An approximate scheduling policy for joint replenishment problem with transport capacity constraint

Abstract

The joint replenishment problem (JRP) has been studied extensively, and many techniques have been applied to find the approximate solution of the minimum total costs and to determine the appropriate basic cycle time. In practice, joint replenishment is always limited by transport capacity. But few papers so far have incorporated the transport capacity constraint (TCC) with the optimal delivery schedule. In this article, the classical JRP model was extended to include TCC, and a model of JRP with TCC was developed. The model of JRP with TCC involves binary decision variables which need to be solved by binary integer programming (BIP). Since the available solution techniques of JRP cannot deal with the JRP with TCC, two algorithms have been proposed to solve this problem. One is the existing RAND method combined with the BIP algorithm (RAND + BIP) and the other is the modified RAND method for constraint problems combined with the BIP algorithm (MC_RAND + BIP). A numerical example solved by two algorithms demonstrates the approximate joint scheduling policy. Computational experiments with 1800 test problems were successfully performed by two algorithms and the results are compared. The MC_RAND + BIP method outperforms RAND + BIP on solution quality as well as running time for the large-size problems. The statistical estimating optimization technique was applied to evaluate the MC_RAND + BIP approximate solution quality, and the estimating optimal values of 18 groups of test problems all lie within the individual interval with 99% confidence. It indicates that the proposed algorithm can find the statistical optimal solution.