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| Stochastic Inventory Model for the Global Supply Chain Problem |
Kizito Paul Mubiru, Senfuka Christopher, Maureen N Ssempijja
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Abstract:
We consider a single-item three-echelon global supply chain problem; consisting of manufacturing plants in worldwide locations. The item marketers consist of major distributors, wholesalers, and retailers at the respective locations.. Associated with each echelon at the respective location is stochastic stationary demand of item; where inventory replenishment periods are uniformly fixed over the echelons. Considering on-hand inventory positions of item, we determine the total inventory cost matrix for echelons; representing the long run measure of performance or the markov decision process problem. We formulate a finite-state markov decision process model where states of a markov chain represent possible states of demand. The objective is to determine over each echelon of the selected location; an optimal inventory replenishment policy of item so that the long run inventory costs are minimized for the given state of demand. The decisions of replenishing versus not replenishing additional units of item are made using dynamic programming over a finite period planning horizon. We present a numerical example for illustrative purposes. The model demonstrates the existence of an optimal state-dependent inventory replenishment policy and costs of item over the echelons and locations of the global supply chain network.
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