On a Basic Class of Multi-Item Inventory Problems

Abstract

The paper evaluates and compares classes of multi-item inventory problems, where joint order of several items may save a part of the setup cost. A cost ratio and simple decision rule are determined for joint versus individual orders in specified cases. The comparisons call for the necessity of a new policy for reorder point-triggered random output multi-item systems. This policy, the "random joint order policy," operates through the determination of a reorder range within which several items can be ordered. The existence of an optimum reorder range is proved, and a computational technique is demonstrated with the help of a machine-interference type queueing model. Under favorable conditions the results exhibited on the diagram of optimum reorder ranges are generally applicable. The random joint order policy model is especially suitable for computer controlled inventory systems.

A systematic literature review on the joint replenishment problem solutions: 2006-2015

“…On the stochastic demand models, there are two main replenishment policies: The can-order policy (COP), by Balintfy (1964), in which if any item reaches a must-order point, a replenishment order is made, and if the other items present inventory levels below a can-order point, they are included in the same order (Johansen & Melchiors, 2003;Balintfy, 1964;Khouja & Goyal, 2008). The periodic replenishment policy (PRP), by Atkins & Iyogun (1988), or (T, M) policy, considers a Poisson distributed demand, in which all products follow the same replenishment periodic interval T, and each one is replaced to a pre-determined inventory level M. Later, it has been considered that a set of products would follow the periodic review interval T, while other products that also should be replenished would follow a section of T (Atkins & Iyogun, 1988;Khouja & Goyal, 2008).…”

A simulation optimisation approach for inventory management decision support based on incomplete information

“…An often used stochastic model is the canorder system. Balintfy (1964) was the first to propose the use of this system. In such a system, whenever item i's inventory position drops to its must-order point s i or lower, it triggers a replenishment action that raises the item's level to its order-upto-level S i .…”

The stochastic joint replenishment problem: A new policy, analysis, and insights

“…This stream of research has begun with the earliest work on joint replenishment with stochastic demand by Balintfy [4], who introduced the continuous review (s, c, S) joint ordering policy-also called the can-order policy. The policy operates as follows.…”

“…SJRP is the determination of replenishment and stocking decisions for N different items to minimize the expected total ordering, holding, and shortage costs per unit time in the presence of random demands and ordering cost structures with firstorder interaction. The first-order-interaction structure for ordering costs is defined as the setting where there are (i) a common fixed cost associated with a replenishment order regardless of its composition and (ii) an item-specific fixed cost for each item that is included in the replenishment order [4,10]. The ordering cost structure presents an opportunity to exploit the economies of scale in replenishment by ordering items jointly.…”