Integrated production and distribution in a milk supply chain under uncertainty with the Hurwicz criterion

In this paper, we propose a credibility-based fuzzy mathematical programming model for integrating the production and distribution in a milk supply chain under uncertainty. The proposed model is a mixed integer linear programming, which takes into account technological constraints and aims to maximize the total profit including the total costs such as production, storage, and distribution. To bring the model closer to real-world planning problems, the objective function coefficients (e.g. production cost, inventory holding and transport costs) and other parameters (e.g. demand, production capacity, and safety stock level) are all considered fuzzy numbers. In the uncertain environment, the most known criteria widely employed are optimistic and pessimistic value criterions. Both criteria present some deficiency. For the optimistic criterion, it suggests an audacious decision maker who is attracted by high payoffs (low cost), while for the pessimistic criterion, it suggests a conservative decision-maker who tries to make sure that in the case of an unfavorable outcome (loss), there is at least (in most) a known minimum payoff (maximum loss). The Hurwicz criterion is used to overcome these problems. By varying the value of θ, it can balance the optimistic and pessimistic levels of the decision makers. Moreover, the different property of the credibility measure is used to build the crisp equivalent model, which is a MILP model that can solve problems by using a commercial solver such as GAMS. Finally, numerical results are reported for a real case study to demonstrate the efficiency and applicability of the proposed model.