THE MULTIITEM JOINT REPLENISHMENT PROBLEM WITH TRANSPORTATION AND CONTAINER EFFECTS

We address the problem of scheduling the delivery of multiple items fr om a single supplier to a manufacturer. The items are packaged into co ntainers, and the containers are shipped by truck. There is a fixed ch arge per truck shipment, and inventory holding costs are charged on en d-of-period inventory. We seek to minimize the sum of transportation a nd inventory costs. The problem is a combination of a bin-packing prob lem (due to the presence of containers and finite-capacity trucks) and a multi-item joint replenishment problem. We present a heuristic solu tion procedure which starts with the optimal solution of the problem i n which the integrality of the containers is relaxed. (A solution proc edure for this relaxed problem appears in BEN - KHEDER and YANO[2]. We develop a method to modify this solution to account for the integrali ty of containers. This modification scheme involves sequentially consi dering each item and optimally scheduling the fractional containers in the relaxed solution. To solve this single-item problem, we devise a procedure that accounts for the availability of ''free'' remaining cap acity of trucks that have been partially filled with other items. In a computational study, our heuristic is compared with a lower bound, wi th variations of our heuristic, and with simple rule-of-thumb policies . The results suggest that our heuristic performs very well, especiall y in problems where considering tradeoffs between inventory and transp ortation costs is important.