الگوریتم ژنتیک پارتو اصلاح شده برای برنامه ریزی زنجیره تامین سفارش برای ساخت همراه با مونتاژ محصول

The build-to-order supply chain (BOSC) model is a key operation model for providing services/products at present. This study focuses on performing the supply chain planning for the BOSC network. The planning is designed to integrate supplier selection, product assembly, as well as the logistic distribution system of the supply chain in order to meet market demands. With multiple suppliers and multiple customer needs, the assembly model can be divided into several sub-assembly steps by applicable sequence. Considering three evaluation criteria, namely costs, delivery time, and quality, a multi-objective optimization mathematical model is established for the BOSC planning in this study. The multi-objective problems usually have no unique optimal solution, and the Pareto genetic algorithm (PaGA) can find good trade-offs among all the objectives. Therefore, the PaGA is applied to find solutions for the mathematical model. In addition, regarding BOSC problems solving, this study proposes a modified Pareto genetic algorithm (mPaGA) to improve the solution quality through revision of crossover and mutation operations. After application and analysis of cases, mPaGA is found to be superior to traditional PaGA (tPaGA) in solution performance.

In 21st century, supply chain management (SCM) is a key strategy to improve competitive edge. In particular, due to the success of several high-tech corporations such as Dell, BMW, Compaq, and Gateway, BOSC has received more attention in recent years. Some auto makers have also proceeded to adopt BOSC [14]. In BOSC model, production activities are not executed until receiving orders from customers, that can effectively reduce the costs of demand prediction and inventory and credibly reflect market demands. As BOSC is started, supplier selection becomes the priority. After a proper part supplier is selected, product assembly begins. Consequently, we should select suitable assembly planning and a qualified assembly factory, and distribute the assembled products in accordance with customer requirements. Among previous supply chain studies, there were quite a few researches involving the argument of supplier selection [4], [10] and [15], product assembly [26], [35] and [21], and logistic distribution issues [1], [3] and [34]. However, most of the issues were examined separately in earlier studies. To be consistent with the BOSC model, these issues should be further explored in an integrated manner, lest the overall benefits of supply chain should not be increased. In terms of supplier selection, Dickson [6] proposed 23 criteria for supplier selection in his research and identified quality, delivery, and performance history as the three major criteria. Weber et al. [32], Weber et al. [33], Liaoa and Rittscherb [22], and Wadhwa and Ravindran [31] used cost, quality, and time for evaluation criteria. For this reason, this study also applies these three criteria for supplier selection and extends them to production and distribution of the entire supply chain to form a multi-objective programming issue. Moreover, this study additionally considers the quantity discount in cost. Gen and Cheng [9] indicated that multi-stage logistic problems can be treated as the combination of the multiple-choice knapsack problem with the capacitated location allocation problem as an NP-hard problem. Goossens et al. [11] indicated when various goods should be procured from multiple suppliers with considering the quantity discount, and these problems refer to the total quantity discount problems. They argued that it is NP-hard, and also there exists no polynomial-time approximation algorithm with a constant ratio (unless P = NP). In this study, the BOSC planning problem has considering multi-stage logistic system, quantity discount, and assembly problem, that thus it becomes even more complex. Simaria and Vilarinho [29] argued that the genetic algorithm (GA) can be used to effectively solve the assembly line balancing problem. Sha and Che [28], Altiparmak et al. [1], and Xu et al. [34] had applied GA to deal with supply chain problems. In addition, Poulos et al. [24] and Hosung et al. [16] have successfully employed PaGA for dealing with the multi-objective optimization problems. Hence, this study present the mPaGA based on PaGA for solving the multi-objective optimization mathematical model of BOSC planning. The main purposes of the study are described as follows: (1) Establish a multi-objective optimization mathematical model for BOSC problems. This model integrates supplier selection, product assembly, and the logistic distribution system. As far as we are concerned, the mathematical model for integrated multi-objective BOSC problems has not been developed up till now. (2) Propose the mPaGA model for solving the optimization mathematical model. Principally, mPaGA based on PaGA is intended to improve the crossover and mutation operators for higher solving efficiency. In addition, after the crossover and mutation operators have been used, the equilibrium and feasibility-adjustment mechanisms proposed for maintaining the feasibility of each individual, that can reduce the computational time for searching the feasible individuals. (3) Compare the solving efficiency between mPaGA and tPaGA to verify that mPaGA is superior in calculation capabilities. The tPaGA based on PaGA employs one-point crossover and one-point mutation operators for finding the new individuals. The framework of the study is as described in the following. Literature review for BOSC and PaGA is provided in Section 2. Section 3 provides the optimization mathematical model for BOSC problems. The proposed mPaGA model is described in Section 4. Section 5 provides an illustrative example to illustrate the application of mPaGA for obtaining the optimal plans. Results thus obtained are also compared with those of tPaGA to validate the efficiency of the proposed mPaGA. Conclusions, limitations of the proposed model, and the future research are drawn in Section 6.

In this study, we propose an optimization mathematical model for BOSC problems in connection with supplier selection, assembly scheme, and logistic distribution planning, with three evaluation criteria, including cost, time, and quality. With the minimum cost and time and the maximum quality, a multi-objective optimization SCM problem is derived. To effectively solve this multi-objective optimization problem, this study develops the mPaGA for problem solving. Based on chromosome coding methods, the mPaGA is intended to improve the crossover and mutation operators in the evolution steps and apply in cases to effectively obtain reasonable management strategies. To identify whether mPaGA is superior to tPaGA in solving problems, we design three evaluation criteria as three multi-objective optimization problems, including two dual-objective problems and a triple-objective problem. Further, we compare the average number of Pareto optimal solutions with the average ratio of Pareto optimal solutions for these three problems and calculate CV values based on the data obtained. According to the results, mPaGA is superior to tPaGA in effectively solving all three problems. The variation can also be observed in the distribution figure of Pareto optimal solutions. The result shows that mPaGA features higher integrity, less variation, and better solution stability when solving the Pareto optimal solution set, and is unlikely to cause exaggerated strategy differences that may result in additional losses.