An optimization method for order placement in a multi-variety production line considering the priority processing of emergency orders

Abstract

The present invention discloses an optimization method for order release in a multi-variety production line considering the priority processing of emergency parts, and its steps include: S1. Calculate the utilization rate of product type k processed by workstation m; S2. Model each workstation and obtain the expected waiting time E(W); S3. Calculate the total waiting time of product type k on workstation m within cycle p; S4. Calculate the time required for product type k put into the l-th process until the completion of this process within cycle p; S5. Calculate the output quantity of product type k within planned cycle p; S6. Calculate the work-in-process quantity of product type k in the system at the end of planned cycle p, the inventory quantity of product type k in the system at the end of planned cycle p, and the delayed delivery quantity of product type k in the system at the end of planned cycle p; S7. Calculate the cost; Step S8. Traverse the cost results corresponding to different arrival rates λ and select the optimal solution. The present invention can find the optimal release plan for the order release problem.

Description

Technical Field

[0001] The present invention relates to the technical field of multi-variety production lines, and in particular to an optimization method for order placement of a multi-variety production line considering the priority processing of emergency parts. Background Technique

[0002] To meet the production and processing requirements of product diversification, that is, to enable the production line system to realize the mixed production and processing of multiple types of products on the production line, a multi-variety production line has emerged.

[0003] For a multi-bottle production line system, it is provided with multiple workstations, and each workstation includes at least one production and processing device. Different types of products are processed by selecting different workstations or different devices according to their different process paths.

[0004] For a multi-variety production line, when emergency parts arrive at some workstations, there is a priority distinction for the products processed on these workstations. Emergency parts have a high priority, and the products originally produced in the production line have a low priority.

[0005] When considering the priority processing of emergency parts, it is particularly important to optimize the order placement of a multi-variety production line. Summary of the Invention

[0006] The purpose of the present invention is to provide an optimization method for order placement of a multi-variety production line considering the priority processing of emergency parts. This optimization method for order placement of a multi-variety production line considering the priority processing of emergency parts can calculate the sum of the minimized work-in-process cost, inventory cost, and late delivery cost when considering the arrival of emergency parts at the workstation, and select the optimal solution by traversing the sum of the minimized work-in-process cost, inventory cost, and late delivery cost corresponding to different arrival rates λ, so as to find the optimal placement plan for the order placement problem of the multi-variety production line.

[0007] To achieve the above purpose, the present invention is realized through the following technical solutions.

[0008] An optimization method for order placement of a multi-variety production line considering the priority processing of emergency parts includes the following steps, specifically:

[0009] Step S1, calculate the utilization rate ρ of the product of type k processed by workstation m at a specific arrival rate λ k,m,p :

[0010]

[0011] λ 0,m (k, p) represents the raw material arrival rate of the product of type k on workstation m within period p, λ n,m(k, p) represents the semi-finished product re-entry arrival rate of product type k within cycle p at workstation m, and μ m represents the service rate of workstation m;

[0012] M k,l represents the workstation corresponding to the l-th process of product type k. The arrival rate λ of the raw materials corresponding to product type k at workstation m within cycle p 0,m (k, p) = x k,p · [M k,1 = m];

[0013] The arrival rate of semi-finished products corresponding to product type k at workstation m within cycle p

[0014] where k represents the product type, p represents the planning cycle, m represents the workstation type, K represents the number of product types processed by the multi-product production line, and L k identifies the number of processes of product type k, l represents the process number, l ∈ {1, 2,..., L k}; x k,p represents the quantity of raw materials put into product type k within the planning cycle p, and x k,p is a decision variable;

[0015] Step S2: Since the arrival process and service time of the queuing system in the multi-product production line follow a general distribution, considering the emergency part priority processing rule and using the GI / G / 1 queuing model to model each workstation, and obtaining the expected waiting time on the queuing system as E(W);

