each vehicle. The vehicle departs from {0} and returns to {n+1} after delivery. E represents the edge set, E = {(i,j)|i,j∈V,i≠j}. The specific parameters and variable settings are shown in Table 2.

[0140] Table 4 Model collection

[0141]

[0142] Table 3 Model parameters

[0143]

[0144] Table 4 Model decision variables

[0145]

[0146] The objective function of the mixed integer programming model of the IRPSD-SC problem is:

[0147] min(f1+f2+f3)

[0148]

[0149] The goal of the IRPSD-SC model is to minimize the total cost, which is composed of the following three parts: vehicle transportation cost, which is related to the vehicle's driving distance; out-of-stock cost, which is represented by the sales loss during the out-of-stock period, that is, the reduced sales profit of the oil tank due to out-of-stock; inventory holding cost, which is related to the inventory holding level of the oil tank.

[0150] The constraints of the mixed integer programming model of the IRPSD-SC problem include node access constraints, vehicle loading constraints, time constraints, and multi-period inventory holding level constraints, as follows:

[0151] Node access constraints include:

[0152]

[0153]

[0154] The above formulas indicate that the oil tank node needs to satisfy the flow balance, that is, the vehicle must leave after arriving at the customer node to ensure the flow balance of the node; the access order constraint between nodes ensures that the vehicle starts from the starting distribution center, visits several customers, and then returns to the distribution center; the vehicle cannot visit the distribution center continuously and multiple times; in a certain delivery of any customer node, the node can only be visited once at most; it is guaranteed that the vehicle only runs once at most; the r+1th delivery must occur under the premise of the existence of the rth delivery, which guarantees the order of the number of times the customer is visited multiple times, reflecting the characteristics of demand segmentation.

[0155] Vehicle loading constraints include:

[0156]

[0157] Among them, formulas 1 to 3 are used to track the changes in the number of available compartments of the vehicle during driving. Among them, formula 1 indicates that the available compartments of the vehicle when it departs from the distribution center yard are all c; formulas 2 and 3 represent the changing trend of the number of compartments of the vehicle when the vehicle visits between nodes, that is, the number of available compartments at the rear node is equal to the available compartments at the front node minus the used compartments; formula 4 indicates that the delivery volume is limited by the vehicle capacity; formula 5 establishes the decision variable and The relationship between indicates that if there is a visit to a customer, the compartment required for its delivery quantity must be no less than 1, otherwise it is 0, that is, if there is a visit, it must be delivered.

[0158] Time-related constraints include:

[0159]

[0160] Among them, formula 1 describes the order The mid-term out-of-stock situation, when the arrival time is later than the out-of-stock time point, there is an out-of-stock situation, and its value is the difference between the order arrival time and the out-of-stock time point, otherwise the out-of-stock duration is 0; Formulas 2 and 3 are used to determine the relationship between the starting service time of the vehicle serving each node. Specifically, the vehicle journey starts from the distribution center, and the time to serve the next node should be greater than the customer's accommodation time point and the time required to reach the node. If the vehicle arrives earlier than the accommodation time point, it is necessary to wait for the arrival of the accommodation time point at the node before starting the service; Formula 4 represents the time sequence of the start service time between the previous and next visits to the same node, and ensures that if the r+1th visit exists, the r+1th visit is after the rth visit; Formula 5 indicates that the vehicle must work within the scheduling period, that is, it starts from the distribution center after the start of the scheduling period and must return to the distribution center before the end of the scheduling period; Formula 6 represents the time relationship between the visits between cycles, that is, the visit of the t+1 cycle must be after the visit of the t cycle; Formula 7 indicates that the oil tank may also be out of stock between the last delivery and the end of this cycle, and this part of the out-of-stock duration is recorded as It can be obtained by comparing the out-of-stock time point after the last delivery of oil tank i with the beginning and end time of the next cycle.

[0161] Multi-period inventory level constraints include:

[0162]

[0163] is a non-negative integer

[0164] Formula 1 represents the relationship between customer inventory levels between adjacent cycles. The beginning inventory level of customer i at the beginning of the next cycle is equal to the beginning inventory level of the current cycle plus the total delivery volume of the customer in this cycle, minus the sales volume of customer i in this cycle; Formula 2 indicates that the customer inventory level must not exceed the storage capacity; Formula 3 is a constraint on the decision variables.

[0165] In order to clearly represent the status of vehicles in the distribution network, the distribution network of the IRPSD-SC problem regards the smallest individual that issues a demand as a customer, that is, the vertex set V in the network graph G = (V, E). Figure 3 A schematic diagram of the relationship between a gas station and an oil tank in a distribution network provided by an embodiment of the present invention. Figure 3 In the gas station distribution network, the customers are tanks rather than gas stations. In a certain period, the distribution plan of vehicle k is called the trip of vehicle k, and the set of trips of all vehicles in period T is called the tour set of period T.T , the set of itineraries of all cycles constitutes a solution (plan) of the IRPSD-SC problem. Figure 4 This is a schematic diagram of the solution to the IRPSD-SC problem. In fact, the oil tanks belonging to the same gas station have the same geographical location. Figure 4 A schematic diagram of a solution to an IRPSD-SC problem provided by an embodiment of the present invention, Figure 4 In order to clearly illustrate the relationship between trip, tour and plan, the geographical location of the oil tank is discretized. Figure 4 The solution of an IRPSD-SC problem is shown, which consists of two trip sets, Tour1 and Tour2. Tour represents the solution of IRPSD-SC in a cycle, which consists of all the trips of the vehicles used in this cycle. As shown in the small figure on the left, the solution of the IRPSD-SC problem in the first cycle (tour1) uses three vehicles in this cycle, so tour1 consists of trip1 to trip3.

[0166] Specifically, the above step S30 includes:

[0167] Initial solution generation

[0168] (1) Path construction

[0169] The parallel path strategy is used to construct the vehicle path. The parallel path construction strategy means that for a fleet of m vehicles, the vehicles K select the visited nodes in turn and perform state transfer. After traversing all the vehicles, traverse each vehicle in K again to perform the second state transfer, and repeat until a feasible solution is formed. For example, first select vehicle k1 to move from the oil depot to tank1 once, then select k2 to move from the oil depot to tank2... After all vehicles move to the next node, return to vehicle k1 and move it from tank1 to the next node until the journey set tour1 is generated, and then construct the journey set for the next cycle. The pseudo code of the parallel path construction rule is shown below.

