A Reverse Logistics Network Design Method for Addressing Intrinsic Uncertainties in Construction Machinery

Abstract

This invention discloses a reverse logistics network design method for addressing the inherent uncertainties of construction machinery, comprising: Step S1: determining the endogenous and exogenous uncertainties and the construction machinery recycling and remanufacturing objectives that need to be considered in formulating a reverse logistics network construction machinery recycling and remanufacturing plan; Step S2: constructing a mathematical optimization model for maximizing the total profit of the reverse logistics network, determining the influence relationship between decision variables and endogenous uncertainties, and constructing a decision-dependent uncertainty set; Step S3: obtaining the final mixed-integer linear programming model, solving it using Python and the operations research optimization software Gurobi, and obtaining the optimal profit value and the optimal solution for the recycling and remanufacturing decision variables; Step S4: determining the influence of uncertainties on the pricing strategy, expected profit, and recycling objectives of each node center in the reverse logistics network based on sensitivity analysis. This method can resist the disturbance effects caused by uncertainty and achieve robustness in the recycling decisions of the main enterprise.

Description

Technical Field

[0001] This invention relates to the field of reverse logistics network design for construction machinery, and in particular to a reverse logistics network design method for construction machinery that addresses the inherent uncertainties of construction machinery. Background Technology

[0002] In recent years, with the increasing awareness of environmental protection and the strengthening of environmental protection constraints by laws and regulations, large manufacturers have also realized that the economic value created by reverse logistics is the key to leveraging their competitive advantage.

[0003] The reverse logistics network is characterized by its complex and diverse nature, high degree of uncertainty, and the interplay of various uncertainties, directly impacting the robustness of enterprise manufacturing and service decisions. Current research largely focuses on the design and optimization of reverse logistics networks in deterministic environments, or only considers the impact of exogenous uncertainties, neglecting the issue of endogenous uncertainties. For example, most reverse logistics networks fail to consider the dependency between exogenous uncertainties in the quality of returned products and endogenous uncertainties in processing costs, significantly affecting the profits and costs of the reverse logistics entity. Therefore, quantitatively analyzing the uncertainties present in the reverse logistics process is essential. A reverse logistics network framework considering endogenous uncertainties is not only applicable to the construction machinery industry but can also provide new reference ideas for many other industries, holding significant engineering implications for manufacturing enterprises. Summary of the Invention

[0004] This invention addresses the aforementioned technical problems by providing a reverse logistics network design method for engineering machinery that addresses inherent uncertainties.

[0005] The objective of this invention can be achieved through the following technical solution: a reverse logistics network design method for engineering machinery that addresses inherent uncertainties, characterized by comprising the following steps:

[0006] Step S1: Identify the endogenous and exogenous uncertainties and recycling and remanufacturing goals of construction machinery that need to be considered when developing a reverse logistics network construction machinery recycling and remanufacturing plan;

[0007] Step S2: Construct a mathematical optimization model for maximizing the total profit of the reverse logistics network, determine the influence relationship between decision variables and endogenous uncertainty, and construct a decision-dependent uncertainty set;

[0008] Step S3: Obtain the final mixed-integer linear programming model, solve it using Python and the operations research optimization software Gurobi, and obtain the optimal profit value and the optimal solution for the recycling and remanufacturing decision variables;

[0009] Step S4: Based on sensitivity analysis, determine the impact of uncertainty factors on the pricing strategy, expected profit, and recovery target of each node center in the reverse logistics network;

[0010] Step S5: Based on the analysis results of Step S4 above, adjust the reverse logistics network of construction machinery and determine the optimal reverse logistics network recycling and remanufacturing target.

[0011] Furthermore, in step S1 above, the uncertainties include endogenous uncertainties in processing costs and exogenous uncertainties in the quantity and quality of returned products.

[0012] Furthermore, in step S2 above, the mathematical optimization model for maximizing the total profit of the reverse logistics network is as follows:

[0013]

[0014] It is total revenue, Location cost, It is transportation cost, The costs of collection and disposal, Processing costs.

[0015] Furthermore, in step S2 above, the decision-dependent uncertainty set is constructed as follows:

[0016]

[0017] Where ξ st This indicates uncertainty in the quality of repatriated products; XA st Indicates the detection decision; ci st Indicates the cost of testing; τ st Indicates a general coefficient; Γ s represents the uncertainty base; s represents the scenario; t represents the period.

