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Mathematical Problems in Engineering
Volume 2011, Article ID 406398, 14 pages
Research Article

A Multiobjective Stochastic Production-Distribution Planning Problem in an Uncertain Environment Considering Risk and Workers Productivity

1Department of Industrial Engineering, Iran University of Science and Technology, 16846113114 Tehran, Iran
2LIESP-DISP Laboratory, INSA-Lyon, Université de Lyon, 69621 Lyon, France

Received 29 December 2010; Accepted 21 February 2011

Academic Editor: Cristian Toma

Copyright © 2011 S. M. J. Mirzapour Al-e-Hashem et al. 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.


A multi-objective two stage stochastic programming model is proposed to deal with a multi-period multi-product multi-site production-distribution planning problem for a midterm planning horizon. The presented model involves majority of supply chain cost parameters such as transportation cost, inventory holding cost, shortage cost, production cost. Moreover some respects as lead time, outsourcing, employment, dismissal, workers productivity and training are considered. Due to the uncertain nature of the supply chain, it is assumed that cost parameters and demand fluctuations are random variables and follow from a pre-defined probability distribution. To develop a robust stochastic model, an additional objective functions is added to the traditional production-distribution-planning problem. So, our multi-objective model includes (i) the minimization of the expected total cost of supply chain, (ii) the minimization of the variance of the total cost of supply chain and (iii) the maximization of the workers productivity through training courses that could be held during the planning horizon. Then, the proposed model is solved applying a hybrid algorithm that is a combination of Monte Carlo sampling method, modified 𝜀 -constraint method and L-shaped method. Finally, a numerical example is solved to demonstrate the validity of the model as well as the efficiency of the hybrid algorithm.