An accelerated Benders decomposition algorithm for reliable facility location problems in multi-echelon networks

In this paper, we present an accelerated Benders decomposition algorithm for solving the multi-echelon reliable capacitated facility location problem (ME-RCFLP). The objective is a tradeoff between system reliability, and total investment and operational costs while the facilities can be “hardened” (Increase their capacity and decrease their probability of full and partial failure) with more cost. We allow the facilities to have different partial and full failure rates, and more than one facility may be assigned to a client (partial assignment). A new scenario-based formulation is proposed for the problem to effectively cover the outcomes of uncertainty and it is used to introduce an efficient Benders decomposition algorithms as well as a sample average approximation algorithm (SAA) for solving the ME-RCFLP. Computational results show the validity of the proposed model and the efficiency of the proposed solution methods in solving the problem.