[0018] Furthermore, in step S3 above, the decision-dependent uncertainty set is transformed into new constraints as follows:

[0019]

[0020]

[0021]

[0022] Where r st n st o1 s XB is the dual variable; st To recover decision variables; prob s Let u be the scenario probability; u is the coefficient. m1 is the nominal processing cost; m1 is a constant.

[0023] The beneficial effects of this invention are:

[0024] 1. This invention addresses the current situation in reverse logistics networks where the relationships between key enterprises are complex, multiple types of uncertainties overlap and influence each other, target relationships are unclear, and there is a lack of systematic modeling methods and targeted optimization approaches. By constructing a reverse logistics network design method that addresses the inherent uncertainties of engineering machinery, this invention builds a total profit maximization optimization model for the reverse logistics network's recycling and remanufacturing plan, proposing a hybrid optimization method that considers decision-dependent uncertainty. Based on sensitivity analysis, it clarifies the impact of different pricing strategies and different recycling demand volumes specified by relevant enterprises in the reverse logistics network on the total profit target. Furthermore, it resists the disturbance effects caused by uncertainty, achieving robustness in the recycling decisions of key enterprises.

[0025] 2. In response to the interdependent and synergistic relationship between the two endogenous and exogenous uncertainties of the quality of returned products and processing costs, a set of decision uncertainty was constructed. This set can effectively reduce the economic impact of uncertain factors in the reverse logistics network, significantly increase the total profit of the main enterprise in the reverse logistics network, and help accelerate the intelligentization and refinement of the reverse logistics network's recycling and remanufacturing plan. Attached Figure Description

[0026] Figure 1 This paper presents a reverse logistics network design method for engineering machinery to address the inherent uncertainties.

[0027] Figure 2 This is a graph showing the trend of the optimal profit mean as a function of the uncertainty base.

[0028] Figure 3 This is a graph showing the trend of the optimal average profit as a function of testing costs. Detailed Implementation

[0029] The present invention will now be described in detail with reference to the accompanying drawings and specific examples.

[0030] This invention discloses a reverse logistics network design method for engineering machinery with inherent uncertainties, the method comprising the following steps:

[0031] Step S1: Identify the endogenous and exogenous uncertainties and recycling and remanufacturing goals of construction machinery that need to be considered when developing a reverse logistics network construction machinery recycling and remanufacturing plan;

[0032] Step S101: From the perspective of the operation process of returned products, returned products are first tested and classified by the testing center to determine their next processing method, including four processing methods: repair and resale, disassembly, disposal, and recycling and remanufacturing.

[0033] Construct a reverse logistics network capable of handling multiple products, multiple cycles, and capacity constraints. A schematic diagram of the four-layer reverse logistics network structure is shown below. Figure 1 As shown.

[0034] The first tier includes a testing center responsible for collecting returned products and testing their quality levels. After quality testing, a recycling decision and pre-processing procedures are determined. Returned products are subsequently divided into two categories: one is sent to a repair or dismantling center, with a very small number of substandard products directly transported to a disposal center. The second tier consists of repair, dismantling, and disposal centers. A portion of the returned products are upgraded through core component upgrades at the repair center, refurbishing high-quality products for direct sale. Another portion of scrapped products are dismantled and added to the bill of materials, including modules and materials. The remaining scrap is discarded directly. The third tier includes remanufacturing and recycling centers. Substandard returned products are dismantled into modules or materials, processed, and then sold on the market. Non-recyclable materials are sent to the disposal center. Ultimately, the market receives products including refurbished returned products, remanufactured modules, and recycled materials.

[0035] Step S2: Construct a mathematical optimization model for maximizing the total profit of the reverse logistics network, determine the influence relationship between decision variables and endogenous uncertainty, and construct a decision-dependent uncertainty set;

[0036] Step S201: The parameters and variables required to build the model are as follows:

[0037] B represents a collection of repair centers;

[0038] C represents the set of dismantling centers;

[0039] D represents the set of remanufacturing centers;

[0040] E represents the set of recycling centers;

[0041] G represents the set of abandoned centers;

[0042] L indicates the module type;

[0043] M indicates the type of material;

[0044] S represents the set of scenarios involving the quantity of returned products and nominal processing costs;

[0045] T represents the set of time periods within the planning period;

[0046] prob s Represents the probability of a scenario;

[0047] RP represents the unit price of refurbished and resold products in the secondary market.