[0170]

[0171]

[0172] The difficulty of generating paths in parallel in the IRPSD-SC problem lies in the size of the fleet. The present invention considers a fleet with no quantity limit, so it is necessary to estimate a suitable initial solution vehicle when generating the initial solution and use the vehicle addition and deletion operators in the algorithm to adjust to the global optimal number of vehicles. The determination of the number of vehicles in the initial solution takes into account two principles: first, it does not cause excessive redundancy and avoids deleting a large number of vehicles in VND; second, there are no large shortages to avoid the initial solution causing excessive shortage costs and resulting in poor initial solution generation. Combining the above two points, the number of vehicles m0 in the initial solution selects a number of vehicles that can just carry the total sales volume of oil tanks during the scheduling period, as shown in the following formula.

[0173]

[0174] (2) Initial solution generation algorithm

[0175] An initial solution generation flow chart provided by an embodiment of the present invention is as follows: Figure 5 As shown. Based on the greedy idea, the initial solution is constructed based on the principle of avoiding out-of-stock. That is, the vehicle selects the customer node with the shortest out-of-stock time based on the current distribution network status each time, and distributes the maximum amount of oil to the node to ensure that it will not be out of oil within the cycle while meeting the vehicle's remaining capacity limit. If the vehicle's remaining capacity is not enough to accommodate any customer demand, or the vehicle cannot return to the oil depot within the cycle after delivering to the next node, the vehicle is ordered to return to the oil depot immediately. After all vehicles return to the oil depot, the distribution plan for the next cycle is generated until the distribution plan for all cycles is generated. The specific steps for generating the initial solution are as follows:

[0176] Step 1: Initialize all parameters, set T = 1;

[0177] Step 2: Calculate the list of tank nodes in this cycle at the time of out-of-stock based on the inventory at the beginning of the cycle and the sales speed of each tank. T , list T This is the set of orders that may be out of stock during this period.

[0178]

[0179] Step 3: Judge, if list T If not empty, execute Step 4, otherwise execute Step 12;

[0180] Step 4: Select list T The customer tank with the smallest out-of-stock time a , traverse each car from i=1 and execute step5;

[0181] Step 5: Determine k i Whether it has been returned to the warehouse (vehicles that have not left the warehouse are also considered not returned to the warehouse), if ki If not returned, execute step 6, otherwise execute step 10;

[0182] Step 6: Determine k i Are there any remaining compartments? If yes, execute step 7, otherwise execute step 9;

[0183] Step 7: Determine k i Is to visit the tank a After that, check whether it can return to the oil depot within the cycle. If yes, execute step 8, otherwise execute step 9;

[0184] Step 8: k i Move to tank a And confirm the order quantity Q=min(Q i_MIN ,Q k-remain ), where Q i_MIN It indicates the minimum oil quantity to ensure that customer i does not run out of oil during this cycle, Q k―remain Indicates the remaining capacity of vehicle k, updates all customer and vehicle status information, and updates the list T , execute step 10;

[0185] Step 9: Let k i Return to the oil depot immediately, z=z+1;

[0186] Step 10: Let i = i + 1, and repeat steps 5-8 until i>m, that is, traverse every car in the fleet;

[0187] Step 11: Determine whether all vehicles have been returned to the warehouse. If so, execute step 12, otherwise return to step 4;

[0188] Step 12: Let T = T + 1, update all vehicle information and oil depot information, where the oil depot inventory holding level inherits the inventory of the previous cycle, and determine whether all cycle distribution plans have been generated. If T>T max , output the initial solution, otherwise return to step 2.

[0189] Variable neighborhood search: This paper combines the characteristics of the IRPSD-SC problem and designs 14 neighborhood structures from the dimensions of vehicles, orders, and periodic inventory. Among them, order increase and decrease, removal, random tank adjustment, vehicle addition, and minimum vehicle removal operators are perturbation operators, and all neighborhoods are used for VND. The neighborhood structure design is as follows:

[0190] (1) Bicycle Order Exchange Neighborhood Structure

[0191] “Swap” refers to swapping the visit order of two order nodes in the same vehicle trip. Figure 6A schematic diagram of a bicycle order exchange neighborhood structure provided by an embodiment of the present invention, such as Figure 6 As shown in Figure 1, randomly select the trip of vehicle k in period t, select the two orders O1 and O2 it visits, and exchange the positions of the two orders. The number inside the gas station icon in the figure represents the number of vehicle compartments required to deliver the tank.

[0192] After orders O1 and O2 are exchanged, the vehicle may arrive before the capacity point of O2 and wait there, and an order adjustment of a small capacity-to-sales ratio tank will inevitably affect the status of subsequent tanks, so the constraint that all vehicles in this cycle return to the oil depot within the scheduling period should be met; in addition, in order not to affect vehicle loading, the order exchange should meet the constraint that the number of compartments of the tank truck required by the order is consistent.

[0193] (2) Multiple-vehicle order exchange neighborhood in the same cycle

[0194] An embodiment of the present invention provides a neighborhood structure for exchanging orders of multiple vehicles in the same period. Figure 7 As shown in the tour t The trip of vehicle A is trip A , the trip of vehicle B is trip B . Find trip A The order O1 with the largest out-of-stock cost (if trip A There is no out-of-stock order, then randomly select an order), randomly select a trip B For order O2 that satisfies the following constraints, the positions of the two orders are exchanged to form a new solution.

[0195] The constraints that the neighborhood structure needs to satisfy for the exchange of multiple vehicle orders in the same cycle are the same as those for the exchange of single vehicle orders.

[0196] (3) Neighborhood structure of order exchange between weeks

[0197] An embodiment of the present invention provides a neighborhood structure for periodic order exchange as follows: Figure 8 As shown in Figure 1, we exchange orders between multiple cycles of the IRPSD-SC problem to increase flexibility in adjusting the solution. Specifically, we select the cycle tour. T1 Randomly select the trip of vehicle A A Order O1, then in tour T2 Select vehicle B trip B Order O2 on the network can be exchanged with rows O1 and O2 to form a new solution while satisfying the constraints.

[0198] The constraints that need to be satisfied for order exchanges between cycles are the same as those for order exchanges for individual bikes.

[0199] (4) Random oil tank adjustment neighborhood structure

[0200] Fig. 9 A schematic diagram of a random oil tank adjustment neighborhood structure provided by an embodiment of the present invention. The random oil tank adjustment neighborhood structure changes the quality of the solution and finds a better solution by randomly adjusting nodes. Specifically, from x cur Randomly select an order node O1, randomly select an oil tank O2 that is different from O1, replace the O1 oil tank with O2 and recalculate the objective function value. If the new solution is better, accept the solution and enter the next iteration, otherwise continue to randomly select oil tanks and adjust until a better solution is found or a certain number of iterations is reached.