[0016] Step S3: Calculate the total waiting time Z of product type k at workstation m within cycle p under a specific arrival rate λ k,m,p :

[0017] The total waiting time Z of product type k at workstation m within cycle p k,m,p includes the following three parts: the time τ when at least one idle resource appears from the arrival of this product at workstation m k,m,p , the processing time σ of all emergency parts queued in front of this product k,m,p , and the processing time δ of the newly arrived emergency parts during the waiting process of this product k,m,p ;

[0018] Z k,m,p = τ k,m,p + σ k,m,p + δ k,m,p ;

[0019]

[0020] σ k,m,p =T m ·E(W)·λ out,m,p ;

[0021] δ k,m,p =T m ·Z k,m,p ·λ out,m,p ;

[0022] Among them, μ m =1 / T m ,λ out,m,p represents the arrival rate of urgent parts to be processed at workstation m in period p, The squared coefficient of variation corresponding to the general distribution of the arrival interval of the product at workstation m is represented by, The squared coefficient of variation corresponding to the general distribution of the service time of workstation m;

[0023] Step S4: Calculate the time f(k,p,l) required for a product of type k to be delivered to the lth process in cycle p and complete the process under a specific arrival rate λ, and the total processing cycle time F(k,p,L) of the product of type k k ):

[0024] The process l of product type k is processed by workstation m, denoted by M k,l = m; for any process l∈{1,…,L k}, the product is in the corresponding workstation M k,l Processing time and waiting time Composition, therefore

[0025]

[0026] Among them, processing time is known;

[0027]

[0028] Step S5: based on the time f(k,p,l) required for the product of type k to be put into the lth process in cycle p until the process is completed, and the total processing cycle time F(k,p,L) of the product of type k k ), calculate the output quantity y of product type k in planning period p under a specific arrival rate λ k,p ;

[0029] Step S6: Calculate the WIP of product type k in the system at the end of planning period p under a specific arrival rate λ k,p , the inventory level h of product type k in the system at the end of planning period pk,p 1. The number of backorders b of product type k in the system at the end of the planning period p k,p :

[0030]

[0031]

[0032]

[0033]

[0034] where D k,p represents the demand for product type k within the planning period p, and in a multi-product production line, D k,p is known;

[0035] Step S7: Calculate the sum of the work-in-process cost, inventory cost, and backorder cost at a specific arrival rate λ, with the sum of the work-in-process cost, inventory cost, and backorder cost as the objective function, which is expressed as:

[0036]

[0037] where W k represents the unit work-in-process cost corresponding to product type k, H k represents the unit inventory cost corresponding to product type k, and B k represents the unit backorder cost corresponding to product type k;

[0038] Step S8: Traverse the sum of the work-in-process cost, inventory cost, and backorder cost corresponding to different arrival rates λ, and select the optimal solution by comparing the total cost results.

[0039] Among them, in this multi-product production line, the product process route, available processing equipment, and processing time are known and determined.

[0040] Among them, in this multi-product production line, each workstation contains at least one piece of equipment, and processing is carried out according to the first-come, first-served rule. One piece of equipment can only process one product at a time.

