Abstract
In this work, we introduce the fuzzy relation inequalities with min-plus composition for describing the pricing problem in a product transportation system. Some basic properties of the min-plus inequalities system are investigated. We define the concept of feasible index chain and further investigate the corresponding quasi-maximal solution. Moreover, it is found that the solution set of a min-plus system could be generated by a unique minimum solution and a finite number of quasi-maximal solutions. As a consequence, one is able to find the complete solution set of a min-plus system. Besides, motivated by the optimal managerial objective, we establish an optimization model with the min-plus inequalities constraints. A so-called FIS-based algorithm is developed for searching an optimal solution of our studied optimization model. We have provided a simple numerical example for checking the effectiveness of our proposed FIS-based algorithm. The obtained optimal solution would be helpful for the system manager, as an optimal pricing scheme.
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