[0201] The neighborhood structure of random tank adjustment needs to meet certain constraints, that is, the solution after replacing O2 needs to meet the following constraints: 1) During the period of random tank adjustment, all vehicles can return to the tank depot before the end of the period.

[0202] (5) Carpooling optimizes neighborhood structure

[0203] In IRPSD-SC, the distance of movement within a gas station is not taken into account, and the distance between oil tanks at the same gas station is zero. Carpooling and delivering orders from the same gas station will significantly optimize costs. Carpooling optimization is based on this design.

[0204] Carpooling optimization from tour T Randomly select different oil tanks belonging to the same gas station and non-same-trip orders O1 and O2 that meet the constraints. Move O1 and O2 to the delivery itinerary of the same vehicle to save the transportation cost of the vehicle traveling between different gas stations.

[0205] Assume that orders O1 and O2 that meet the constraints have been selected and belong to trip A 、trip B There are four ways to implement the above process: 1) Move O1 out of the trip A And insert it into trip B Before O2; 2) Move O1 out of the trip A And insert it into trip B After O2; 3) Remove O2 from the trip B And insert it into trip A Before O1; 4) Move O2 out of the trip B And insert it into trip A After O1. The optimization of the neighborhood structure of carpooling with oil tanks at the same gas station aims to select new solutions where O1 and O2 meet the constraints and minimize the cost.

[0206] Constraints: The service start times of O1 and O2 should be less than a certain time interval (e.g., 30 minutes); the order insertion method can meet the capacity constraints of the new car; all cars in the new plan can return within the scheduling period.

[0207] (6) Adding more cars to optimize neighborhood structure

[0208] In the IRPSD-SC problem, the fleet size is infinite, so the number of vehicles can be adjusted up and down as needed. The number of vehicles used in the scheme to increase the optimization of the neighborhood structure is increased to reduce the total cost. T , tour T The number of vehicles used is V T , the tour T The oil tanks that are out of stock at the end of the period are put into set A, and are arranged from small to large according to the out-of-stock time to form set B. The newly added vehicle k selects the access node from set A to form its trip k Specifically, the vehicle visits the earliest oil tank that is out of stock and confirms the order quantity Q = min (Q i_MIN ,Q k―remain ), where Q i_MIN It indicates the minimum oil quantity to ensure that customer i does not run out of oil during this cycle, Q k―remain Represents the remaining volume of vehicle k. If the new solution satisfies the relevant constraints, calculate whether the total cost is saved. If so, replace the current solution with the new solution. The pseudo code of the process of optimizing the neighborhood structure by adding vehicles alone is as follows: Fig.11 shown.

[0209] The constraints that the neighborhood structure must satisfy are: 1) Each cycle vehicle must return to the oil depot before the end of the cycle; 2) Adding a trip k Meet vehicle capacity constraints.

[0210] (7) Minimum vehicle removal optimizes neighborhood structure

[0211] The minimum vehicle removal neighborhood structure and the vehicle addition optimization neighborhood structure both aim to adjust the number of vehicles in the solution. Specifically, the minimum vehicle removal operator sorts all vehicles in the same cycle from small to large according to the load, and inserts the orders of the minimum loaded vehicle into the itinerary of other vehicles one by one. When the order carried by the minimum vehicle is empty, the itinerary of the vehicle is deleted and a new solution is formed.

[0212] The minimum vehicle removal optimization reduces the fleet size and optimizes the overall cost. The constraints that the new solution needs to meet are: (a) all vehicles meet the loading requirements; (b) all vehicles return to the oil depot within their respective cycles.

[0213] (8) Optimizing the neighborhood structure for out-of-stock orders within the trip

[0214] The optimization of out-of-stock orders in a trip is to optimize the neighborhood structure for out-of-stock orders in a bicycle trip. T Randomly select the trip of car k k , find trip k Order O1 with the largest out-of-stock cost, randomly select tripk For other orders O2 on the itinerary, exchange O1 and O2 to form a new solution x_new. If x_new satisfies the relevant constraints, compare the costs of the solutions brought by the new and old solutions. If the optimization of out-of-stock orders within the itinerary can bring cost savings, accept the new solution immediately, otherwise enter the next iteration until cost savings are brought or the maximum number of local iterations is reached.

[0215] The optimization of out-of-stock orders within the trip needs to consider the following constraints: 1) All vehicles in the new plan can return to the oil depot within the corresponding scheduling period; 2) The number of vehicle compartments occupied by orders O1 and O2 is the same; 3) After O1 and O2 are exchanged, O1 does not need to wait at the oil tank node, that is, the time it takes for the vehicle to arrive at O1 is greater than the accommodation time of O1.

[0216] (9) Optimizing the neighborhood structure for out-of-stock orders of multiple vehicles in the same period

[0217] The optimization of the neighborhood structure of multiple out-of-stock orders in the same period reduces the total out-of-stock cost by changing the multi-vehicle itinerary. T Randomly select the trip of car A A , find trip A Order O1 with the largest out-of-stock cost is removed from trip A Remove it and insert O1 into tour T In other trips.

[0218] The constraints that need to be satisfied by the optimization structure of multiple vehicles out of stock orders in the same period are: 1) All vehicles in the new plan can return to the oil depot within their respective scheduling periods; 2) O1 is inserted into the new trip and the vehicle loading constraints of the vehicle must be satisfied.

[0219] (10) Neighborhood structure optimization for out-of-stock orders during the week

[0220] For the multi-period problem, the main purpose of optimizing the neighborhood structure for out-of-stock orders between cycles is to deliver the out-of-stock orders at the end of the cycle in advance, thereby reducing the out-of-stock cost in the final solution. A , find trip A The order O1 with the largest out-of-stock cost. Randomly select the trip of car B within the T-1 period B , insert O1 into trip without violating constraints B The end of .

[0221] The constraints that need to be satisfied for the optimization of out-of-stock orders during a cycle are: 1) All vehicles in the new solution can return to the oil depot within their respective scheduling periods; 2) O1 is inserted into the new trip and the vehicle loading constraints of the vehicle must be satisfied; 3) In order to make the optimization effective, T∈(2, T max), that is, the neighborhood structure does not optimize the out-of-stock orders at the end of the first period.

