Document Type : Original Article


1 Professor, Allameh Tabatabaei University.

2 M.Sc., Faculty of Management and Accounting, Islamic Azad University, Qazvin.

3 M.Sc., Islamic Azad University, Qazvin Branch.


The aim of this paper is to develop a mixed-integer non-linear programming (MINLP) for an integrated production–distribution problem in a three-level supply chain, consisting of multiple manufacturers, multiple distributors and multiple consumers at each level. In the particular case of this problem, customer’s demand and transportation costs are uncertain and robust optimization approach is utilized. First, a deterministic MINLP model is designed for this supply chain network. Then, the robust counterpart of the proposed model is presented by using the recent extensions in robust optimization theory. Finally, a numerical example with different scenarios and uncertainty levels is proposed, and their results are discussed.


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