A joint replenishment problem considering multiple trucks with shipment and resource constraints

A joint replenishment problem (JRP) is presented to determine the optimal reordering policy for multi-items with a percentage of defective items. This JRP also has several constraints, such as shipment constraint, budget constraint, and transportation capacity constraint. At the meantime, multiple trucks, each with a fixed transportation cost, are considered and also order quantities of restricted items are not shared among the trucks during the shipment. 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. Extensive computational experiments are performed to test the performance of the GA. The JRP is also solved by using an evolutionary algorithm (EA) and the results obtained from GA and EA are compared.