A transportation problem with fuzzy-stochastic cost

作者：Ojha Anupam^*; Das Barun; Mondal Shyamal Kumar; Maiti Manoranjan

来源：Applied Mathematical Modelling, 2014, 38(4): 1464-1481.

DOI：10.1016/j.apm.2013.08.022

• Transportation models
• Fuzzy stochastic
• Credibility
• Mean chance

In this paper, we consider some transportation problems (TPs) with different types of fuzzy-stochastic unit transportation costs and budget constraints. These fuzzy stochastic costs are reduced to corresponding crisp ones in two different ways. For the first method, using the definition of alpha-cut of the fuzzy numbers, expectation is taken separately on both lower and upper alpha-cuts and then mean expectation is calculated with the help of signed distance. In the second procedure, we realize fuzzy random events (xi >= r) and (xi <= r) for the fuzzy random variable (xi). Using credibility measure of these events, mean chances for the above fuzzy random events are calculated and then expectation is taken to get the crisp expressions. The reduced deterministic problems of the fuzzy stochastic TP are solved using a real' coded genetic algorithm with Roulette wheel selection, arithmetic crossover and random mutation. Few numerical examples are demonstrated to find the optimal solutions of the proposed models.

• 出版日期2014-2-15