Abstract
We present an algorithm for solving an infinite horizon discrete time lot sizing problem with deterministic non-stationary demand and discounting of future cost. Besides non-negativity and finite supremum over infinite horizon, no restrictions are placed on single period demands. (In particular, they need not follow any cyclical pattern). Variable procurement cost, fixed ordering cost, and holding cost can be different in different periods. The algorithm uses forward induction and its essence lies in the use of critical periods. Period j following t is the critical period of t if satisfying demands in any subset of the set of periods between t and j, including j and excluding t, from an order in t is not more expensive than satisfying it from an order in a later period and j is the last period with this property. When deciding whether to place an order in period t, all demands from t to its critical period are taken into account.
Highlights
Firms’ activities are dynamic in their nature and conditions for them can change
The use of finite horizon discrete time models of dynamic lot sizing with deterministic non-stationary demand should be supplemented by the use of infinite horizon discrete time models of dynamic lot sizing with deterministic non-stationary demand, keeping the usual assumptions of the former, namely periodic review of Correspondence: milan.horniacek@fses.uniba.sk Institute of Economics, Faculty of Social and Economic Sciences, Comenius University in Bratislava, Mlynské luhy 4, SK-82105 Bratislava, Slovak Republic inventory, zero lead time, impossibility of backorders
In the present paper we develop an algorithm for computing optimal inventory strategy for a general infinite horizon lot sizing with deterministic demand
Summary
Dynamic models for optimization of inventories are needed This requirement is satisfied (within the class of deterministic models) by dynamic discrete time lot sizing models with deterministic non-stationary demand. (See ([3], Chapter 4) for their description) Infinite horizon discrete time models are more appropriate for analysis and optimization of their activities, including inventory management. The use of finite horizon discrete time models of dynamic lot sizing with deterministic non-stationary demand should be supplemented by the use of infinite horizon discrete time models of dynamic lot sizing with deterministic non-stationary demand, keeping the usual assumptions of the former, namely periodic review of
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