Inventory and transportation decisions in a two-stage supply chain
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In this study a two stage supply chain with two distribution centers (DCs) and multiple retailers is analyzed. The retailers and the DCs use a continuous review (Q, r) inventory policy, and demand at each retailer follows a Poisson process. The reorder points (r) and the order quantities (Q) are assumed to be known. As the retailers receive customer demands they fulfill these demands immediately if there is enough inventory, otherwise the demands are backlogged. As a retailer's inventory level drops down to the reorder point r or below, the retailer requests an order of size Q from the closest DC. Although each DC is able to serve all retailers with different cost structures, initially each retailer is assigned to the closest DC in an effort to decrease the transportation cost. However, if the assigned DC is not able to fulfill the demand within a promised lead time, then the retailer's demand is directed to another DC which has inventory. If none of the DCs has enough inventory to satisfy the retailer's demand, the order is partially fulfilled and the remaining part is backlogged. Unlike the retailers, the DCs do not necessarily ship the orders immediately. They may wait to consolidate several orders in one shipment. When a DC's inventory level reaches the reorder point r or below, the DC places an order of size Q to an outside supplier. We assume the outside supplier has infinite supply. The DC's order arrives after a constant lead time. Two different scenarios are studied. Under the first scenario all DCs and retailers use a (Q, r) policy with different Q and r values. Under the second scenario, a central decision maker controls the inventories at the retailers and at the DCs to initiate vendor managed inventory (VMI) at the retailers. These two scenarios are compared with respect to their overall cost reduction and how the cost is shared among each supply chain member. The overall cost consists of inventory holding cost, backlog cost, ordering cost, and transportation cost. The objective of the study is to determine an optimal promised lead time from DCs to retailers. Two simulation models are developed for the given scenarios and the effects of different parameters such as lead time from outside supplier to the DCs, number of retailers, and truck capacity are investigated. Preliminary results show that when the lead time to the DCs is decreased problem reduces to several one supplier multi retailer supply chains. When the number of retailers increases, the promised lead time to the retailers tend decrease. Also when the truck capacity is small, the promised lead time tends to be small in order to decrease inventory holding cost during the waiting time for order consolidation.
