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| The Dynamic Production/Inventory Lot sizing Problem with Stochastic Demand |
Kizito P Mubiru, Senfuka Christopher, Ssempijja Maureen
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Abstract:
The paper addresses the multi-period single-item production-inventory lot sizing problem where demand is stochastic and non-stationary. Over the entire planning horizon, the inventory replenishment periods are uniformly fixed and considering inventory positions of the product, we formulate a finite state Markov decision process model where states of a Markov chain represent possible states of demand for the product. The objective is to determine for each period of the production -inventory problem an optimal lot sizing policy so that the long run production-inventory costs are minimized for the given state of demand. The decision of whether or not to produce additional inventory units is made using dynamic programming over a finite period planning horizon. The approach demonstrates the existence of an optimal state dependent production lot size (PLS) and produces an optimal lot sizing policy as well as the corresponding total production and inventory costs.
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