[0048] rs represents the unit price of the module on the secondary market;

[0049] rm represents the unit price of the material on the secondary market;

[0050] cc represents the unit collection cost of the recycled products;

[0051] ud represents the unit waste cost of the material;

[0052] ci st This indicates the pre-processing cost of the returned products;

[0053] This represents the nominal processing cost of each returned product within time period t in scenario s;

[0054] up(ξ) st This indicates that the total processing cost of each returned product unit is uncertain within time period t in scenario s;

[0055] α represents the proportion of remanufacturable modules from the disassembly center to the remanufacturing center;

[0056] β represents the proportion of recyclable materials that move from the dismantling center to the recycling center;

[0057] θ represents the type of module in each product unit;

[0058] η represents the type of material per unit of product;

[0059] τ represents the coefficient that reduces potential uncertainty;

[0060] μ represents the uncertainty coefficient of the impact on the quality of each reflowed product;

[0061] UDP represents the cost of discarding each product;

[0062] f IC This refers to the fixed costs of establishing a testing center;

[0063] This indicates the fixed cost of establishing a maintenance center;

[0064] This represents the fixed cost of establishing a dismantling center;

[0065] This represents the fixed cost of establishing a remanufacturing center;

[0066] This indicates the fixed cost of establishing a recycling center;

[0067] This indicates the fixed cost of establishing an abandoned facility;

[0068] This indicates the capacity of the repair center;

[0069] Indicates the dismantling center's production capacity;

[0070] Indicates the capacity of the remanufacturing center;

[0071] Indicates the capacity of the recycling center;

[0072] Indicates the production capacity of the abandoned center;

[0073] The tab indicates the transportation cost of each product from the testing center to the repair center;

[0074] TAC represents the transportation cost of each product from the testing center to the disassembly center.

[0075] TBS represents the transportation cost per product from the repair center to the secondary market;

[0076] TCD represents the transportation cost per module from the disassembly center to the remanufacturing center;

[0077] TCE represents the transportation cost per module from the dismantling center to the recycling center;

[0078] TDS represents the unit transportation cost per module from the remanufacturing center to the secondary market;

[0079] TES represents the transportation cost of each piece of material from the recycling center to the secondary market;

[0080] teg represents the transportation cost of each piece of material from the recycling center to the processing center;

[0081] The tag represents the transportation cost of each product from the testing center to the processing center;

[0082] XA st This represents a binary variable; it is 1 when the returned product is detected by the preprocessing procedure, and 0 otherwise.

[0083] XB st This represents a binary variable, with a value of 1 when the returned product is classified as a refurbishable product, and a value of 0 otherwise.

[0084] This represents a binary variable, which is 1 when the repair center is established and 0 otherwise.

[0085] This represents a binary variable, which is 1 when the maintenance center is established, and 0 otherwise.

[0086] This represents a binary variable, which is 1 when a remanufacturing center is established, and 0 otherwise.

[0087] This represents a binary variable, which is 1 when a recycling center is established, and 0 otherwise.

[0088] This represents a binary variable, which is 1 when a discard center is established, and 0 otherwise.

[0089] QA st This represents the total number of returned products transported to the testing center within time period t in scenario s.

[0090] This represents the number of products transported from the testing center to the repair center within time period t in scenario s.

[0091] This represents the number of products transported from the inspection / collection center to the dismantling center within time period t in scenario s.

[0092] This represents the number of products transported from the dismantling center to the remanufacturing center within time period t in scenario s.

[0093] This represents the number of products transported from the dismantling center to the recycling center within time period t in scenario s.

[0094] This represents the number of products transported from the recycling center to the secondary market within time period t in scenario s.

[0095] This represents the number of products transported from the recycling center to the processing center within time period t in scenario s.

[0096] This represents the number of products that travel from the testing center to the disposal center within time period t in scenario s.

