Replenishing routing under vendor managed inventory systems


Student thesis: Doctoral Thesis

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  • Jingan LI

Related Research Unit(s)


Awarding Institution
  • Kin Keung LAI (Supervisor)
Award date3 Oct 2006


This study is inspired by an empty container allocation problem that is related to the management of importing or exporting empty containers in anticipation of future requirements or in response to reduce the redundancy at the port, respectively. We consider the problem to be a non-standard inventory problem with positive and negative demands at the same time. Under a general holding-penalty cost function and one-time period delay for the availability of full containers just arriving at the port, we show that there exists an optimal pair (U,D) of critical policies when only one port is discussed, which is to import empty containers up to U units when the number of empty containers at the port is less than U, or export down to D units when the number is more than D, and do nothing otherwise. When multi-ports are considered, a modified (u, d) policy for each port is introduced to direct the allocation. In the previous case, the replenishment of empty containers at each port is controlled by a decision-maker and the containers are kept at independent servicing ports. Such an instance can be considered as a Vendor managed in- ventory (VMI) problem. In a VMI system, the supplier decides which retailer should be replenished at what time, and with what quantities of items. Then, an interesting problem is, whether the suppler can replenish all the retail- ers? We consider a replenishment problem where the supplier has only one vehicle and can replenish only one retailer per period using the vehicle, while different retailers need different periodical replenishments. We model this problem as a single item inventory replenishment routing problem between a single supplier and multiple retailers with direct delivery. Using Chinese Remainder Theorem, for the simple cases satisfying certain conditions, we can obtain the optimal simple routing by which the supplier can replenish each retailer periodically and avoid shortages. For the complicated cases, we present an algorithm to calculate one feasible routing that the supplier can use to replenish selected retailers on selected periods without shortages. With reference to our shopping in the supermarket, we always purchase a batch of units of a particular item. Usually, consumption is not instanta- neous, but lasts for several days. It seems that a part of inventory of the supermarket is shifted to our homes. Because we can step into the supermar- ket and purchase on our own initiative at any time, the supermarket cannot control our inventory. However, considering the instance where we cannot step in but only wait until the traveling salesman brings the goods, the sales- man can partially control our inventory. We discuss the problem from the point of view of the salesmen, and design a specific inventory routing for the salesman. That is, the salesman spends a certain amount of time peddling at certain locations. During this time span, the salesman waits for the arrival of customers’ demand.

    Research areas

  • Inventory control