A Robust Flexible Stochastic Mathematical Model for Logistics Coordination in a Two-echelon Supply Chain

Abstract

Uncertainty approaches have been studied by many scholars. What makes them more interesting is the combination of a few approaches in order to make stronger and more flexible mathematical models. In this paper, we have proposed a robust flexible stochastic mathematical model which combines the robust optimization techniques, fuzzy soft constraint approach, and scenario-based stochastic approach. The created approach can provide a framework for better and simultaneous tackling different types of uncertainties in mathematical models. We have embedded the given general model into a bi-level supply chain problem, called location-inventory-routing problem. In this problem, we have considered a two-echelon supply chain consisting of some warehouses in the first echelon as leader and several retailers in the second echelon as follower. The supply chain tries to distribute a perishable item from the central warehouses to the retailers. The major uncertain parameters are demand of the retailers as well as some supply chain operational costs. The developed approach considers two different attitudes to uncertainty by the players in the game. We have employed the general fuzzy measures to implement the pessimistic-optimistic attitude of decision-makers. Furthermore, scenario-based robust programming techniques are utilized. A combination of fuzzy goal programming and multi-choice goal programming techniques are customized in order to solve the bi-level problem. A number of numerical samples with different sizes are solved and the results are analyzed. The results show that by increasing the pessimistic-optimistic attitude parameter of the leader, the leader's costs increases while by increasing the pessimistic-optimistic attitude parameter of the follower, the follower's total cost partially decreases.