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Mathematical Problems in Engineering
Volume 2017, Article ID 4389064, 29 pages
Research Article

Optimization of Production-Distribution Problem in Supply Chain Management under Stochastic and Fuzzy Uncertainties

Department of Industrial Engineering, Kırıkkale University, 71451 Kırıkkale, Turkey

Correspondence should be addressed to Umit Sami Sakalli; rt.ude.ukk@illakass

Received 4 April 2017; Revised 4 July 2017; Accepted 12 July 2017; Published 17 October 2017

Academic Editor: Anna M. Gil-Lafuente

Copyright © 2017 Umit Sami Sakalli. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Production-Distribution Problem (PDP) in Supply Chain Management (SCM) is an important tactical decision. One of the challenges in this decision is the size and complexity of supply chain system (SCS). On the other side, a tactical operation is a mid-term plan for 6–12 months; therefore, it includes different types of uncertainties, which is the second challenge. In the literature, the uncertain parameters were modeled as stochastic or fuzzy. However, there are a few studies in the literature that handle stochastic and fuzzy uncertainties simultaneously in PDP. In this paper, the modeling and solution approaches of PDP which contain stochastic and fuzzy uncertainties simultaneously are investigated for a SCS that includes multiple suppliers, multiple products, multiple plants, multiple warehouses, multiple retailers, multiple transport paths, and multiple time periods, which, to the best of the author’s knowledge, is not handled in the literature. The PDP contains deterministic, fuzzy, fuzzy random, and random fuzzy parameters. To the best of the author’s knowledge, there is no study in the literature which considers all of them simultaneously in PDP. An analytic solution approach has been developed by using possibilistic programming and chance-constrained programming approaches. The proposed modeling and solution approaches are implemented in a numerical example. The solution has shown that the proposed approaches successfully handled uncertainties and produce robust solutions for PDP.