From Wagner-Whitin's dynamic lot size model towards zero inventory

Abstract

This article discusses the interface between zero inventory (ZI) and the dynamic lot size problem. The conventional Wagner-Whitin dynamic lot size model shows a good ffi computational e ciency when obtaining the optimal lot-sizing policy, but it ignores reduction of lot size and total cost. The 'zero inventory' philosophy strives for the goals of zero inventory at the end of each period and minimum total cost. The setup cost is fixed in the Wagner-Whitin model, but is considered as a parameter in zero inventory (ZI) philosophy: in general, the setup cost is treated as a policy variable in ZI. Zangwill examined the case of stationary setup cost reduction, but did not discuss the case of nonstationary setup cost reduction. This paper presents a new expression for total setup cost and total holding cost for the Wagner-Whitin model. By adopting this new expression, we obtain a sufficient and necessary con dition such that ZI is the optimal policy in the Wagner-Whitin model. Regardless of whether the setup cost reduction is stationary or nonstationary, the total setup cost reduction over all periods increases when the amount of setup cost reduction increases. This result suggests that the optimal policy for the Wagner-Whitin model is close to ZI. Most presentations of ZI have been descriptive with very few mathematical models. This paper seeks to demonstrate by a mathematical approach that reducing the setup cost can make the Wagner-Whitin model approach ZI.