[0222] (11) Order delivery volume optimizes neighborhood structure

[0223] The delivery volume optimization neighborhood structure adjusts the optimization solution cost by adjusting the order delivery volume fluctuation. T In the example, randomly select the trip of car A. A , randomly select trip A Order O i , while keeping the number of compartments unchanged, randomly increase or decrease the delivery units for the order.

[0224] The constraints that need to be met by the neighborhood structure for optimizing the delivery volume are: 1) All vehicles in the new plan can return to the oil depot within their respective scheduling periods; 2) The adjustment of the order delivery volume does not change the number of compartments loaded on the original vehicle.

[0225] (12) Order removal neighborhood structure

[0226] The order removal neighborhood structure forms a new solution by removing an order from the vehicle itinerary. Specifically, in x cur T cycle tour T In the example, randomly select the trip of car A. A , randomly select trip A Order O i Delete it and form a new solution x new , if x cur If the constraints are satisfied and the cost is saved, the new solution is accepted, otherwise it proceeds to the next iteration until it brings cost savings or reaches the maximum number of local iterations.

[0227] The relevant constraints that the order removal operator needs to consider are: 1) trip A The number of orders on is greater than 1, that is, the vehicle trip is not cleared due to the use of the removal operator.

[0228] (13) New Neighborhood Structure for Orders

[0229] The order-added neighborhood structure forms a new solution by adding new orders. Specifically, in the tour of T period T In the example, randomly select the trip of car A. A , randomly select a tank that is out of stock at the end of the period i Generate an order O for it i , randomly generate the delivery quantity Q under the condition of satisfying relevant constraints i ,Then, insert the order into the insertable position of the current solution.

[0230] The constraints that need to be met by the new neighborhood structure of the order are: 1) All vehicles in the new plan can return to the oil depot within their respective scheduling periods; 2) All vehicles must meet the vehicle loading constraints.

[0231] (14) Service time optimization neighborhood structure

[0232] The service time optimization neighborhood structure advances the order delivery time to the point where the delivery tank is filled, making the solution more compact and reducing a certain amount of end-of-period inventory.

[0233] The relevant constraints that the service time optimization neighborhood structure needs to meet are: 1) All vehicles in the new solution can return to the oil depot within their scheduling period.

[0234] In the IRPSD-SC problem, due to the segmentation of customer demand, multiple vehicle visits are allowed, so partial adjustments to the solution (exchanging access paths, increasing or decreasing delivery volume, etc.) will inevitably affect the inventory level and vehicle status of each oil tank. Customers with a small capacity-to-sales ratio have multiple deliveries within a cycle, and adjustments to a certain delivery plan will cause fluctuations in the entire network status through customers with a small capacity-to-sales ratio. Therefore, in order to determine the feasibility of the newly generated solution and calculate the cost change, it is necessary to update all node states (the start service time of the node) and vehicle states after each new plan is generated, and recalculate the cost. The present invention adopts an event scheduling algorithm in the field of system simulation, and the start service time of each customer node is determined by the FIFO (First in First out) rule.

[0235] Event scheduling (ES) is an event-oriented algorithm that analyzes real systems from an event perspective. The basic components of ES are the Future Event List (FEL), the time control program, and the event handler. The Future Event List stores the events that occur and their related attributes in order, the time control program advances the simulation clock at the interval of the event, and the event handler handles the state changes of the entire system when the event occurs.

[0236] Specifically, a schematic diagram of an application of an event scheduling method provided by an embodiment of the present invention in the IRPSD-SC problem is shown in FIG. Fig.10 shown. Fig.10 The squares represent oil depots, and the circles represent the oil tank nodes in each order. Assume that two vehicles A and B are used in this cycle. A 、trip B are the trips of vehicles A and B in a certain cycle, where trip A The route is {0,b,a,0}, which means that vehicle A starts from the oil depot node 0 in the T cycle, goes to nodes b and a to deliver oil, and finally returns to the oil depot node (0). Similarly, trip BThe route is {0, a, c, d, 0}. First, initialize the simulation clock to 0. According to the order of vehicle travel, select the first node visited by A, namely oil tank b, and the first node visited by B, namely oil tank a. The event that vehicle A starts serving oil tank b is recorded as The event that vehicle B starts servicing tank a is and will Put in FEL, the start service time of both is Then Removed from FEL, the simulation clock advances to and the future events of car B Put it into FEL, assuming Will Remove FEL and advance the simulation clock to Pick up car A future event Enter FEL. This is the second delivery of the entire fleet to tank a. Calculate like Will Remove FEL and advance the simulation clock to Repeat this process until all nodes in the solution are traversed.

[0237] The present invention designs a rich neighborhood structure in combination with the problem characteristics of IRPSD-SC. The perturbation neighborhood should generally have a certain degree of randomness and diversity, so as to introduce greater changes near the current solution, so as to have the possibility of jumping out of the local optimal solution and exploring a new search space. The present invention uses all 14 neighborhoods as local search operators to fully explore the problem space, and uses order increase and decrease, removal, random oil tank adjustment, vehicle increase, and minimum vehicle removal operators as perturbation operators. In order to fully expand the perturbation solution space, the selection of perturbation operators in the VNS framework is random, that is, each time VND ends, an operator is randomly selected from the perturbation operator set for perturbation.

[0238] The search order of the local search operator is:

[0239] Order delivery quantity optimization → Access sequence optimization operators (random oil tank adjustment, order exchange between weeks, order exchange of multiple vehicles in the same cycle, and order exchange of single vehicle) → Order increase and decrease operators (vehicle increase optimization) → Out-of-stock order optimization operators (out-of-stock order optimization within the trip, out-of-stock order optimization of multiple vehicles in the same cycle, and out-of-stock order optimization between weeks) → Carpooling optimization → Vehicle number adjustment operators (minimum vehicle removal optimization) → Service time optimization.

[0240] Both the VNS algorithm and the SA algorithm are heuristic optimization algorithms that can be used to find the global optimal solution to complex problems. Previous researchers have proven that the combination of VNS and SA is a more flexible search strategy that is more likely to escape the local optimum and find a better solution.

[0241] The present invention designs a variable neighborhood search algorithm (VNSA) integrated with simulated annealing, and adds the temperature control strategy of the SA algorithm to the outer loop of the VNS algorithm. In addition to accepting improved new solutions, the algorithm also accepts poor new solutions with a certain probability, and uses the new solution as the current solution, returning to the first neighborhood to continue searching. The probability depends on the target value difference between the new solution and the current solution and the cooling temperature, and the calculation formula is as follows:

[0242]

[0243] in is the current temperature, and its initial temperature is Whenever VNS enters the external loop, it enters the cooling program. The traditional simulated annealing temperature update uses the cooling coefficient, that is, the temperature is updated to δ is the temperature reduction coefficient, 0<δ<1. The present invention uses a half-decay method to control the temperature, that is, to set the temperature half-decay position, and control the temperature at σ n The temperature decays to half of the cooling process at the 10th VNS iteration. In this way, the relationship between temperature and iteration number is directly controlled.

