Abstract
This paper studies a multi-item dynamic lot size problem for perishable products where stock deterioration rates and inventory costs are age-dependent. We explore structural properties in an optimal solution under two cost structures and develop a dynamic programming algorithm to solve the problem in polynomial time when the number of products is fixed. We establish forecast horizon results that can help the operation manager to decide the precise forecast horizon in a rolling decision-making process. Finally, based on a detailed test bed of instance, we obtain useful managerial insights on the impact of deterioration rate and lifetime of products on the length of forecast horizon.
Highlights
In a multi-period, dynamic decision-making environment, forecast horizon is a period with the property that the data for periods beyond it are not required in order to determine the decisions of the first few periods
We conclude that (i) as the inventory deterioration rate increases, the length of forecast horizon decreases, remains invariant; (ii) as the lifetime of products increases, the length of forecast horizon increases, remains invariant; (iii) for a given deterioration rate, the length of forecast horizon is higher for higher values of joint setup costs; for a given lifetime of products, the length of forecast horizon is higher for higher values of joint setup costs, remains invariant
The following notion is used in our model: T: the problem horizon; i.e., the number of periods; N: total number of products; dtn: demand of product n in period t, 1 n N, 1 t T; Kt: joint setup cost when one or more products are ordered in period t, 1 t T; snt : individual setup cost when product n is ordered in period t, 1 n N, 1 t T; cnt : unit order cost of product n in period t, 1 n N, 1 t T; hnit: unit holding inventory cost of product n in period t, which is ordered in period i, 1 n
Summary
In a multi-period, dynamic decision-making environment, forecast horizon is a period with the property that the data for periods beyond it are not required in order to determine the decisions of the first few periods. The earliest study of forecast horizons in operations management is due to Wagner and Whitin [1], who analyze a dynamic lot sizing (DLS) problem in the presence of setup costs, holding cost, deterministic time-varying demands They demonstrate the optimality of Zero Inventory Property (ZIP) and use it to develop an efficient dynamic programming (DP) which solves the problem. In this paper we investigate forecast horizon in a multi-product DLS problem with agedependent stock deterioration and inventory cost function and joint ordering. Kim and Lee [46] study a dynamic inbound ordering and shipment scheduling problem for multiple products that are transported from a supplier to a warehouse by common freight containers They show their problem is NP-hard and present a heuristic algorithm that exploits the properties of an optimal solution.
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