presenting a joint replenishment-location model under all-units discount and solving by genetic algorithm and harmony search algorithm

In this paper a model is propose for joint replenishment and locations distribution centers (dcs) of a distribution system that is responsible for ordering and dispatching shipments of a single product to dcs. the warehouse spaces dcs are limited and these can determine amount of requirement product by considering proposed discount. the propose model is develop to minimize total costs consists of locating, ordering, holding and purchasing under condition all-units discount. in this model number and location of dcs, joint replenishment frequencies and optimum order quantity of each dc are defined. to solve joint replenishment problem (jrp) determining optimal limits upper and lower replenishment cycle time t is very important. for determining this limits we use quantity discount rand algorithm (qd-rand). to use this method need to determine the location each of dcs. therefore, first we consider the limits between a very small amount and 2 then the model solved by genetic algorithm (ga). after obtaining the optimal upper and lower replenishment cycle time t, the model will be resolved by harmony search algorithm (hsa) and ga. the parameters of all algorithms are first calibrated by means of the response surface methodology (rsm). the comparison results based on different problem sizes are in favor of hs.