[0244]

[0245] SA has a higher probability of accepting inferior solutions at a higher temperature in the early stage of the algorithm. Therefore, the algorithm is very likely to jump out of the local optimum at this stage. As the algorithm gradually cools down, the probability of accepting inferior solutions gradually decreases, so it can converge to the global optimal solution more stably.

[0246] Small-scale and large-scale examples of IRPSD-SC problems are prepared respectively. Each example is taken from the Solomon example set and appropriately adapted.

[0247] Make 15 small-scale examples. Each example includes 2 to 3 gas stations and 3 to 5 oil tanks. The small-scale example contains 1 oil tank with a small capacity-to-sales ratio. Consider 2 cycles. The location data of the gas stations are taken from the Solomon example. According to the horizontal division of the geographical location distribution of the nodes, the examples are divided into three types: R, C, and RC. The node positions in the R-type example are randomly distributed, the C-type example is clustered, and the RC type has both. Node 0 is used as the oil depot node of the distribution network of the example. The business data of each oil tank is taken from the actual data of the gas stations of Sinopec.

[0248] 24 large-scale examples are created. The creation process is similar to that of the small-scale examples. Each example contains 50 gas stations, 75 to 88 oil tanks, and 2 scheduling cycles. Each example contains 15% to 20% of small capacity-to-sales ratio oil tanks. The location data of gas stations are also taken from the Solomon example. The business data of each oil tank is taken from the actual data of Sinopec gas stations.

[0249] Small-scale example experiments: This paper designs 15 groups of small-scale example experiments to verify the correctness of the model and the effectiveness of the algorithm. The naming rules of the examples reflect the source of their location information and demand information. The following table shows the R5_5 example data, where "R" indicates that the location information is sampled from the R-type example in the Solomon benchmark example set, and "_5" indicates that the customer scale of this example is 5, that is, 5 oil tanks are considered in the 5th small-scale example extracted from the Solomon R-type example.

[0250] Table 5 Small-scale example R5_5 settings

[0251]

[0252] *Indicates that this customer is a customer with a small volume-to-sales ratio

[0253] CPLEX (12.9) and VNSA algorithms were used to solve each small-scale example. The maximum running time of CPLEX was set to 7200 seconds. VNSA and CPLEX were run once, and their target values ​​and solution times were recorded. The results are shown in Table 5. In the table, Gap represents the relative error between VNSA and CPLEX solutions, and its calculation formula is shown below.

[0254]

[0255] Table 6 Small-scale example solution results

[0256]

[0257]

[0258] It can be seen that in 10 of the 15 examples, both CPLEX and VNSA obtained the optimal solution, but in terms of time, VNSA's solution speed was much faster than CPLEX. This result verifies the correctness of the model and the effectiveness of the operator designed by the present invention. In addition, there are 5 examples in which CPLEX only obtained the upper bound solution within 7200 seconds, while VNSA obtained a better solution. The node scales of these 5 examples are 3, 4, 4, 5, and 5, respectively. Among them, in the example (R1_3) with a tank scale of 3, the capacity-to-sales ratio of the small capacity-to-sales ratio tank is only 0.86, which is the lowest among all the examples, which means that the small capacity-to-sales ratio tank requires more deliveries, thereby increasing the difficulty of solving the example. It can be seen that in the IRPSD-SC problem, the size of the node and the capacity-to-sales ratio of the tank jointly determine the complexity of the problem. Overall, the solution obtained by VNSA is 1.67% better than that of CPLEX on average. In terms of running time, the average running time of CPLEX is 2632.86 seconds, while VNSA only takes 14.50 seconds.

[0259] Large-scale example experiments: VND is a typical local search optimization process, and the search strategies include best improvement (Best Improvement) and first improvement (First Improvement). Under the best improvement strategy, the goal of the local search algorithm is to find the solution with the smallest objective function in the search space N(x) of x as the optimal solution for the local search. This local search method works very well, but when the problem scale increases, the local search space N(x) grows rapidly, and the duration of the local search is uncontrolled, which often makes the feasibility of the algorithm worse. The first improvement strategy avoids this problem very well. FI sets a maximum number of local searches for local searches. If the new solution x' obtained by the FI search is not better than the optimal solution, iter+1 is recorded, and the optimal solution is updated immediately when a better solution is found. The FI strategy greatly improves the efficiency of local search, and the search speed is faster when solving large-scale problems, but it may converge slowly due to insufficient search. Usually, when the scale of the problem is small, the VNS-BI with the optimal improvement strategy can be used to fully explore the solution space, and when solving large-scale problems, the VNS-FI strategy can be selected to obtain a better solution in a shorter time. The algorithm of the present invention simultaneously implements the HVNS algorithm that integrates the two local search strategies of BI and FI, and designs a variable neighborhood search algorithm VNSA that integrates simulated annealing based on the optimal improvement strategy of VNS.

[0260] The three algorithms VNS-BI, VNS-FI and VNSA were used to solve each large-scale case. In 19 of the 24 cases, VNSA obtained the best solution compared with other algorithms. In general, the optimization effect of VNSA is better than that of INIT, VNS-BI and VNS-FI, and the average improvement rate of the three is 189.12%, 14.74% and 7.35% respectively.

[0261] Between VNS-BI and VNS-FI, both search improvement strategies can effectively optimize the initial solution within a limited time. The average optimization rates of BI and FI for the initial solution reached 60.47% and 66.00%, respectively, which proves the effectiveness of the operator design of the present invention. VNS-BI will traverse all possibilities in each neighborhood to find the best, so it has a strong local search ability. Therefore, VNS-BI can usually converge to a better solution in a shorter time. However, the strong local search ability of VNS-BI may also cause it to easily fall into the local optimal solution and be unable to jump out of the local optimal solution to find the global optimal solution. For example, in R8_82, VNS-BI falls into the local optimal solution of 144938.75, while VNS-FI can obtain a better solution of 92152.85, saving 36.42% in cost. Therefore, when designing an algorithm, it is necessary to consider how to avoid falling into the local optimal solution while making full use of the local search ability. This is also the design significance of VNSA.

