On the retention of finished goods inventory when reorder-occurrence is uncertain

Finished goods inventory may accumulate for a variety of reasons in the production of low-demand or slow-moving items. In this article a simple model is developed and some results are presented to aid in making inventory retention decisions when there exists uncertainty about whether reorders for a slow-moving item will be received in the future. In formulating the model, it is assumed that some excess inventory remains after filling a customer order and that a single reorder for the item is possible. The problem is to determine how long to retain the inventory before disposing of it. The relevant expected costs of retaining some quantity of inventory for a period of time consists of two types: (1) the inventory carrying cost less the salvage value from disposal; and (2) the future production cost incurred due to premature disposal. Using conventional optimization, a relationship for finding the optimal retention period is derived and conditions are identified that ensure that the optimal retention period can be obtained directly from the relationship. To determine the optimal retention period, probability distributions are required for the interarrival time until the reorder occurs and for the reorder quantity. While it seems logical to assume that each item would have its own distributions, this argument leads to a specification problem since the data needed to establish distributions for individual items will generally not be available for slow-moving items. One approach used to overcome this problem in practice is to combine data for a selected group of items and use the combined data to obtain distributions useful for any or all of the items in the group. An example illustrating this approach is provided.