A Lower Bound for a JRP Obsolescence Model

The Joint Replenishment Problem (JRP) minimizes the total cost by coordinating the replenishment of multiple items. The complexity of the problem increases when the items are subject to obsolescence, meaning that they may undergo a sudden drop in demand at an uncertain time in the future. The present article describes an existing JRP model under obsolescence of the items and discusses an existing recursive optimization process that may require a high and time-consuming computational effort, particularly when the number of items is big. A strategy to overcome this shortcoming is proposed through the definition of a lower bound to use in place of the optimal solution. Some numerical results are presented in terms of both the costs and the running times obtained. At the end, some conclusions are summarized.