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International Journal of Mathematics and Mathematical Sciences
Volume 2014, Article ID 690435, 14 pages
Research Article

Optimal Manufacturing-Remanufacturing Production Policy for a Closed-Loop Supply Chain under Fill Rate and Budget Constraint in Bifuzzy Environments

1Department of Applied Mathematics, University of Calcutta, 92 APC Road, Kolkata, West Bengal 700009, India
2Department of Applied Science, Haldia Institute of Technology, Purba Midnapur, West Bengal 721657, India

Received 31 December 2013; Accepted 12 May 2014; Published 24 June 2014

Academic Editor: Tamer Eren

Copyright © 2014 Soumita Kundu 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.


We study a closed-loop supply chain involving a manufacturing facility and a remanufacturing facility. The manufacturer satisfies stochastic market demand by remanufacturing the used product into “as-new” one and producing new products from raw material in the remanufacturing facility and the manufacturing facility, respectively. The remanufacturing cost depends on the quality of used product. The problem is maximizing the manufacturer’s expected profit by jointly determining the collected quantity of used product and the ordered quantity of raw material. Following that we analyze the model with a fill rate constraint and a budget constraint separately and then with both the constraints. Next, to handle the imprecise nature of some parameters of the model, we develop the model with both constraints in bifuzzy environment. Finally numerical examples are presented to illustrate the models. The sensitivity analysis is also conducted to generate managerial insight.