Inventory policies for a make‐to‐order system with a perishable component and fixed ordering cost

Abstract

Abstract:We consider a make-to-order production system where two major components, one nonperishable (referred to as part 1) and one perishable (part 2), are needed to fulfill a customer order. In each period, replenishment decisions for both parts need to be made jointly before demand is realized and a fixed ordering cost is incurred for the nonperishable part. We show that a simple (s n , S 1 n , S 2 n ) policy is optimal. Under this policy, S 2 n along with the number of backorders at the beginning of a period if any and the availability of the nonperishable part (part 1) determines the optimal order quantity of the perishable part (part 2), while (s n , S 1 n ) guide when and how much of part 1 to order at each state. Numerical study demonstrates that the benefits of using the joint replenishment policy can be substantial, especially when the unit costs are high and/or the profit margin is low.

Inventory models for managing deteriorating products: a literature review

“…With respect to the inventory models with uncertain demand and shortages, nearly all of the authors assumed that all of the excess demand during the stock-out period become either lost sales [8, 51, 66, 68, 70, 73, 90, 98, 272, 273, 275, 276, 278, 281, 282, 288-290, 294, 296-300, 302, 303, 306, 309-311, 313, 316, 320-322, 326, 332, 335, 337-340], or shortages that are fully backlogged [8,35,112,278,284,286,287,295,297,308,315,319,321,323,325,329,341,343,347]. However, some models with uncertain demand consider a partial backlogging rate: [305,330,331,333] assume that a fixed fraction of shortages are backlogged while [328,342] assume a waiting time function for unmet demand.…”

“…Although in most inventory systems the assumption of a single item is not real, very few studies have been found in the literature dealing with multi-item inventory control compared to single-item models. Two or more items in combination with shortages are taken into account in [34,35,70,99,101,102,105,123,155,245,279,284,292,296,299,311,315,341]. Inventory models considering an optimal price decision and multiple items can be found in [62,223].…”

“…In some mathematical models with stochastic demand, the inventory is controlled explicitly with a periodic review system [8,66,273,274,276,279,280,282,284,287,289,292,293,296,300,303,320,321,324,330,339], while in others, it is controlled with a continuous review system [272,278,290,297,304,306,308,309,311,312,316,323,332,335,336,338,341,[343][344][345][346]. On one hand, among items monitored continuously, [272,306,311,312,323,332,335,…”

“…On the other hand, among periodic inventory systems, [8,276,282,284,293,300,330,339] study the determination of inventory policies myopically, that is, at the beginning of each given period, decisions are only made upon replenishment (one period at a time). From these papers: [322] uses a (s, S) policy, i.e., an order is placed to raise the inventory toS when the inventory level is less than, or equal to, the reorder point s; [276,305,320] apply a base-stock policy of level S in which the total inventory level at the beginning of each period is always raised to S; [287,288] suggest a stock-level dependent ordering policy (s, S, q min , Q max ), which is a (s, S) policy with the order quantity being restricted between q min andQ max ; and [274,319] investigate a class of proportional balancing (PB) policy that balances a proportion of expected marginal costs.…”

Shelf Life Extending Packaging, Inventory Control and Grocery Retailing

“…Frank et al. (2009) considered an assembly system in which one product has a finite lifetime and the other is nonperishable. Zhou et al.…”