Companies are frequently confronted with the need to order different types of items from a single supplier or to manufacture the items in a production line. Indeed, coordinated ordering of multiple items may lead to important savings whenever a family of items can be ordered from a common supplier, produced in a common facility, or use a common mode of transportation. The Joint Replenishment Problem (JRP) tackles the coordinated replenishment of multiple items by minimizing the total cost, composed of ordering (or setup) costs and holding costs, while satisfying the demand. On the other hand, when items are subject to obsolescence, they may face an abrupt decline in demand as they are no longer needed. This decline can be caused by reasons such as rapid advancements in technology, going out of fashion, or ceasing to be economically viable. The present article develops an extension of the JRP where the items may suddenly become obsolete during an infinite planning horizon. The point at which an item becomes obsolete is uncertain. The lifetimes of the items are assumed to follow independent negative exponential distributions. A model is proposed by using the total expected discounted cost as the minimization criterion. The time value of money is considered through an appropriate discount rate. Extensive tests were performed to assess the impact of obsolescence rates and discount rates on the ordering policies. The progressive increase of the obsolescence rates determines smaller periods between successive replenishments, while the progressive increase of the discount rate determines smaller lot sizes.

Real life inventory lot sizing problems are frequently challenged with the need to order different types of items within the same batch. The Joint Replenishment Problem (JRP) addresses this setting of coordinated ordering by minimizing the total cost, composed of ordering (or setup) costs and holding costs, while satisfying the demand. The complexity of this problem increases when some or all item types are prone to obsolescence. In fact, the items may experience an abrupt decline in demand because they are no longer needed, due to rapid advancements in technology, going out of fashion, or ceasing to be economically viable. This article proposes an extension of the Joint Replenishment Problem (JRP) where the items may suddenly become obsolete at some time in the future. The model assumes constant demand and the items’ lifetimes follow independent negative exponential distributions. The optimization process considers the time value of money by using the expected discounted total cost as the minimization criterion. The proposed model was applied to some test cases, and sensitivity analyses were performed, in order to assess the impact of obsolescence on the ordering policy. The increase in the obsolescence risk, through the progressive increase of the obsolescence rates of the item types, determines smaller lot sizes on the ordering policy. The increase in the discount rate causes smaller quantities to be ordered as well.