Optimal design of cross docking supply chain networks with time-varying uncertain demands

This paper proposes an integrated network design model for a post-distribution cross-docking strategy, comprising multi product production facilities with shared production resources, capacitated cross docks with setup cost and customer zones with time windows constraints. The model is dynamic in terms of time-varying uncertain demands, whereas uncertainty is expressed with scenario approach and contains both ‘‘wait-and-see’’ and ‘‘here-and-now’’ decisions. Inventory is just permitted in plants and over several time periods. The objective of the model is to minimize the sum of the fixed location costs for establishing cross docking centers and inventory related costs across the supply chain while ensuring that the limited service rate of cross docking centers and production facilities, and also the lead time requirements of customers are not violated. The problem is formulated as a mixed-integer linear programming problem and solved to global optimality using CPLEX. Due to the difficulty of obtaining the optimum solution in medium and large-scale problems, two heuristics that generate globally feasible, near optimal solution, Imperialistic competitive algorithm (ICA) and simulated annealing (SA), are also proposed as heuristics. We find that CPLEX is not able to solve some of the sets to optimality and turned out to run out of memory, but it performs quite well for small test sets, as compared with the two heuristics. While SA is a faster heuristic method in terms of runtime, ICA generates better results on average, but in more time.