Abstract
We analyze an infinite horizon discrete time inventory model with deterministic but non-stationary demand for a single product at a single stage. There is a finite cycle of vectors of characteristics of the environment (demand, fixed ordering cost, variable procurement cost, holding cost) which is repeated after a finite number of periods. Future cost is discounted. In general, minimization of the sum of discounted total cost over the cycle does not give the minimum of the sum of discounted total cost over the infinite horizon. We construct an algorithm for computing of an optimal strategy over the infinite horizon. It is based on a forward in time dynamic programming recursion.
Highlights
Standard finite horizon inventory models with deterministic but non-stationary demand
If demands and other characteristics of the environment that differ between periods exhibit some finite cycle, we can obtain a numeric solution of an infinite horizon inventory model
We develop an algorithm for computing of an optimal procurement strategy in this model that minimizes the sum of discounted total costs over the infinite horizon of the model
Summary
Standard finite horizon inventory models with deterministic but non-stationary demand (see, for example, [1]). For any optimal procurement strategy, inventories at the end of the last period are zero. The optimal procurement strategy should result from an infinite horizon model with discounting of cost in future periods. If demands and other characteristics of the environment that differ between periods exhibit some finite cycle, we can obtain a numeric solution of an infinite horizon inventory model. In this case, after a finite number of periods, the same finite cycle of characteristics of the environment is repeated (Stationary characteristics of the environment are a special case of this, with cycle length equal to one).
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