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Fuzzy transportation problem with random transportation costs. (English) Zbl 1188.90266

Summary: We consider the following transportation problem with both random and fuzzy factors. There exist \(m\) supply points and \(n\) demand points. For each route between supply point and demand point, unit transportation cost is a random variable according to a normal distribution and existence possibility denoting the preference choosing this route is attached. The probability that the total transportation cost is not greater than the budget \(F\) should be not less than the fixed probability level. Under the above setting, we seek transportation pattern minimizing \(F\) and maximizing the minimal preference among the routes used in a transportation. Since usually there is no transportation pattern optimizing two objectives at a time, we propose a solution algorithm to find some non-dominated transportation patterns after defining non-domination. Finally we discuss the further research problems.

MSC:

90C35 Programming involving graphs or networks
90B06 Transportation, logistics and supply chain management
90C70 Fuzzy and other nonstochastic uncertainty mathematical programming
90C15 Stochastic programming
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