A genetic algorithm for a joint replenishment problem with resource and shipment constraints and defective items

A joint replenishment problem (JRP) is presented to determine the optimal reordering policy for multiple items with defective quantity and several restrictions such as shipment constraint, budget constraint, and transportation capacity constraint. The objective is to minimize the total expected cost per unit time. A two-dimensional genetic algorithm (GA) is provided to determine an optimal family cycle length and the reorder frequencies. A numerical example is presented and the results are discussed including the effect of defective items on the ordering policy. Extensive computational experiments are performed to test the performance of the GA. The JRP was also solved by a differential evolution (DE) algorithm and the results obtained from DE were compared with those obtained from GA.