یک رویکرد تکاملی برای بهینه سازی چند هدفه مشکل شبکه توزیع یکپارچه شده محل - موجودی در مدیریت موجودی فروشنده

Vendor-managed inventory (VMI) is one of the emerging solutions for improving the supply chain efficiency. It gives the supplier the responsibility to monitor and decide the inventory replenishments of their customers. In this paper, an integrated location–inventory distribution network problem which integrates the effects of facility location, distribution, and inventory issues is formulated under the VMI setup. We presented a Multi-Objective Location–Inventory Problem (MOLIP) model and investigated the possibility of a multi-objective evolutionary algorithm based on the Non-dominated Sorting Genetic Algorithm (NSGA2) for solving MOLIP. To assess the performance of our approach, we conduct computational experiments with certain criteria. The potential of the proposed approach is demonstrated by comparing to a well-known multi-objective evolutionary algorithm. Computational results have presented promise solutions for different sizes of problems and proved to be an innovative and efficient approach for many difficult-to-solve problems.

Recently, two generic strategies for supply chain design have emerged: efficiency and responsiveness. Efficiency aims to reduce operational costs; responsiveness, on the other hand, is designed to react quickly to satisfy customer demands. A crucial question in the supply chain is the design of distribution networks and the identification of facility locations. Ballou and Masters (1993) put forward four strategic planning areas in the design of a distribution network system, as shown in Fig. 1. The first issue deals with customer service levels. The second one deals the placement of facilities and demand assignments made to them. The third deals with inventory decisions and policies that involve inventory control. The fourth deals with transportation decisions of how transport modes are selected, utilized, and controlled. All four of these areas are inter-related and the customer service level is determined by the other three decision areas. There are practical challenges for firms when they try to simultaneously reduce operating costs (for efficiency) and customer service (for responsiveness). In traditional supply chain network design, the optimization focus is often placed on minimizing cost and maximizing profit as a single objective. However, very few distribution network systems should be considered as intrinsically single objective problems. It is not always desirable to reduce costs if this results in a degraded level of customer service. Thus, it is necessary to set up a multi-objective network design problem. Full-size image (22 K) Fig. 1. Four strategic planning issues in distribution network design. Figure options Research on integrated location–inventory distribution network systems is relatively new. Jayaraman (1998) developed an integrated model which jointly examined the effects of facility location, transportation modes, and inventory-related issues. However, Jayaraman’s study did not contain any demand and capacity restrictions. Erlebacher and Meller (2000) formulated an analytical joint location–inventory model with a highly nonlinear objective function to maintain acceptable service while minimizing operating, inventory and transportation costs. Nozick and Turnquist (2001) proposed a joint location–inventory model to consider both cost and service responsiveness trade-offs based on an uncapacitated facility location problem. Miranda and Garrido (2004) studied a MINLP model to incorporate inventory decisions into typical facility location models. They solved the distribution network problem by incorporating a stochastic demand and risk pooling phenomenon. Sabri and Beamon (2000) presented an integrated multi-objective, multi-product, multi-echelon model that simultaneously addresses strategic and operational planning decisions by developing an integrated two sub-module model which includes cost, fill rates, and flexibility. Gaur and Ravindran (2006) studied a bi-criteria optimization model to represent the inventory aggregation problem under risk pooling, finding out the tradeoffs in costs and responsiveness. Recently, Daskin et al., 2002 and Shen et al., 2003 introduced a joint location–inventory model with risk pooling (LMRP) that incorporates inventory costs at distribution centres (DCs) into location problems. LMRP solved the problem in two special cases: deterministic demand and Poisson demand. It assumed direct shipments from DCs to buyers which extended the uncapacitated fixed-charge problems to incorporate inventory decisions at the DCs. The uncapacitated assumption at DCs is usually not the case in practice. Shu, Teo, and Shen (2005) solved LMRP with general stochastic demand. Shen and Daskin (2005) extended the LMRP model to include the customer service component and proposed a nonlinear multi-objective model including both cost and service objectives. In contrast to LMRP and its variants that consider inventory cost only at the DC level, Teo and Shu, 2004 and Romeijn et al., 2007 proposed a warehouse-retailer network design problem in which both DCs and retailers carried inventory. These are actually the two major streams of integrated distribution network design problems. Our model builds upon the initial LMRP model but with some differences. First, a capacitated version of a similar model is established. Second, to make an original contribution, the proposed model incorporates two extra performance metrics corresponding to customer service. With these considerations, we present a capacitated Multi-Objective Location–Inventory Problem (MOLIP) which results in a Mixed-Integer Non-Linear Programming (MINLP) formulation. Some noteworthy innovative research aspects that are incorporated in our research include: (i) Multi-Objective Location–Inventory Problem. Very few studies have addressed this problem; (ii) multi-objective evolutionary algorithms (MOEAs). Most previous works have focused on traditional optimization techniques, but few have performed these techniques successfully and efficiently. In contrast, MOEAs have been successfully developed for various optimization problems, creating potential for the proposed MOLIP. This study is organized as follows: Section 2 describes our research problem and details the model formulation. Section 3 proposes a hybrid evolutionary algorithm with a heuristic procedure for MOLIP. Section 4 illustrates our experimental results including (i) the computational results of a base-case problem (ii) scenario analysis (iii) computational evaluation of the proposed algorithm for MOLIP. Finally, conclusions and suggestions for the direction of future research are provided in Section 5.

This study presented a MOLIP model initially represented as an integrated MOLIP formulation which examines the effects of facility location, distribution, and inventory issues under a vendor managed inventory (VMI) coordination mechanism. The MOLIP model is solved with a proposed hybrid evolutionary algorithm which is preliminarily based on a well-known NAGA-II evolutionary algorithm with an elitism strategy and a non-dominated sorting mechanism. We implemented two experiments. First, we investigated the possibility of a NSGAII-based evolutionary algorithm solving the MOLIP model. Computational results revealed that the hybrid approach performed well and presented promising solutions for the MOLIP model in solving practical-size problems. Second, we compared our approach with SPEA2 to understand the efficiency among two approaches. The experiment indicates that two algorithms obtained similar approximations of the Pareto front but our approach outperformed SPEA2 in terms of the diversity quality of the approximation of the Pareto front. Moreover, SPEA2 was only efficient in terms of execution time in small or tight capacity instances. This indicates that the proposed approach could be an efficient approach for providing feasible and satisfactory solutions to large-scale difficult-to-solve problems. In future works, we intend to adapt the proposed hybrid evolutionary algorithm to other location, inventory and distribution systems that have different characteristics or network structures. For instance, a network system may have stockpiles or inventories within the suppliers and the customer sites, and the shortage penalty needs to be considered in the overall supply chain operating cost. In addition, the inclusion of other inventory decisions would be a direction worth pursuing. Such inventory decisions could include frequency and size of the shipments from plants to the DCs and from DCs to the retailers based on different replenishment policies, and lead time in addition to safety-stock inventory in the model,. Finding ways to adapt our hybrid evolutionary algorithm into such systems is the task of future research. Other possible research directions are to explore more competitive MOEAs or other existing optimization technologies, such as Lagrangian relaxation, particle swarm optimization, ant colony optimization, or other soft intelligent computing techniques. Comparative studies of these techniques are worth investigating in the future. In addition, some possible methods of hybridizations include the adaption of new genetic operators for integrated systems and the incorporation of other heuristic search techniques into the evolutionary algorithms, such as hill-climbing or local repair procedure.