Solving a Supply-Chain Management Problem Using a Bilevel Approach

Supply-chain management problems are common to most industries and they involve a hierarchy of subtasks, which must be coordinated well to arrive at an overall optimal solution. Such problems involve a hierarchy of decision-makers, each having its own objectives and constraints, but importantly requiring a coordination of their actions to make the overall supply chain process optimal from cost and quality considerations. In this paper, we consider a specific supply-chain management problem from a company, which involves two levels of coordination: (i) yearly strategic planning in which a decision on establishing an association of every destination point with a supply point must be made so as to minimize the yearly transportation cost, and (ii) weekly operational planning in which, given the association between a supply and a destination point, a decision on the preference of available transport carriers must be made for multiple objectives: minimization of transport cost and maximization of service quality and satisfaction of demand at each destination point. We propose a customized multi-objective bilevel evolutionary algorithm, which is computationally tractable. We then present results on state-level and ZIP-level accuracy (involving about 40,000 upper level variables) of destination points over the mainland USA. We compare our proposed method with current non-optimization based practices and report a considerable cost saving.