Joint replenishment problem under continuous unit cost change

The joint replenishment problem determines order quantities and the grouping of products replenished from the same supplier. The objective is to minimize the ordering and holding cost of the purchasing firm. The problem is frequently solved assuming products with constant unit cost. An efficient algorithm for solving the joint replenishment problem for products that may be experiencing unit cost increase or decrease is developed. The proposed algorithm is tested on a sample of randomly generated problems containing up to 25 items and it is shown that it identifies the global optimal solutions for most of these problems. For the worst case where the algorithm fails to identify the global optimal solution, the solution it provides had a total cost 0.007% above the global minimum.