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| Stochastic Joint Replenishment Model For The Petroleum Supply Chain |
Kizito P. Mubiru, Christopher Senfuka, Maureen N. Ssempijja
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Abstract:
In this paper, a stochastic two-echelon supply chain model is proposed for petroleum products; consisting of a fuel depot, petrol stations and end customers. The petrol stations face stochastic stationary demand; where inventory replenishment periods are uniformly fixed over the echelons. A finite state Markov decision model is formulated where states of a Markov chain represent possible states of demand for kerosene and diesel products. The inventory cost matrix is determined for each petroleum product by multiplying the unit (replenishment, holding and shortage costs) by the demand and inventory positions of products. The objective is to determine over 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 whether to replenish or not replenish additional fuel are made using dynamic programming over a finite period planning horizon. Furthermore, use of the model is tested on a real case extracted from Oilcom fuel depot with petrol stations in Kampala, Uganda. The model demonstrates the existence of an optimal state-dependent replenishment policy and inventory costs for kerosene and diesel products in managing the fuel supply chain.
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