[0262] Analysis of the impact of customers with small volume-to-sales ratio

[0263] The existence of customers with small volume-to-sales ratios will greatly increase the complexity of problem solving. In order to explore the impact of customers with small volume-to-sales ratios on the solution, this experiment, based on the large-scale example C3_80, controls the number of customers with small volume-to-sales ratios by adjusting the existing oil tank volumes in the distribution network, while keeping the sales speed of each oil tank unchanged, that is, the total demand unchanged. The proportion of oil tanks with small volume-to-sales ratios varies within the range of 0 to 30%. The VNSA algorithm is used to solve the problem, and each case is run 10 times and the best solution is taken. The results are shown in Table 8.

[0264] Table 8 Analysis of the impact of customers with small volume-to-sales ratio

[0265]

[0266] The results show that with the increase of customers with small volume-to-sales ratio, the complexity of the problem gradually increases and the solution time gradually increases. Fig.11 A schematic diagram of a customer impact analysis of a small capacity-to-sales ratio provided by an embodiment of the present invention is shown in FIG. Fig.11As shown in the figure, when the proportion of customers with small capacity-to-sales ratio gradually increases from 0 to 30%, under the premise that the total sales demand does not change, the total distribution volume in the obtained solution does not change much, but the total cost of the solution increases by 47.9%, and the solution time increases by 22.9%. Customers with small capacity-to-sales ratio need more frequent replenishment, which brings changes in the number of vehicles, total distribution volume, and other aspects. At the same time, the increase in the proportion of oil tanks with small capacity-to-sales ratios brings an increase in out-of-stock costs. This is because oil tanks need to be replenished frequently, which brings more intensive distribution decisions, and at the end of each cycle, in order to balance the inventory holding cost, the inventory holding level of oil tanks in the distribution network is relatively low. After the next cycle begins, each oil tank will quickly reach the out-of-stock point, and the tanker fleet must return to the oil depot at the end of the period and start again at the beginning of the next period, which will cause unavoidable shortages at the beginning of the period, resulting in a direct increase in costs. In summary, the embodiment of the present invention introduces customers with small capacity-to-sales ratios into the IRPSD problem for the first time, breaking the assumption that existing studies on the IRPSD problem do not consider customers with small capacity-to-sales ratios. In the existing IRPSD problem research system, there are generally two ways to handle customer sales and inventory: one assumes that the customer's sales volume in a cycle is very small, so the vehicle can visit the customer at any time; the other assumes that the customer's inventory capacity limit is not considered, so there is no problem of small capacity-to-sales ratio. Based on the research of IRPSD, the present invention introduces the real-life scenario of small capacity-to-sales ratio, enriches the theoretical research basis of IRPSD, and the existence of the accommodating time point and the out-of-stock time point makes the research problem closer to reality and more difficult.

[0267] In terms of algorithms, 14 kinds of neighborhood structures are designed according to the characteristics of the IRPSD-SC problem. On this basis, a hybrid variable neighborhood search algorithm (VNSA) integrating simulated annealing is designed and implemented. The VNSA algorithm introduces the idea of ​​accepting a worse solution with a certain probability in the simulated annealing algorithm into the variable neighborhood search algorithm, which improves the global search capability of the algorithm. The algorithm of the present invention can solve the actual scale IRPSD-SC problem, thereby providing decision support for enterprises to formulate secondary distribution plans for refined oil products.

[0268] The method of the present invention can effectively solve the distribution problem of gas stations under the active distribution mode, achieve cost reduction and efficiency improvement, energy conservation and emission reduction, and promote the high-quality development of my country's petrochemical industry. In addition to gas stations, with the rapid development of hydrogen fuel cell vehicles, the scale of hydrogen distribution to hydrogen stations by trucks will be increasingly expanded, and the present invention can also be applied to hydrogen distribution scenarios at hydrogen stations. In addition, the algorithm developed by the present invention can be embedded in the company's distribution management software to provide decision-making support for the company to formulate scientific and reasonable distribution plans, thereby greatly reducing the labor intensity of dispatchers, coordinating transportation resources, reducing logistics costs, realizing the intelligent development of logistics distribution, and promoting the high-quality development of my country's oil companies.

[0269] Those skilled in the art can understand that the accompanying drawings are only schematic diagrams of an embodiment, and the modules or processes in the accompanying drawings are not necessarily required to implement the present invention.

[0270] It can be known from the description of the above implementation methods that those skilled in the art can clearly understand that the present invention can be implemented by means of software plus a necessary general hardware platform. Based on such an understanding, the technical solution of the present invention is essentially or the part that contributes to the prior art can be embodied in the form of a software product, which can be stored in a storage medium such as ROM / RAM, a magnetic disk, an optical disk, etc., and includes a number of instructions for enabling a computer device (which can be a personal computer, a server, or a network device, etc.) to execute the methods described in the various embodiments of the present invention or certain parts of the embodiments.

[0271] Each embodiment in this specification is described in a progressive manner, and the same or similar parts between the embodiments can be referred to each other, and each embodiment focuses on the differences from other embodiments. In particular, for the device or system embodiment, since it is basically similar to the method embodiment, the description is relatively simple, and the relevant parts can be referred to the partial description of the method embodiment. The device and system embodiments described above are merely schematic, wherein the units described as separate components may or may not be physically separated, and the components displayed as units may or may not be physical units, that is, they may be located in one place, or they may be distributed on multiple network units. Some or all of the modules may be selected according to actual needs to achieve the purpose of the scheme of this embodiment. Ordinary technicians in this field can understand and implement it without paying creative labor.

[0272] The above is only a preferred specific embodiment of the present invention, but the protection scope of the present invention is not limited thereto. Any changes or substitutions that can be easily thought of by a person skilled in the art within the technical scope disclosed by the present invention should be included in the protection scope of the present invention. Therefore, the protection scope of the present invention should be based on the protection scope of the claims.

Claims

1. A multi-cycle distribution method for a gas station with a small capacity-to-sales ratio under an active distribution mode, characterized in that: include: For gas stations with small capacity-to-sales ratio under active distribution mode, a mixed integer programming model for the inventory routing problem with demand splitting (IRPSD-SC) is constructed considering multiple cycles and the storage capacity constraints of gas stations. The objective function and constraint conditions of the mixed integer programming model of the IRPSD-SC problem are set, with the transportation cost, the out-of-stock cost of the gas station and the inventory holding cost being minimized as the objective function; the node access constraint, the vehicle loading constraint, the time constraint and the multi-period inventory holding level constraint being used as the constraint conditions; Based on the greedy idea and the principle of avoiding stockouts, an initial solution of the mixed integer programming model of the IRPSD-SC problem is constructed, and the initial solution is used as the input of a hybrid variable neighborhood search algorithm. The hybrid variable neighborhood search algorithm outputs a multi-period distribution result of the gas station with a small capacity-to-sales ratio, which includes which vehicle delivers which grade of refined oil and how much quantity to which gas station at which time in which period.

