A stochastic multi objective mathematical model to optimize a production and distribution system with stochastic demand and stochastic lead time

Production and distribution network (PDN) planning in multi-stage status is commonly complex. These conditions cause significant amount of uncertainty relating to demand and lead time. In this study, we introduce a PDN to deliver the products to customers in the least time and optimize the total cost of the network, simultaneously. The proposed network is four stage PDN including suppliers, producers, potential entrepots, retailers and customers with multi time period horizon with allowable shortage. A mixed integer programming model with minimizing total cost of the system and minimizing total delivery lead time is designed. We present a novel heuristic method called selective firefly algorithm (SFA) in order to solve several sized especially real world instances. In SFA, each firefly recognizes all better fireflies with more brightness and analyses its brightness change before moving, tacitly. Then, the firefly that makes best change is selected and initial firefly moves toward the selected firefly. Finally, the performance of the proposed algorithm is examined with solving several sized instances. The results indicate the adequate performance of the proposed algorithm.