Abstract
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In this paper, a new mathematical model is developed to optimize replenishment policies and inventory costs of a two-echelon supply chain system of kerosene product under demand uncertainty. The system consists of a fuel depot at the upper echelon and four petrol stations at the lower echelon. The petrol stations face stochastic stationary demand where inventory replenishment periods are uniformly fixed over the echelons. Adopting a Markov decision process approach, the states of a Markov chain represent possible states of demand for the inventory item. The replenishment cost, holding cost and shortage costs are combined with demand and inventory positions in order to generate the inventory cost matrix over the echelons. The matrix represents the long run measure of performance for the decision problem. The objective is to determine in each echelon of the planning horizon an optimal replenishment policy so that the long run inventory costs are minimized for a given state of demand. Using weekly equal intervals, the decisions of when to replenish additional units are made using dynamic programming over a finite period planning horizon. A numerical example demonstrates the existence of an optimal state-dependent replenishment policy and inventory costs over the echelons. DOI:10.12660/joscmv8n2p67-76 URL: http://dx.doi.org/10.12660/joscmv8n2p67-76