2. The method according to claim 1, characterized in that: The mixed integer programming model for the IRPSD-SC problem is constructed for gas stations with a small capacity-to-sales ratio under the active distribution mode, taking into account multiple cycles and the storage capacity constraints of gas stations, including: For gas stations with small capacity-to-sales ratio under active distribution mode, the minimum sum of transportation cost, out-of-stock cost and inventory holding cost is taken as the objective function, and a mixed integer mathematical programming model for the IRPSD-SC problem with multiple consecutive deliveries, multiple cycles, multiple oil products and compartments is established. The basic assumptions of the mixed integer mathematical programming model are as follows: (1) The oil depot and gas station remain in operation during each cycle; (2) Any fuel product at a gas station is allowed to be delivered multiple times within one cycle; (3) In the IRPSD-SC problem, the inventory holding cost of the gas station in each period is calculated based on the initial inventory holding level, and the inventory holding cost per unit time is known; (4) Allowing for stockouts, the cost of which is related to the duration of the stockout and the speed at which the oil product is sold; (5) Each compartment of the vehicle can only carry one type of oil, and all oil products in a compartment can only be delivered to one gas station, that is, the vehicle compartments are indivisible; (6) Each vehicle is only allowed to run once in a cycle. A vehicle departs from the oil depot, delivers the products it carries to the relevant gas station, and then returns to the oil depot. This is called a trip. Each trip of the vehicle must be within the same cycle and is not allowed to run across cycles. (7) The delivery volume of a vehicle to a gas station is an integer multiple of a fixed volume, and the volume delivered by a vehicle to a single gas station at a time cannot exceed its total onboard capacity; (8) When a vehicle is in motion, it incurs transportation costs, which are related to mileage; (9) Ignoring the time and cost of loading and unloading vehicles; (10) The vehicle’s unit distance traveled cost, travel speed, number of compartments, and compartment capacity are known.

3. The method according to claim 1, characterized in that: The objective function and constraints of the mixed integer programming model for setting the IRPSD-SC problem are set to minimize transportation cost, out-of-stock cost of gas stations and inventory holding cost as the objective function; The constraints include node access constraints, vehicle loading constraints, time constraints, and multi-period inventory holding level constraints, including: In the mixed integer programming model of the IRPSD-SC problem, the distribution network of the supply chain system is represented by a directed graph G = (V, E), where V is a vertex set, V = C∪{0}∪{n+1}, {0} and {n+1} both represent the same distribution center oil depot, and the oil tank of each oil product at each gas station is regarded as a customer, and each customer is represented as a node, C = {1,…,n} represents the set of customer nodes. After loading, the vehicle departs from the distribution center, delivers the loaded goods to the relevant customers, and returns to the distribution center. The vehicle only delivers once in each cycle. A pair of virtual start and end nodes is set for each vehicle. The vehicle departs from {0} and returns to {n+1} after delivery. E represents the edge set, E={(i,j)|i,j∈V,i≠j}. The specific parameters and variable settings are shown in Table 2: Table 1 Model collection Table 3 Model parameters Table 4 Model decision variables The total cost is composed of vehicle transportation cost, out-of-stock cost and inventory holding cost. The objective function of the mixed integer programming model of the IRPSD-SC problem is set to minimize the total cost: min(f1+f2+f3) The constraints of the mixed integer programming model for setting the IRPSD-SC problem include node access constraints, vehicle loading constraints, time constraints, and multi-period inventory holding level constraints, as follows: Node access constraints include: The above formulas indicate that the oil tank node needs to satisfy the flow balance, that is, the vehicle must leave after arriving at the customer node to ensure the flow balance of the node; the access order constraint between nodes ensures that the vehicle starts from the starting distribution center, visits several customers, and then returns to the distribution center; the vehicle cannot visit the distribution center continuously and multiple times; in a certain delivery of any customer node, the node can only be visited once at most; it is guaranteed that the vehicle only runs once at most; the r+1th delivery must occur under the premise of the existence of the rth delivery, which guarantees the order of the number of times the customer is visited multiple times, reflecting the characteristics of demand segmentation; Vehicle loading constraints include: Among them, formulas 1 to 3 are used to track the changes in the number of available compartments of the vehicle during driving. Among them, formula 1 indicates that the available compartments of the vehicle when it departs from the distribution center yard are all c; formulas 2 and 3 represent the changing trend of the number of compartments of the vehicle when the vehicle visits between nodes, that is, the number of available compartments at the rear node is equal to the available compartments at the front node minus the used compartments; formula 4 indicates that the delivery volume is limited by the vehicle capacity; formula 5 establishes the decision variable and The relationship between indicates that if there is a visit to a customer, the compartment required for its delivery volume must be no less than 1, otherwise it is 0, that is, if there is a visit, it must be delivered; Time-related constraints include: Among them, formula 1 describes the order The out-of-stock situation during the period, when the arrival time is later than the out-of-stock time point, there is an out-of-stock situation, and its value is the difference between the order arrival time and the out-of-stock time point, otherwise the out-of-stock duration is 0; Formulas 2 and 3 are used to determine the relationship between the starting service time of the vehicle serving each node. Specifically, the vehicle journey starts from the distribution center, and the time to serve the next node should be greater than the customer's accommodation time point and the time required to reach the node. If the vehicle arrives earlier than the accommodation time point, it is necessary to wait for the arrival of the accommodation time point at the node before starting the service; Formula 4 represents the time sequence of the start service time between the previous and next visits to the same node, and ensures that if the r+1th visit exists, the r+1th visit is after the rth visit; Formula 5 indicates that the vehicle must work within the scheduling period, that is, it starts from the distribution center after the start of the scheduling period and must return to the distribution center before the end of the scheduling period; Formula 6 represents the time relationship between the visits between cycles, that is, the visit of the t+1 cycle must be after the visit of the t cycle; Formula 7 indicates that the customer may also be out of stock from the last delivery to the end of this cycle, and the out-of-stock duration of this part is recorded as This can be obtained by comparing the out-of-stock time point after the last delivery to customer i with the beginning and end time of the next cycle; Multi-period inventory level constraints include: is a non-negative integer Formula 1 represents the relationship between customer inventory levels between adjacent cycles. The beginning inventory level of customer i at the beginning of the next cycle is equal to the beginning inventory level of the current cycle plus the total delivery volume of the customer in this cycle, minus the sales volume of customer i in this cycle; Formula 2 indicates that the customer inventory level must not exceed the storage capacity; Formula 3 is a constraint on the decision variables.

