Fuzzy approach for multi-level programming problems

Shih, Hsu-Shih; Lai, Young-Jou; Lee, E. Stanley

doi:10.1016/0305-0548(95)00007-9

Cited by 284 publications

(188 citation statements)

References 24 publications

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“…Cao and Chen (2006) present an example where the sacrifice of the leader's objective on behalf of the followers results in a better solution for both levels. Similar solution strategies have also been studied (Tabucanon 1988;Lai 1996;Shih et al 1996;Cao and Chen 2006). Theorem 1 (Vicente 1992) If for each x ∈ X, f and g are twice continuously differentiable functions for every y ∈ C(x), f is strictly convex for every y ∈ C(x) and C(x) is a convex and compact set, then M(·) is a real-valued function, continuous and closed.…”

Section: Global Optimum Of a Bilevel Programming Problemmentioning

confidence: 95%

Parametric global optimisation for bilevel programming

et al. 2006

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We propose a global optimisation approach for the solution of various classes of bilevel programming problems (BLPP) based on recently developed parametric programming algorithms. We first describe how we can recast and solve the inner (follower's) problem of the bilevel formulation as a multi-parametric programming problem, with parameters being the (unknown) variables of the outer (leader's) problem. By inserting the obtained rational reaction sets in the upper level problem the overall problem is transformed into a set of independent quadratic, linear or mixed integer linear programming problems, which can be solved to global optimality. In particular, we solve bilevel quadratic and bilevel mixed integer linear problems, with or without right-hand-side uncertainty. A number of examples are presented to illustrate the steps and details of the proposed global optimisation strategy.

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Section: Global Optimum Of a Bilevel Programming Problemmentioning

confidence: 95%

Parametric global optimisation for bilevel programming

et al. 2006

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“…Lai [7] at first proposed hierarchical optimization method and obtained a satisfactory solution using the concept of tolerance membership functions based on fuzzy set theory in 1996. Shih et al [8] extended the concept of satisfactory solution of Lai [7] using non-compensatory max-min aggregation operator for solving MLPPs. Shih and Lee [9] studied MLPPs using the compensatory fuzzy operator.…”

Section: Introductionmentioning

confidence: 99%

Multilevel Programming Problems with Fuzzy Parameters: A Fuzzy Goal Programming Approach

Pramanik¹

2015

IJCA

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This paper presents fuzzy goal programming approach for solving multilevel programming problems with fuzzy parameters. The proposed approach is based on  -cut and fuzzy goal programming. In the proposed approach, the tolerance membership functions for the fuzzily described objective functions are defined by determining individual best solution of the objective function of every decision maker. Since the objectives of the level decision makers are potentially conflicting in nature, decision deadlock may arise due to the dissatisfaction of the solution of upper level decision makers. Sometimes upper level decision makers insist to work more than stipulated working hours or overtime duty in order to meet the heavy demand of the market arising for festivals or emergency reasons. In order to survive in the open competitive market, the relaxations of lower level decision makers are very crucial for the upper level decision makers and for the organization. So in the proposed model relaxation of decision for each level decision maker is considered. The relaxation of decision is performed by providing preference bounds on the decision variables for avoiding decision deadlock. Then three fuzzy goal programming models for multilevel programming are formulated. In general, the fuzzy goal programming models offer different solutions. In order to find the best compromise solution Euclidean function is used. An illustrative numerical example is provided to demonstrate the efficiency of the proposed approach.

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“…On the other hand, in the case of a project selection problem in the administrative office of a company and its autonomous divisions, the situation that these DMs can cooperate with each other seems to be natural rather than the noncooperative situation. Lai [11] and Shih et al [38] proposed solution concepts for two-level linear programming problems or multi-level ones such that decisions of DMs in all levels are sequential and all of the DMs essentially cooperate with each other. In their methods, the DMs identify membership functions of the fuzzy goals for their objective functions, and in particular, the DM at the upper level also specifies those of the fuzzy goals for the decision variables.…”

Section: Introductionmentioning

confidence: 99%

Interactive Fuzzy Programming for Stochastic Two-level Linear Programming Problems through Probability Maximization

Sakawa

Matsui²

2013

AIR

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ForewordIn this paper, we focus on stochastic two-level linear programming problems involving random variable coefficients both in objective functions and constraints. Using the concept of chance constraints, stochastic constraints are transformed into deterministic ones. Following the probability maximization model, the minimization of each stochastic objective function is replaced with the maximization of the probability that each objective function is less than or equal to a certain value. Under some appropriate assumptions for distribution functions, the formulated stochastic two-level linear programming problems are transformed into deterministic ones. Taking into account vagueness of judgments of the decision makers, we present interactive fuzzy programming. In the proposed interactive method, after determining the fuzzy goals of the decision makers at both levels, a satisfactory solution is derived efficiently by updating the satisfactory degree of the decision maker at the upper level with considerations of overall satisfactory balance among both levels. It should be emphasized here that the transformed deterministic problems for deriving an overall satisfactory solution can be easily solved through the combined use of the bisection method and the phase one of the simplex method. An illustrative numerical example is provided to demonstrate the feasibility of the proposed method.-iii - AbstractThis paper considers stochastic two-level linear programming problems. Using the concept of chance constraints and probability maximization, original problems are transformed into deterministic ones. An interactive fuzzy programming method is presented for deriving a satisfactory solution efficiently with considerations of overall satisfactory balance.

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Fuzzy approach for multi-level programming problems

Cited by 284 publications

References 24 publications

Parametric global optimisation for bilevel programming

Parametric global optimisation for bilevel programming

Multilevel Programming Problems with Fuzzy Parameters: A Fuzzy Goal Programming Approach

Interactive Fuzzy Programming for Stochastic Two-level Linear Programming Problems through Probability Maximization

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