A solution method for the joint replenishment problem with correction factor

In this paper, we give a rather complete analysis of the joint replenishment problem (JRP) under constant demands and continuous time. We first investigate several methods for bounding the optimal cycle time. Next we show that under certain restrictions on the input data the standard JRP can be solved in polynomial time, implying that exact algorithms are practically feasible. Then we present a solution method for the JRP when a correction is made for empty replenishments. We show that the solutions obtained differ from the standard JRP when no correction is made in the cost function. The theoretical findings are corroborated by applying the proposed methods to a large set of experiments.