Modeling and solving a three-stage fixed charge transportation problem considering stochastic demand and price

This paper considers a three-stage fixed charge transportation problem regarding stochastic demand and price. The objective of the problem is to maximize the profit for supplying demands. Three kinds of costs are presented here: variable costs that are related to amount of transportation cost between a source and a destination. Fixed charge exists whenever there is a transfer from a source to a destination, and finally, shortage cost that incurs when the manufacturer does not have enough products for supplying customer’s demand. The model is formulated as a mixed integer programming problem and is solved using a multicriteria scenario based solution approach to find the optimal solution. Mean, standard deviation, and coefficient of variation are compared as the acceptable criteria to decide about the best solution.