Joint Location-inventory Problem With Economies And Diseconomies Of Scale In Facility Operating Cost

Supply chain network design can help enterprises reduce costs and improve efficiency,and thereby bring sustainable competitive advantage.Problems of this kind have been studied extensively.In the literature,the total cost usually includes location cost,transportation cost,inventory holding cost,and other relevant facility operating costs.The facility operating cost is generally assumed to be either a fixed cost or a linear function of the volume of allocated demand.Some works assume the facility operating cost as a concave function of demand volume with decreasing marginal cost due to economies of scale.However,practical evidence suggests that when the volume of allocated demand exceeds a certain level,the marginal operating cost may increase due to reasons such as facility congestion,overtime,limited management capability,and over-utilization of resources,leading to a convex cost function.Therefore,it is necessary to study supply chain network design with general facility operating costs.This thesis studies a location-inventory problem,which jointly optimizes the location and inventory decisions of distribution centers(DCs),and the allocation of retailers with uncertain demand to DCs.In this thesis,we capture the facility operating cost as a general function of the volume of allocated demand,which is concave first due to economies of scale and then convex due to diseconomies of scale.This problem is formulated as a set-covering model and a column generation(CG)algorithm is proposed to solve its linear relaxation.The corresponding pricing problem has nice structural properties and can be solved efficiently by a branch-and-bound(B&B)method.Extensive numerical studies are conducted based on randomly generated instances with two types of inverse S-shaped facility operating cost functions.The results show that all the instances with retailer size less than 100 can be solved within 20 minutes on average,which validate the effectiveness of the proposed algorithm.Sensitivity analysis on economic points of facility operating cost function indicates that the number of open DCs is nonincreasing with the increase of the economic point.Furthermore,sensitivity analysis is carried out for various cost weight factors to demonstrate the impacts of different cost components on the network design decisions in this problem.