An optimal solution technique for the joint replenishment problem with storage and transport capacities and budget constraints

The joint replenishment problem, which is concerned with the problem of coordinating the replenishment of a group of items that may be ordered jointly, has been studied extensively and many heuristic solution procedures have been presented in the literature. To obtain the minimum of the total cost, the main complexity lies in determining the appropriate lower bound of the basic cycle time. Also there is a lack of a global optimal solution technique of the problem. This paper presents its extended model to include some practical issues and develops a simple procedure to calculate the appropriate lower bound of the basic cycle time. By a comparative study of a numerical example, it demonstrates the inabilities of the available lower bound formulae in the literature. It also develops a generalized global optimal solution algorithm of the extended model and illustrates this with a numerical example. Then a comparative study of the results of seven numerical examples is carried out to highlight the global optimality of the solution technique.