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.