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Mathematical Problems in Engineering
Volume 2017, Article ID 2159281, 14 pages
Research Article

A Multiproduct Single-Period Inventory Management Problem under Variable Possibility Distributions

1Risk Management & Financial Engineering Laboratory, College of Management, Hebei University, Baoding, Hebei 071002, China
2Fundamental Science Department, North China Institute of Aerospace Engineering, Langfang, Hebei 065000, China

Correspondence should be addressed to Zhaozhuang Guo; moc.361@4002gnauhzoahz

Received 2 August 2017; Revised 21 September 2017; Accepted 4 December 2017; Published 20 December 2017

Academic Editor: Jean-Pierre Kenne

Copyright © 2017 Zhaozhuang Guo 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.


In multiproduct single-period inventory management problem (MSIMP), the optimal order quantity often depends on the distributions of uncertain parameters. However, the distribution information about uncertain parameters is usually partially available. To model this situation, a MSIMP is studied by credibilistic optimization method, where the uncertain demand and carbon emission are characterized by variable possibility distributions. First, the uncertain demand and carbon emission are characterized by generalized parametric interval-valued (PIV) fuzzy variables, and the analytical expressions about the mean values and second-order moments of selection variables are established. Taking second-order moment as a risk measure, a new credibilistic multiproduct single-period inventory management model is developed under mean-moment optimization criterion. Furthermore, the proposed model is converted to its equivalent deterministic model. Taking advantage of the structural characteristics of the deterministic model, a domain decomposition method is designed to find the optimal order quantities. Finally, a numerical example is provided to illustrate the efficiency of the proposed mean-moment credibilistic optimization method. The computational results demonstrate that a small perturbation of the possibility distribution can make the nominal optimal solution infeasible. In this case, the decision makers should employ the proposed credibilistic optimization method to find the optimal order quantities.