[0041] The beneficial effects of the present invention are as follows: An order release optimization method for a multi-product production line considering the priority processing of emergency parts according to the present invention includes the following steps: Step S1: Calculate the utilization rate ρ of the workstation m for processing products of type k at a specific arrival rate λ k,m,p; Step S2: Considering the rule of preferentially processing urgent orders, since the arrival process and service time of the queuing system in the multi-product production line follow a general distribution, that is, the queuing model GI / G / 1 is used to model each workstation, and the expected waiting time E(W) in the queuing system is obtained; Step S3: Calculate the total waiting time Z of products of type k on workstation m within cycle p at a specific arrival rate λ k,m,p ; Step S4: Calculate the time f(k, p, l) required for products of type k put into the l-th process until the completion of this process within cycle p at a specific arrival rate λ, and the total processing cycle time F(k, p, L k ); Step S5: Based on the time f(k, p, l) required for products of type k put into the l-th process until the completion of this process within cycle p, and the total processing cycle time F(k, p, L k ), calculate the output quantity y of product type k within the planned cycle p at a specific arrival rate λ k,p ; Step S6: Calculate the work-in-process quantity w of product type k in the system at the end of the planned cycle p at a specific arrival rate λ k,p , the inventory quantity h of product type k in the system at the end of the planned cycle p k,p , and the delayed delivery quantity b of product type k in the system at the end of the planned cycle p k,p : Step S7: Calculate the sum of minimizing the work-in-process cost, inventory cost, and delayed delivery cost at a specific arrival rate λ; Step S8: Traverse the sum of minimizing the work-in-process cost, inventory cost, and delayed delivery cost corresponding to different arrival rates λ, and select the optimal solution by comparing the total cost results. Through the above steps, the present invention can calculate the sum of minimizing the work-in-process cost, inventory cost, and delayed delivery cost considering the arrival of urgent orders at the workstation, and select the optimal solution by traversing the sum of minimizing the work-in-process cost, inventory cost, and delayed delivery cost corresponding to different arrival rates λ to find the optimal placement plan for the order placement problem in the multi-variety production line. Description of the Drawings

[0042] The present invention will be further described below with reference to the drawings, but the embodiments in the drawings do not constitute any limitation to the present invention.

[0043] Figure 1 It is a schematic diagram of the production order placement for the multi-variety production line.

[0044] Figure 2 It is a schematic diagram of the placement and output relationship of the l-th process of products of type k.

[0045] Figure 3 It is a schematic diagram of the placement and output relationship of products in the p-th cycle. Detailed Embodiment

[0046] The present invention will be described below in conjunction with specific embodiments.

[0047] An optimization method for order placement in a multi-variety production line considering priority processing of emergency parts. In this multi-variety production line, the product process routes, available processing equipment, and processing times are known and determined, and each workstation contains at least one piece of equipment, and processing is carried out according to the first-come, first-served rule. A piece of equipment can only process one product at a time; the production order placement process of this multi-variety production line is as Figure 1 shown;

[0048] Specifically, the optimization method for order placement in a multi-variety production line considering priority processing of emergency parts includes the following steps: Specifically:

[0049] Step S1: Calculate the utilization rate ρ of the product of processing type k at workstation m under a specific arrival rate λ k,m,p :

[0050]

[0051] λ 0,m (k, p) represents the raw material arrival rate of the product of type k at workstation m within period p, and λ n,m (k, p) represents the semi-finished product re-entry arrival rate of the product of type k at workstation m within period p, and μ m represents the service rate of workstation m;

[0052] M k,l represents the workstation corresponding to the l-th process of the product of type k. The arrival rate λ of the raw materials corresponding to the product of type k arriving at workstation m within period p 0,m (k, p) = x k,p ·[M k,1 = m];

[0053] The arrival rate of the semi-finished products corresponding to the product of type k arriving at workstation m within period p

[0054] where k represents the product type, p represents the planning period, m represents the workstation type, K represents the number of product types processed by the multi-variety production line, L k identifies the number of processes of product type k, l represents the process number, l ∈ {1, 2,..., L k}; x k,p represents the raw material placement quantity of product type k within the planning period p, and x k,p is a decision variable;

[0055] Step S2: Since the arrival process and service time of the queuing system in the multi-product production line follow a general distribution, considering the rule of preferential processing of emergency parts and using the GI / G / 1 queuing model to model each workstation, and obtaining the expected waiting time on the queuing system as E(W);

[0056] Step S3: Calculate the total waiting time Z of the product of type k on workstation m within the cycle p at a specific arrival rate λ k,m,p :

