A Novel Method for Solving the Fully Fuzzy Bilevel Linear Programming Problem

We address a fully fuzzy bilevel linear programming problem in which all the coefficients and variables of both objective functions and constraints are expressed as fuzzy numbers. This paper is to develop a new method to deal with the fully fuzzy bilevel linear programming problem by applying interval programming method. To this end, we first discretize membership grade of fuzzy coefficients and fuzzy decision variables of the problem into a finite number of α-level sets. By using α-level sets of fuzzy numbers, the fully fuzzy bilevel linear programming problem is transformed into an interval bilevel linear programming problem for each α-level set. The main idea to solve the obtained interval bilevel linear programming problem is to convert the problem into two deterministic subproblems which correspond to the lower and upper bounds of the upper level objective function. Based on the Kth-best algorithm, the two subproblems can be solved sequentially. Based on a series of α-level sets, we introduce a linear piecewise trapezoidal fuzzy number to approximate the optimal value of the upper level objective function of the fully fuzzy bilevel linear programming problem. Finally, a numerical example is provided to demonstrate the feasibility of the proposed approach

Tropical analogues of a Dempe-Franke bilevel optimization problem

We consider the tropical analogues of a particular bilevel optimization problem studied by Dempe and Franke and suggest some methods of solving these new tropical bilevel optimization problems. In particular, it is found that the algorithm developed by Dempe and Franke can be formulated and its validity can be proved in a more general setting, which includes the tropical bilevel optimization problems in question. We also show how the feasible set can be decomposed into a finite number of tropical polyhedra, to which the tropical linear programming solvers can be applied.Comment: 11 pages, 1 figur

Integer Bilevel Linear Programming Problems: New Results and Applications

Integer Bilevel Linear Programming Problems: New Results and Application

Integer Bilevel Linear Programming Problems: New Results and Applications

Integer Bilevel Linear Programming Problems: New Results and Application

A λ-cut and goal-programming-based algorithm for fuzzy-linear multiple-objective bilevel optimization

Bilevel-programming techniques are developed to handle decentralized problems with two-level decision makers, which are leaders and followers, who may have more than one objective to achieve. This paper proposes a λ-cut and goal-programming-based algorithm to solve fuzzy-linear multiple-objective bilevel (FLMOB) decision problems. First, based on the definition of a distance measure between two fuzzy vectors using λ-cut, a fuzzy-linear bilevel goal (FLBG) model is formatted, and related theorems are proved. Then, using a λ-cut for fuzzy coefficients and a goal-programming strategy for multiple objectives, a λ-cut and goal-programming-based algorithm to solve FLMOB decision problems is presented. A case study for a newsboy problem is adopted to illustrate the application and executing procedure of this algorithm. Finally, experiments are carried out to discuss and analyze the performance of this algorithm. © 2006 IEEE

Optimization of bantuan pangan non tunai (BPNT) distribution using bilevel linear programming in siantar martoba subdistrict pematang siantar

Bantuan Pangan Non Tunai (BPNT) is assistance that is in the second decile; in other words, KPMs who are in the first decile will also get assistance. A limited quota of BPNT recipients will result in people in categories such as the elderly group not getting this assistance. This problem arises because there is a significant increase in the population of the elderly group every year. The research method uses secondary data from data sources, namely the social service office, to develop a bilevel model for the problem of distributing food aid on cash by regularizing the bilevel model so that a linear programming model with a single objective function is obtained. In the regularization stage, the gradient descent method is used to find the optimal value of the penalty parameter. From the calculation results of the regularized model, it is found that the values of the variables  x_1= 2956,  x_2= 583, and x_3 = 250 have a value of Z = 3804. This bilevel linear programming model approach provides a strong basis for planning and decision-making related to the distribution of Non-Cash Food Assistance (BPNT) in Siantar Martoba Subdistrict. Therefore, it can be assumed that this bilevel linear programming approach can be used as a guideline for related agencies in allocating resources efficiently