[0097] The objective function maximizes the total profit of the reverse logistics network, including total revenue. Location cost Transportation costs Collection and disposal costs and processing costs The optimization objective is to find the best worst-case solution on a given set of uncertainties. The objective function is constructed as follows:

[0098]

[0099] Of which, total revenue as follows:

[0100]

[0101] Location cost

[0102]

[0103] Transportation costs

[0104]

[0105] Collection and disposal costs

[0106]

[0107] Processing costs

[0108]

[0109] The following constraints limit the capacity of each center, ensuring no product flow exists between unestablished centers, while guaranteeing that the transportation volume between centers is less than the maximum capacity. The capacity constraints are as follows:

[0110]

[0111]

[0112]

[0113]

[0114]

[0115] The following constraints are product flow balancing constraints, representing the transport volume of returned products from the inspection center to the repair center and dismantling center, and determining the transport volume of returned products from the dismantling center to the remanufacturing center and recycling center. The product flow balancing constraints are as follows:

[0116]

[0117]

[0118]

[0119]

[0120] The following constraints are classification balance constraints, which respectively ensure that the collection volume of the testing center equals the total transportation flow of the repair center, dismantling center, and disposal center; that returned products have only one flow direction; that high-value returned products are assigned to the repair center; that inferior and low-value products are assigned to the dismantling center; and that non-recyclable products are directly transported to the waste center. The product classification balance constraints are as follows:

[0121]

[0122]

[0123]

[0124]

[0125] The decision depends on the following set of uncertainties:

[0126]

[0127] Decision uncertainty refers to the uncertainty of decision variable XA st This determines whether to reduce the maximum uncertainty. Such reduction is typically accompanied by increased preprocessing costs. st Preprocessing includes expert consultation information or preprocessing of the product. Decision variable XA st The uncertainty parameter ξ for the quality of returned products exists only in inspection centers within the reverse logistics network. st It exists in the set of decision-dependent uncertainties where the upper limit can be reduced. When τ st When = 0, the decision-dependent uncertainty set will degenerate into a general cardinal uncertainty set.

[0128] Step S3: Obtain the final mixed-integer linear programming model, solve it using Python and the operations research software Gurobi, and obtain the optimal profit value and the optimal solution for the recycling and remanufacturing decision variables.

[0129] Step S301: Further, let

[0130] Furthermore,

[0131]

[0132] Furthermore,

[0133]

[0134]

[0135] ξ st ≤1-τ st ·XA st :π1 st

[0136]

[0137] Where q1 s and π1 stThis represents the dual variable.

[0138] Furthermore, according to duality theory, we obtain:

[0139]

[0140]

[0141]

[0142] Let r st =π1 st -П·XA st ,n st =π1 st ,o1 s =q1 s and

[0143] Furthermore,

[0144]

[0145]

[0146]

[0147]

[0148] Each Equal to m1, XB in the entire mathematical model st The maximum value that can be taken (i.e., m1 = 1).

[0149] Furthermore, the decision-dependence uncertainty set constraint is transformed into:

[0150]

[0151]

[0152]

[0153]

[0154] Including the aforementioned capacity constraints, product flow balance constraints, and product classification balance constraints, the final mixed-integer linear programming model is obtained. The transformed problem involves a general operations research optimization problem. The established mathematical model is a mixed-integer linear programming model, which can be programmed in Python and solved using the optimization software Gurobi.

[0155] Step S4: Based on sensitivity analysis, determine the impact of uncertainty factors on the pricing strategy, expected profit, and recovery target of each node center in the reverse logistics network;

[0156] Sensitivity analysis was conducted using the pricing of different components in the remanufacturing center as an example. The profit values ​​under different coefficient adjustments are shown in Table 1.

[0157] Table 1. Relative increases and profit margins for different parts priced at the remanufacturing center.

[0158]

[0159] The relative improvement is defined as the percentage improvement of the method of the present invention compared to the traditional reverse logistics network model that does not consider endogenous uncertainties.

[0160] Table 1 clearly shows that decreasing the price of remanufacturing center parts has a relatively constant impact on the optimal profit of the entire reverse logistics network, but the relative increase is the largest. As the price of remanufacturing center parts gradually increases, the gain effect on the optimal profit of the entire reverse logistics network is huge, but the relative increase is very poor. Therefore, the pricing strategy for remanufacturing center parts should be dynamically adjusted according to the expected profit. To achieve the highest possible expected profit, the price of remanufacturing center parts can be appropriately increased. The above analysis also applies to the adjustment of pricing schemes at each node center.

