Optimal Replenishment Policies and Profits for Two-Echelon Inventory Problems with Stochastic Demand
Journal Title: International Journal for Research in Applied Science and Engineering Technology (IJRASET) - Year 2015, Vol 3, Issue 2
Abstract
In this paper, a new mathematical model is developed to optimize replenishment policies and profits of a two-echelon distribution inventory system under demand uncertainty. The system consists of a factory warehouse at the upper echelon and a number of supermarkets at the lower echelon. The supermarkets face stochastic stationary demand where sales price and 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, shortage cost and sales price are combined with demand and inventory positions in order to generate the profit matrix corresponding to a given echelon. 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 profits are maximized 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 profits over the echelons.
Authors and Affiliations
Kizito Paul Mubiru
Keywords
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