جستجوی محله ای متغیر برای مسیریابی موجودی و مشکل زمان بندی در یک زنجیره تامین

The inventory, routing and scheduling decisions are three major driving factors for supply chain performance. Since they are related to one another in a supply chain, they should be determined simultaneously to improve the decision quality. In the past, the inventory policy, vehicle routing and vehicle scheduling are determined sequentially and separately. Hence, the total cost (inventory, routing and vehicle costs) would increase. In this paper, an integrated model for the inventory routing and scheduling problem (IRSP) is proposed. Since searching for the optimal solution for this model is a non-polynomial (NP) problem, a metaheuristic, variable neighborhood search (VNS), is proposed. The proposed method was compared with other existing methods. The experimental results indicate that the proposed method is better than other methods in terms of average cost per day.

The inventory routing and scheduling problem (IRSP) in a supply chain (SC) is to determine delivery routes from suppliers to some geographically dispersed retailers, inventory policy (e.g. replenishment frequency and quantity) for retailers and vehicle scheduling for different routes based on the minimal cost criterion (Raa and Aghezzaf, 2009 and Zachariadis et al., 2009). The IRSP considering inventory policy, vehicle routing and vehicle scheduling simultaneously has gained attentions in designing distribution systems such as beverage industry since the coordination of inventory, routing and scheduling decisions between suppliers and retailers leads to a better overall performance in a vendor managed inventory (VMI) environment (Chopra and Meindl, 2004, Hall, 1987 and Vidal and Goetschalckx, 1997). In the past, the routing is determined first (the retailers are partitioned into disjoint sets (routes) served by a specific vehicle) and then the replenishment frequency for each route is determined at stationary interval with fixed quantity. At last, the vehicle scheduling for different routes is determined based on the minimal replenishment cycle time criterion (Moin and Salhi, 2007, Raa and Aghezzaf, 2009, Zachariadis et al., 2009 and Li et al., 2010). The vehicle routing, replenishment frequency and vehicle scheduling are determined sequentially, separately and fixedly. Hence, the total cost (inventory, routing and vehicle costs) would increase. The purpose of this paper is to resolve the inventory routing and scheduling problem (IRSP) simultaneously and flexibly so that the total cost would decrease. The IRSP is originally evolved from the inventory routing problem (IRP), in which the vehicle scheduling problem is ignored (Andersson, Hoff, Christiansen, Hasle, & Lokketangen, 2010). Since the vehicle scheduling problem becomes important in practice, the IRSP gains a lot of attentions recently. Aghezzaf, Raa, and Van Landeghem (2006) and Raa and Aghezzaf, 2008 and Raa and Aghezzaf, 2009 adopted column generation and saving heuristic to resolve the vehicle routing problem based on the minimal cost criterion. Then power-of-two (POT) policy is adopted to determine the replenishment frequency for each route. At last, the routes served by the same vehicle are scheduled based on the minimal replenishment cycle time criterion. However, the vehicle routing, replenishment frequency and vehicle scheduling are determined sequentially, separately and fixedly. Zachariadis et al. (2009) adopted an integrated local search for replenishment insertion timing and replenishment removal timing based on the minimal cost criterion to make inventory and routing decisions flexibly. Then tabu search is adopted to find the shortest path for each route. However, the local search may be trapped in the local optimum. In addition, the information of available vehicles and replenishment cycle times is assumed known. Until now, there are still few heuristic methods proposed for resolving the IRSP. Since the structure of IRP is similar to that of IRSP, the IRP is also reviewed. Bell, Dalberto, and Fisher (1983) adopted an optimization method to resolve the IRP. Since the IRP is an NP-hard problem, heuristic methods are needed. Federgruen and Zipkin (1984) developed a nonlinear integer programming model and adopted an exchange method to resolve the IRP. Golden, Assad, and Dahl (1984) adopted an insertion method to resolve the IRP. Anily and Federgruen (1990) proposed a new method to resolve the IRP. First of all, the customers are partitioned into several categories (routes) served by some specific vehicles based on the minimal cost criterion. Then replenishment frequency for each route is determined separately at stationary interval. Since then, the method is adopted in other IRP literature (Anily, 1994, Anily and Federgruen, 1993, Anily and Federgruen, 1994, Gaur and Fisher, 2004 and Jung and Mathur, 2007). The method can obtain the solution quickly especially when the problem size is large. Viswanathan and Mathur (1997) adopted SNJRP (stationary nested joint replenishment policy heuristic) to resolve the IRP based on the minimal cost criterion. The route is determined based on the vehicle capacity and minimal cost criterion. Power-of-two (POT) heuristics is adopted to determine replenishment frequency for retailers in each route. Campbell and Savelsbergh (2004) adopted a two-phase method to resolve the IRP. The first phase adopted an integer programming method to obtain the initial solution. The second phase adopted an insertion method to improve the initial solution. Gaur and Fisher (2004) adopted a randomized sequential matching algorithm (RSMA) to resolve the IRP. An insertion method was adopted to obtain the initial solution. Then a cross-over method was adopted to improve the initial solution. Sindhuchao, Romeijn, Akcali, and Boondiskulchok (2005) adopted a two-phase method for the IRP. The first phase adopted a column generation method to obtain the initial solution. The second phase adopted a very large-scale neighborhood search (VLSN) to improve the initial solution. Lee, Jung, and Lee (2006) adopted a tabu search method to resolve the IRP. Jung and Mathur (2007) adopted the fixed partition method to resolve the routing problem. Then power-of-two (POT) policy is adopted to resolve the inventory problem. Zhao, Wang, and Lai (2007) adopted GENI insertion method to resolve the routing problem. Then tabu search for power-of-two (POT) policy is adopted to resolve the inventory problem. Zhao, Chen, and Zang (2008) resolved the IRP with three layers: manufacturers, warehouse, and retailers. GENI insertion method is adopted to resolve the routing problem. Then Variable Large Neighborhood Search (VLNS) for power-of-two (POT) policy is adopted to resolve the inventory problem. The results show it is better than tabu search. In addition, the CPU time is efficient. In this paper, an integrated model for the IRSP is proposed. Since searching for the optimal solution for this model is a non-polynomial (NP) problem, a metaheuristic, variable neighborhood search (VNS, which is the original type of VLNS and competitive in the combinatorial problem.), is proposed to find the optimal solution for the IRSP.

In this paper, we have developed an effective heuristic method to resolve the IRSP simultaneously and flexibly. The proposed heuristic method is better than the other heuristic method making the inventory, routing and scheduling decisions sequentially and separately based on the minimal cost criterion. In addition, when the unit holding cost increases, the unit vehicle cost per day increases or the vehicle capacity decreases, the average costs for all methods increase. As for the average CPU time, it is not affected by the unit holding cost or the unit vehicle cost per day. However, it increases when the vehicle capacity decreases. Due to the limitations of this paper, some factors such as multiple products, different vehicle fleet, etc. are not considered. So considering these factors would help the inventory routing and scheduling decisions made more realistically.