[0161] Step S5: Based on the analysis results of Step S4 above, adjust the reverse logistics network of construction machinery and determine the optimal reverse logistics network recycling and remanufacturing target;

[0162] like Figure 2 As shown, the optimal average profit is at its highest level when the inspection cost ci is 0 and the uncertainty of the returned product quality is low. This means that at this point, in the reverse logistics network, it is more profitable to have the returned products flow to the repair center while simultaneously targeting the refurbishment and resale of the entire product. However, as the uncertainty increases to a certain level, the total profit of the reverse logistics network will reach a stable period. This means that the returned products will flow to the dismantling center, where the target of recycling tends to be the dismantling and remanufacturing of the returned products for sale as parts, which is less profitable than refurbishing and selling the entire product.

[0163] like Figure 3 As shown, when the uncertainty of the quality of repatriated products is at its highest level, the cost of testing increases with increasing costs. ciAs the cost of inspection gradually increases, the average optimal profit will gradually decrease and eventually stabilize. This means that the reverse logistics network has a limited tolerance for inspection costs. When inspection costs are low and the degree of uncertainty is high, it is more profitable to return products to repair centers and resell the entire product after refurbishment. When inspection costs exceed a certain range and the degree of uncertainty is low, return products flow to dismantling centers. At this point, the recycling target tends to dismantle and remanufacture the returned products for sale as parts, which is less profitable than reselling the entire product after refurbishment.

[0164] Based on the above analysis, for the case of construction machinery companies, there is an influential relationship between the inherent uncertainty of the quality of returned products and the exogenous uncertainty of processing costs. Using the method of this invention, a trade-off between testing costs and processing costs can effectively and proactively reduce the impact of uncertainty, achieving a substantial relative increase in profit compared to traditional reverse logistics networks. Simultaneously, by formulating and implementing a scientific recycling and remanufacturing plan, each node in the reverse logistics network can also implement appropriate pricing strategies through sensitivity analysis, maximizing revenue.

[0165] The above descriptions are merely embodiments of the present invention, and common knowledge regarding specific structures and characteristics of the solutions is not described in detail here. It will be apparent to those skilled in the art that the present invention is not limited to the details of the above exemplary embodiments, and that the present invention can be implemented in other specific forms without departing from the spirit or essential characteristics of the invention. Therefore, the embodiments should be considered exemplary and non-limiting in all respects, and the scope of the present invention is defined by the appended claims rather than the foregoing description. Therefore, it is intended that all variations falling within the meaning and scope of equivalents of the claims be included within the present invention. No reference numerals in the claims should be construed as limiting the scope of the claims.

Claims

1. A method for designing a reverse logistics network to address the inherent uncertainties of engineering machinery, characterized in that, Includes the following steps: Step S1: Identify the endogenous and exogenous uncertainties and recycling and remanufacturing goals of construction machinery that need to be considered when developing a reverse logistics network construction machinery recycling and remanufacturing plan; Step S2: Construct a mathematical optimization model for maximizing the total profit of the reverse logistics network, determine the influence relationship between decision variables and endogenous uncertainty, and construct a decision-dependent uncertainty set; The decision depends on the uncertain set and is constructed as follows: ； in This indicates uncertainty in the quality of returned products; Indicates the testing decision; Indicates the cost of testing; Indicates a general coefficient; Indicates the cardinality of uncertainty; Describe a scenario; Indicates period; Step S3: Obtain the final mixed-integer linear programming model, solve it using Python and the operations research optimization software Gurobi, and obtain the optimal profit value and the optimal solution for the recycling and remanufacturing decision variables; The decision-dependent uncertain set is transformed into new constraints as follows: ； ； ； in , , As dual variables; To recover decision variables; For scenario probabilities; For coefficients; Nominal processing cost; It is a constant; Step S4: Based on sensitivity analysis, determine the impact of uncertainty factors on the pricing strategy, expected profit, and recovery target of each node center in the reverse logistics network; Step S5: Based on the analysis results of Step S4 above, adjust the reverse logistics network of construction machinery and determine the optimal reverse logistics network recycling and remanufacturing target.

2. The reverse logistics network design method for engineering machinery based on the inherent uncertainties according to claim 1, characterized in that, In step S1 above, the uncertainties include the intrinsic uncertainty of processing costs and the exogenous uncertainty of the quantity and quality of returned products.

3. The reverse logistics network design method for engineering machinery based on the inherent uncertainties according to claim 1, characterized in that, In step S2 above, the mathematical optimization model for maximizing the total profit of the reverse logistics network is as follows: ； It is total revenue, Location cost, It is transportation cost, The costs of collection and disposal, Processing costs.

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