Decentralized supply chain management is found to be significantly relevant in today's competitive markets. Production and distribution planning is posed as an important optimization problem in supply chain networks. Here, we propose a multi-period decentralized supply chain network model with uncertainty. The imprecision related to uncertain parameters like demand and price of the final product is appropriated with stochastic and fuzzy numbers. We provide mathematical formulation of the problem as a bi-level mixed integer linear programming model. Due to problem's convolution, a structure to solve is developed that incorporates a novel heuristic algorithm based on Kth-best algorithm, fuzzy approach and chance constraint approach. Ultimately, a numerical example is constructed and worked through to demonstrate applicability of the optimization model. A sensitivity analysis is also made.

In this study, a planning problem for multi-time, multi-product, multiechelon Supply Chains (SCs) is studied and the implications of formulating a tri-level model to integrate Procurement, Production, and Distribution (PPD) while maintaining the existing hierarchy in the decision process are discussed. In our model, there were three di erent decision makers controlling the PPD processes in the absence of cooperation because of di erent optimization strategies. First, a hierarchical Tri-Level Programming (TLP) model was developed to deal with decentralized SC problems. Then, an algorithm was formulated to solve the proposed model. A numerical sample was investigated to scrutinize applicability of the optimization model and the proposed algorithm. In order to evaluate the application of the model and the proposed algorithm, 10 sets of small and large problems were randomly generated and tested. The experimental results showed that our proposed fuzzy-stochastic Simulation-based Hierarchical Interactive Particle Swarm Optimization (Sim-HIPSO) performed well in nding good approximate solutions within reasonable computational times.