[0057] The total waiting time Z of the product of type k on workstation m within the cycle p k,m,p consists of the following three parts: the time τ from the arrival of the product to workstation m until at least one idle resource appears k,m,p , the processing time σ of all emergency parts queued in front of the product k,m,p , and the processing time δ of the newly arrived emergency parts during the waiting process of the product k,m,p ;

[0058] Z k,m,p = τ k,m,p + σ k,m,p + δ k,m,p ;

[0059]

[0060] σ k,m,p = T m · E(W) · λ out,m,p ;

[0061] δ k,m,p = T m · Z k,m,p · λ out,m,p ;

[0062] where, μ m = 1 / T m , λ out,m,p represents the arrival rate of emergency parts to be processed by workstation m within the cycle p, represents the squared coefficient of variation corresponding to the general distribution followed by the inter-arrival time of products arriving at workstation m, the squared coefficient of variation corresponding to the general distribution followed by the service time of workstation m;

[0063] Step S4: Calculate the time f(k, p, l) required for the product of type k put into the l-th process until the completion of the process at a specific arrival rate λ, and the total processing cycle time F(k, p, L k ):

[0064] The process l of the product of type k is processed by workstation m, denoted as Mk,l = m; For any process l ∈ {1, …, L k} of the product of type k, the sojourn time of the product at the corresponding workstation M k,l is composed of the processing time and the waiting time . Therefore

[0065]

[0066] Among them, the processing time is known;

[0067]

[0068] Step S5, Based on the time f(k, p, l) required for the product of type k put into the l-th process until the completion of the process in the cycle p, and the total processing cycle time F(k, p, L k ), calculate the output quantity y of the product type k within the planning cycle p at a specific arrival rate λ k,p ;

[0069] Step S6, Calculate the work-in-process quantity w of the product type k in the system at the end of the planning cycle p at a specific arrival rate λ k,p , the inventory quantity h of the product type k in the system at the end of the planning cycle p k,p , the delayed delivery quantity b of the product type k in the system at the end of the planning cycle k,p :

[0070]

[0071]

[0072]

[0073]

[0074] Among them, D k,[ represents the demand of the product type k within the planning cycle [[. In a multi-product production line, D k,p is known;

[0075] Step S7, Calculate the sum of minimizing the work-in-process cost, inventory cost and delayed delivery cost at a specific arrival rate λ. The sum of minimizing the work-in-process cost, inventory cost and delayed delivery cost is the objective function, and this objective function is expressed as:

[0076]

[0077] Among them, W kDenote the unit in-process cost corresponding to product type k, H k Denote the unit inventory cost corresponding to product type k, B k Denote the unit late delivery cost corresponding to product type k;

[0078] Step S8: Traverse the sum of the minimized in-process cost, inventory cost, and late delivery cost corresponding to different arrival rates λ, and select the optimal solution by comparing the total cost results.

[0079] Through the above steps, the order release optimization method for a multi-product production line considering the priority processing of emergency parts of the present invention can calculate the sum of the minimized in-process cost, inventory cost, and late delivery cost when considering the arrival of emergency parts at the workstation, and select the optimal solution by traversing the sum of the minimized in-process cost, inventory cost, and late delivery cost corresponding to different arrival rates λ, so as to find the optimal release plan for the order release problem of the multi-product production line.

[0080] The above content is only a preferred embodiment of the present invention. For those of ordinary skill in the art, according to the idea of the present invention, there will be changes in the specific implementation manner and application scope. The content of this specification should not be construed as a limitation to the present invention.