4. The method according to claim 3, characterized in that The initial solution of the mixed integer programming model of the IRPSD-SC problem is constructed based on the greedy idea and the principle of avoiding stockouts, including: The parallel path strategy is used to construct the vehicle path. The parallel path construction strategy means that for a fleet of K vehicles, each vehicle selects a visit node in turn and performs a state transfer. After traversing all vehicles, each vehicle in K is traversed again to perform a second state transfer, and this is repeated until a feasible solution is formed. Based on the greedy idea, the initial solution is constructed based on the principle of avoiding stockouts. That is, each time the vehicle selects the tank node with the shortest stockout time based on the current distribution network status, and delivers the maximum amount of oil to the node to ensure that it does not run out of oil within the cycle while meeting the vehicle's remaining capacity limit. If the vehicle's remaining capacity is insufficient to accommodate the demand of any tank, or the vehicle cannot return to the oil depot within the cycle after delivering to the next node, the vehicle is ordered to return to the oil depot immediately. After all vehicles return to the oil depot, the distribution plan for the next cycle is generated until the distribution plan for all cycles is generated. The specific steps for generating the initial solution are as follows: Step 1: Initialize all parameters, set T = 1; Step 2: Calculate the list of tank nodes in this cycle at the time of out-of-stock based on the inventory at the beginning of the cycle and the sales speed of each tank. T , list T This is the set of orders that may be out of stock during this period; Step 3: Judge, if list T If not empty, execute Step 4, otherwise execute Step 12; Step 4: Select list T The customer tank with the smallest out-of-stock time a , traverse each car from i=1 and execute step5; Step 5: Determine k i Has it been returned to the library? If k i If not returned, execute step 6, otherwise execute step 10; Step 6: Determine k i Are there any remaining compartments? If yes, execute step 7, otherwise execute step 9; Step 7: Determine k i Is to visit the tank a After that, check whether it can return to the oil depot within the cycle. If yes, execute step 8, otherwise execute step 9; Step 8: k i Move to tank a And confirm the order quantity Q=min(Q i_MIN ,Q k―remain ), where Q i_MIN It indicates the minimum oil quantity to ensure that customer i does not run out of oil during this cycle, Q k―remain Indicates the remaining capacity of vehicle k, updates all customer and vehicle status information, and updates the list T , execute step 10; Step 9: Let k i Return to the oil depot immediately, z=z+1; Step 10: Let i = i + 1, and repeat steps 5-8 until i>m, that is, traverse every car in the fleet; Step 11: Determine whether all vehicles have returned to the oil depot. If so, proceed to step 12; otherwise, return to step 4. Step 12: Let T = T + 1, update all vehicle information and oil depot information, where the oil depot inventory holding level inherits the inventory of the previous cycle, and determine whether all cycle distribution plans have been generated. If T>T max , output the initial solution, otherwise return to step 2.

5. The method according to claim 4, characterized in that The initial solution is used as the input of the hybrid variable neighborhood search algorithm, and the hybrid variable neighborhood search algorithm outputs the multi-cycle distribution result of the small volume-to-sales ratio gas station, and the multi-cycle distribution result includes which cycle, which vehicle distributes which grade of refined oil to which gas station at what time and how much, including: It is set that there are two types of entities in the hybrid variable neighborhood search algorithm: vehicles and nodes. Nodes include oil tanks and oil depots. From the dimensions of vehicles, orders and periodic inventory, the single-vehicle order exchange neighborhood structure, the same-cycle multi-vehicle order exchange neighborhood structure, the inter-week order exchange neighborhood structure, the random oil tank adjustment neighborhood structure, the carpooling optimization neighborhood structure, the vehicle addition optimization neighborhood structure, the minimum vehicle removal optimization neighborhood structure, the out-of-stock order optimization neighborhood structure within the trip, the multi-vehicle out-of-stock order optimization neighborhood structure in the same cycle, the out-of-stock order optimization neighborhood structure between weeks, the order delivery quantity optimization neighborhood structure, the order removal neighborhood structure, the order addition neighborhood structure and the service time optimization neighborhood structure are designed, providing a total of 14 neighborhood structures; The hybrid variable neighborhood search algorithm is based on the initial solution and uses the 14 neighborhood structures to generate the distribution plan of the gas station with a small capacity-to-sales ratio. The event scheduling algorithm is used to update all node states and vehicle states after each new distribution plan of the gas station is generated, and the cost is recalculated. The start service time of each customer node is determined by the FIFO rule. After multiple iterative calculations, the multi-cycle distribution results of the gas station with a small capacity-to-sales ratio are obtained. The multi-cycle distribution results include which vehicle distributes which grade of refined oil and how much quantity to which gas station at which time in which cycle.

6. The method according to claim 5, characterized in that The hybrid variable neighborhood search algorithm generates a distribution plan for the gas station with a small capacity-to-sales ratio based on the initial solution and using the 14 neighborhood structures, including: In addition to accepting improved new solutions, the hybrid variable neighborhood search algorithm also accepts poor new solutions with a certain probability, and uses the new solution as the current solution, returns to the first neighborhood to continue searching. The probability depends on the target value difference between the new solution and the current solution and the cooling temperature, and the calculation formula is as follows: in is the current temperature, and its initial temperature is Whenever VNS enters external circulation, it enters the cooling process; Use the half-decay method to control the temperature, that is, set the temperature half-decay position to control the temperature at σ n The temperature decays to half of the cooling process at the first VNS iteration, controlling the relationship between temperature and the number of iterations. The search order of the local search operator in the hybrid variable neighborhood search algorithm is: Order delivery quantity optimization → Access sequence optimization operators (random oil tank adjustment, order exchange between weeks, order exchange of multiple vehicles in the same cycle, single vehicle order exchange) → Order increase and decrease operators (vehicle increase optimization) → Out-of-stock order optimization operators (out-of-stock order optimization within the trip, out-of-stock order optimization of multiple vehicles in the same cycle, out-of-stock order optimization between weeks) → Carpooling optimization → Vehicle number adjustment operators (minimum vehicle removal optimization) → Service time optimization; The pseudo code of the hybrid variable neighborhood search algorithm is as follows:

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