Decomposition's Dantzig–Wolfe applied to fuzzy multicommodity flow problems

Abstract

We present, in this paper, a method for solving linear programming problems with fuzzy costs based on the classical method of decomposition's Dantzig-Wolfe. Methods using decomposition techniques address problems that have a special structure in the set of constraints. An example of such a problem that has this structure is the fuzzy multicommodity flow problem. This problem can be modeled by a graph whose nodes represent points of supply, demand and passage of commodities, which travel on the arcs of the network. The objective is to determine the flow of each commodity on the arcs, in order to meet demand at minimal cost while respecting the capacity constraints of the arcs and the flow conservation constraints of the nodes. Using the theory of fuzzy sets, the proposed method aims to find the optimal solution, working with the problem in the fuzzy form during the resolution procedure.

Branch-and-price algorithm for fuzzy integer programming problems with block angular structure

“…The results show that in all three problems, the optimal values are the same, but the number of iterations and the CPU time of the proposed algorithm are less than the corresponding values in [8]. Also, the influence of the hardware used by Ciappina, J.R. et al in the CPU times is considered.…”

“…12 Table 6 Comparing the results of branch-and-price algorithm with fuzzy simulation procedure for different level of satisfaction degree α and β. Table 7 Comparing the results of the algorithm with the results presented in [8]. Ciappina et al [8].…”

“…Table 7 Comparing the results of the algorithm with the results presented in [8]. Ciappina et al [8]. The proposed algorithm is used to solve three problems presented in [8].…”

“…Ciappina et al [8]. The proposed algorithm is used to solve three problems presented in [8]. The results are compared in Table 7.…”

“…Example (4): This example has been studied in [8], as a real network namely COST 239 European Optical Network, with 11 nodes and 50 double-direction links. Fig.…”