A new variable production scheduling strategy for deteriorating items with time-varying demand and partial lost sale

Recently, Wee and Wang (Comput. Oper. Res. 26 (1999) 237) modeled a production-inventory system for deteriorating items with time-varying demands and completely backlogged shortages; we now present an extended cost model that relaxes the assumption of completely backlogged shortages by permitting part of the backlogged shortages to turn into lost sales-which is assumed to be a function of currently backlogged amount. Wee and Wang (Comput. Oper. Res. 26 (1999) 237) constructed production schedules for this system using the traditional scheduling strategy in which each cycle starts with replenishment and ends with shortages. We now consider an alternative scheduling strategy in which each cycle of a schedule starts with a period of shortages, then followed by continuous replenishment. By examining the profit performance of the two scheduling strategies (i.e., "start with replenishment" versus "start with shortages"), we show that our alternative strategy produces schedules with superior cost and profit values. Scope and purpose We consider an inventory item that deteriorates at a constant rate but its demand rate varies through time over a given finite planning horizon. For such an item, Wee and Wang (Comput. Oper. Res. 26 (1999) 2377) recently presented a procedure for determining the optimal "production schedule" (i.e., specifying the number of production runs and the timing and size of each run). Our paper extends Wee and Wang's (Comput. Oper. Res. 26 (1999) 237) work in two directions. Firstly, for an item whose shortages can be backlogged, the traditional strategy of constructing a finite-horizon production schedule starts each cycle by building up (positive) inventory and ends the cycle by clearing remaining backlogs. In this paper, we compare this traditional strategy with the alternative strategy of starting each cycle by accumulating backlogs, followed by inventory buildup via production and ending with depletion of positive inventory. Secondly, we generalize Wee and Wang's (Comput. Oper. Res. 26 (1999) 237) assumption of completely backlogged shortages by modeling the situation in which some backlogged shortages can turn into lost sales. This matches much better many realistic retail situations in which some but nor all customers will wait for backlogged items. Our paper presents procedures for implementing these two extensions, and our numerical examples demonstrate that these procedures can lead to more profitable production schedules. © 2003 Elsevier Science Ltd. All rights reserved.