A sensitivity analysis of solving joint replenishment problems using the RAND method under inaccurate holding cost estimates and demand forecasts

This paper presents a study of solving the joint replenishment problem (JRP) by using the RAND method, a heuristic approach that has been proven to find almost as good as optimal solutions, under uncertain customer demands and inaccurate unit holding cost estimation. The classical JRP deals with the issue of determining a replenishment policy that minimizes the total cost of replenishing multiple products from a single supplier. The total cost considered in the JRP consists of a major ordering cost independent of the number of items in the order, a minor ordering cost depending on the items in the order, and the holding cost. There have been many heuristic approaches proposed for solving the JRP. Most of the research work was done under the assumptions that the demand for each item type and the unit holding cost are known and constant. However, in the real world accurately forecasting customer demands and precisely estimating the unit holding cost are both difficult. Besides, the real values of the demands and the unit holding cost may change over the replenishment horizon. The present study addresses the issue of the uncertain demands and the unit holding cost to the JRP and investigates how misestimates of these demands and holding costs may influence the replenishment policy as determined by the famous JRP heuristic, the RAND method. 2007 Elsevier Ltd. All rights reserved.