A modified firefly algorithm for optimizing a multi stage supply chain network with stochastic demand and fuzzy production capacity

Production-distribution network (PDN) design is among complex problems with dynamic relationships that cause substantial amount of uncertainty including customers' demands, production capacity and others. This paper addresses a multi stage production distribution planning (PDP) problem with multi suppliers, producers, potential entrepots, potential retailers and inland and outland customers under uncertain environment. A mixed integer linear programming (MILP) model is presented to describe the purpose problem for optimizing the integrated total cost of the system. The proposed model considers operational risks involving uncertainties related to producers' capacity and customers' demand with applying probability distribution and fuzzy set theory. Commercial software cannot solve large sized instances in a reasonable run time. So, we presented a novel heuristic based on firefly algorithm (FA) called selective firefly algorithm (SFA) to solve the large sized problems. In the proposed SFA, each firefly identifies all fireflies with more brightness and evaluates its brightness change before moving, implicitly. Afterwards, the firefly that makes the best change is selected and initial firefly moves toward the selected firefly. Several numerical examples in both small and large sizes are applied to demonstrate the performance of the proposed heuristic.