A Stackelberg Location on a Network with Fuzzy Random Demand Quantities Using Possibility Measure
This paper focuses on a competitive facility location problem between leader and follower on a network with demands whose weights are given uncertainly and vaguely. By representing them as fuzzy random variables, the optimal location problem can be formulated as a fuzzy random programming problem for finding Stackelberg equilibrium. For solving the problem, it is reformulated as the problem to find the optimal solutions maximizing a degree of possibility under some chance constraint for the leader. Theorems for its complexity are shown based upon the characteristics of the facility location.
KeywordsFuzzy Number Facility Location Tree Network Fuzzy Goal Chance Constraint
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- 2.Berman, O., Krass, K.: Facility location with stochastic demands and congestion. In: Drezner, Z., Hamacher, H.W. (eds.) Facility Location: Application and Theory, pp. 329–372. Springer, Berlin (2001)Google Scholar
- 6.Hakimi, S.L.: Locations with spatial interactions: Competitive locations and games. In: Mirchandani, P.B., Francis, R.L. (eds.) Discrete Location Theory. Discrete Mathematics and Optimization, pp. 439–478. Wiley Interscience (1990)Google Scholar
- 19.Uno, T., Katagiri, H., Kato, K.: Competitive facility location with random demands. IAENG Transactions on Engineering Technologies 3, 83–93 (2009)Google Scholar
- 20.Uno, T., Katagiri, H., Kato, K.: Competitive facility location with fuzzy random demands. IAENG Transactions on Engineering Technologies 5, 99–108 (2010)Google Scholar
- 22.Uno, T., Katagiri, H., Kato, K.: A competitive facility location problem on a network with fuzzy random weights. Engineering Letters 19, 143–146 (2011)Google Scholar