A Stochastic Vendor Managed Inventory Problem and Its Variations
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We analyze the problem of distributing units of a product, by a capacitated vehicle, from one storage location (depot) to multiple retailers. The demand processes at the retailers are stochastic and time-dependent. Based on current inventory information, the decision maker decides how many units of the product to deposit at the current retailer, or pick up at the depot, and which location to visit next. We refer to this problem as the stochastic vendor managed inventory (SVMI) problem. In the Markov decision process model of the SVMI problem, we show how a retailer continues to be the vehicle's optimal destination as inventory levels of the retailers vary. Furthermore, an optimal inventory action is shown to have monotone relations with the inventory levels. The multi-period SVMI problem and the infinite horizon (periodic) SVMI problem are analyzed. Additionally, we develop three suboptimal solution procedures, complete a numerical study, and present a case study, which involves a distribution problem at the Coca-Cola Enterprises, Inc. We consider four variations of the SVMI problem, which differ in the available state information and/or the vehicle routing procedure. Analytically, we compare the optimal expected total rewards for the SVMI problem and its variations. Our computational experience suggests a complementary relationship between the quality of state information and the size of the set of retailers that the vehicle can visit.