Stochastic dynamic lot-sizing model with shortage and distribution costs: application in a single-item manufacturing company

Abstract

In this work, a dynamic lot-size model with probabilistic normally distributed demand is presented. The model is an extension of the stochastic version of the Wagner-Whitin dynamic lot-size model. The Wagner-Whitin model provides an algorithm for minimizing the production and inventory cost of an item over N time periods. The cost function of the model presented in this paper comprises of fixed set-up cost, variable production cost, holding cost, shortage cost as well as distribution cost. Production of the item is considered to be instantaneous with fixed set-up cost and per unit production cost in any given period. The model presented was illustrated with data collected from a single-item production company, Boltsman Nig. Ltd. With a normally distributed demand for the item and with set-up, production, holding, shortage and distribution costs, an optimal lot-sizing plan that satisfies the demand over a 12-period time interval at minimum total cost was desired. The EXCEL software was used to analyze the data using the backward dynamic programming algorithm. The optimal production, inventory and distribution plan was obtained which satisfied expected demand while minimizing production, inventory and distribution costs in some periods. Also it minimized shortage cost in periods where the expected demands cannot be met. The optimal minimum cost policy of ₦43,622,570.00 was obtained.

Keywords: Dynamic programming, lot sizing, shortage cost, probabilistic demand, inventory cost.