A characterization of the extension principle
Fuzzy Sets and Systems - Special issue: Dedicated to the memory of Richard E. Bellman
Fuzzy set theory—and its applications (3rd ed.)
Fuzzy set theory—and its applications (3rd ed.)
Solving Posynomial Geometric Programming Problems via Generalized Linear Programming
Computational Optimization and Applications
Multi-item stochastic and fuzzy-stochastic inventory models under two restrictions
Computers and Operations Research
Optimal Production and Marketing Planning
Computational Optimization and Applications
Fuzzy decision making of profit function in production planning using S-curve membership function
Computers and Industrial Engineering
A fuzzy DEA/AR approach to the selection of flexible manufacturing systems
Computers and Industrial Engineering
Computers and Industrial Engineering
Computers & Mathematics with Applications
A multi-echelon inventory management framework for stochastic and fuzzy supply chains
Expert Systems with Applications: An International Journal
Computers and Industrial Engineering
Fuzzy pricing and marketing planning model: A possibilistic geometric programming approach
Expert Systems with Applications: An International Journal
Fuzzy measures for profit maximization with fuzzy parameters
Journal of Computational and Applied Mathematics
Computers and Industrial Engineering
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The integration of production and marketing planning is crucial in practice for increasing a firm's profit. However, the conventional inventory models determine the selling price and demand quantity for a retailer's maximal profit with exactly known parameters. When the demand quantity, unit cost, and production rate are represented as fuzzy numbers, the profit calculated from the model should be fuzzy as well. Unlike previous studies, this paper develops a solution method to find the fuzzy profit of the integrated production and marketing planning problem when the demand quantity, unit cost, and production rate are represented as fuzzy numbers. Based on Zadeh's extension principle, we transform the problem into a pair of two-level mathematical programming models to calculate the lower bound and upper bound of the fuzzy profit. According to the duality theorem of geometric programming technique, the two-level mathematical program is transformed into the one-level conventional geometric program to solve. At a specific @a-level, we can derive the global optimum solutions for the lower and upper bounds of the fuzzy profit by applying well-developed theories of geometric programming. Examples are given to illustrate the whole idea proposed in this paper.