A Study On The Joint Replenishment Problem With Quantity Discount And Resource Constraints In The Fuzzy Environment

Inventory control is important for the normal operation of enterprise. Reasonableinventory management can enhance enterprise‘s competitiveness. Companies always havemuch variety of items to purchase from a single supplier or a same place when managinginventory. Joint replenishment strategy can reduce the annual ordering times, get morechance of price discount, and decrease the cost of transportation. This strategy is aneffective way for cost savings. This thesis discussed several practical joint replenishmentmodels and the novel algorithms for the models.Firstly, Joint Replenishment Problem (JRP) had been proved to be a typical NP-hardproblem and the key is to find an algorithm that can solve this problem efficiently andeffectively. Therefore, a differential evolution (DE) algorithm is presented to overcome theshortcomings of existing JRP methods. A modified algorithm is designed and theperformance of improved algorithm is tested by three classic testing functions. Secondly,under certainty environment, we study a joint replenishment problem without restrictionswhich has the quantity discount in static demand and dynamic demand respectively. Then,we expand the problem with resource constraints. We use the differential evolution (DE)algorithm and the genetic algorithm to solve the problem and compare their results toprove the effectiveness and advantage of the differential evolution algorithm. Thirdly,under uncertainty environment, we study a joint replenishment problem with resourceconstraints which has the quantity discount in static demand and dynamic demandrespectively. We also prove that the significance of the fuzzy decision using in actualcompany application. Then we discuss the effect of fuzzy set on decision making andsuggest that enterprises should exploit all the information and estimate the boundary offuzzy set reasonably and scientifically.