Claims

1. A method for optimizing the order placement of multiple product lines by taking into account the priority processing of urgent parts, characterized in that: The following steps are included, specifically: Step S1: Calculate the utilization rate ρ of the product of type k processed by workstation m under a specific arrival rate λ k,m,p : λ 0,m (k,p) represents the raw material arrival rate of product type k at workstation m in period p, λ n,m (k,p) represents the re-entry rate of semi-finished products of type k at workstation m in period p, μ m represents the service rate of workstation m; M k,l represents the workstation corresponding to the lth process of product type k, and the arrival rate λ of the raw materials corresponding to product type k arriving at workstation m in period p 0,m (k,p)=x k,p ·[M k,1 =m]; The arrival rate of semi-finished products corresponding to product type k at workstation m in period p Among them, k represents the product type, p represents the planning period, m represents the workstation type, K represents the number of product types processed by the multi-variety production line, and L k Identifies the number of processes for product type k, l represents the process number, l∈{1,2,…,L k }; x k,p represents the quantity of raw materials put into production of product type k in planning period p, x k,p is the decision variable; Step S2: Since the arrival process and service time of the queuing system in the multi-product production line follow a general distribution, the priority processing rule of urgent parts is considered and the GI / G / 1 queuing model is used to model each workstation, and the expectation of the waiting time in the queuing system is obtained as E(W); Step S3: Calculate the total waiting time Z of products of type k at workstation m within period p under a specific arrival rate λ k,m,p : The total waiting time Z of product type k at workstation m in period p k,m,p It consists of the following three parts: the time τ from the arrival of the product to the time when at least one idle resource appears at workstation m k,m,p , the processing time σ of all urgent parts before this product in the waiting queue k,m,p , the processing time of the newly arrived urgent parts of the product during the waiting processδ k,m,p ; Z k,m,p =t k,m,p +s k,m,p +d k,m,p ; s k,m,p =T m ·E(W)·λ out,m,p ; δ k,m,p =T m ·Z k,m,p ·λ out,m,p ; Among them, μ m =1 / T m ,λ out,m,p represents the arrival rate of urgent parts to be processed at workstation m in period p, The squared coefficient of variation corresponding to the general distribution of the arrival interval of the product at workstation m is represented by, The squared coefficient of variation corresponding to the general distribution of the service time of workstation m; Step S4: Calculate the time f(k,p,l) required for a product of type k to be put into the lth process in cycle p and complete the process under a specific arrival rate λ, and the total processing cycle time F(k,p,L) of the product of type k k ): The process l of product type k is processed by workstation m, denoted by M k,l = m; for any process l∈{1,…,L k }, the product is in the corresponding workstation M k,l Processing time and waiting time Composition, therefore Among them, processing time is known; Step S5: based on the time f(k,p,l) required for the product of type k to be put into the lth process in cycle p until the process is completed, and the total processing cycle time F(k,p,L) of the product of type k k ), calculate the output quantity y of product type k in planning period p under a specific arrival rate λ k,p ; Step S6: Calculate the WIP of product type k in the system at the end of planning period p under a specific arrival rate λ k,p , the inventory level h of product type k in the system at the end of planning period p k,p , the delayed delivery quantity b of product type k in the system at the end of planning period p k,p : Among them, D k,p represents the demand for product type k in planning period p. In a multi-variety production line, D k,p is known; Step S7: Calculate the sum of the work-in-process cost, inventory cost and delayed delivery cost minimized under a specific arrival rate λ. Minimizing the sum of the work-in-process cost, inventory cost and delayed delivery cost is the objective function, which is expressed as: Among them, W k represents the unit work-in-process cost corresponding to product type k, H k represents the unit inventory cost corresponding to product type k, B k represents the unit delayed delivery cost corresponding to product type k; Step S8: traverse the sum of the minimized work-in-process cost, inventory cost and delayed delivery cost corresponding to different arrival rates λ, compare the total cost results and select the optimal solution.

2. According to claim 1, a method for optimizing the order placement of multiple product lines with consideration of priority processing of urgent parts, characterized in that: In this multi-variety production line, the product process path, processable equipment and processing time are known and determined.

3. The method for optimizing order placement of multiple product lines considering priority processing of urgent parts according to claim 1 is characterized in that: In this multi-variety production line, each workstation contains at least one device, which processes on a first-come, first-served basis, and one device can only process one product at a time.

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