Most of the researches which use fuzzy set theory for tackling uncertainty or vagueness in a mathematical programming model, specifically fuzzy numbers, consider the expected value and convert the fuzzy model to crisp one. In some problems like portfolio selection problem in which the decision-maker must consider the risks of his decisions, expected return does not suffice and for this reason, other measures such as variance and Entropy are added to the model. The major objective of this research is to develop a conservative mathematical model which considers risk of return in supply chain decision-making. In this research, the new problem of production–distribution-pricing in a three-echelon supply chain is introduced and studied in which a number of new products are to be produced besides existing products and distributed to final retailers. The annual production capacity, unit production costs and demands of the new products are assumed to be fuzzy numbers. Making decisions on production, distribution and pricing, specifically for the new products, can be very risky. The major output of this research is providing a mathematical framework for considering risk of return. For this purpose, this research can be known one of the few studies in the field of supply chain which considers variance of the profit as well as its expected value. This model can be applied in push supply chains which distribute products to final customers via retailers. The obtained model is nonlinear and solved using optimization package. Numerical results show the expected performance of the developed model.
Chattinnawat et al. (Wed,) studied this question.