A multi-reliability facility location problem

In this paper, we considered a fixed charge facility location with multiple reliability problems. Specifically, a supply chain consisting of a single product set of candidate distribution centres, and set of demand points. Distribution centres are prone to failure; therefore, each demand point must be assigned to both primary and secondary facilities. Besides, at each candidate site, different facility reliability levels can be defined. Each reliability level has a different failure rate and is associated with a different fixed cost. We formulated the model as a large-scale linear integer program. In order for the solution procedure to be achievable, the model complexity was reduced by adding redundant constraints. This resulted in a size reduction up to 98.1%. Finally, lower and upper bounds on the optimal solution were developed using the Lagrangian relaxation procedure. The results confirmed that the solution was 1% within the optimal solution.