We formulate the capacity expansion planning as a bilevel optimization to model the hier-archical decision structure involving industrial producers and consumers. The formulation isa mixed-integer bilevel linear program in which the upper level maximizes the profit of a pro-ducer and the lower level minimizes the cost paid by markets. The upper-level problem includesmixed-in...

In recent years, branch-and-cut algorithms have become firmly established as the most effective method for solving generic mixed integer linear programs (MIPs). Methods for automatically generating inequalities valid for the convex hull of solutions to such MIPs are a critical element of branch-and-cut. This paper examines the nature of the so-called separation problem, which is that of generat...

we present a new model and a new approach for solving fuzzylinear programming (flp) problems with various utilities for the satisfactionof the fuzzy constraints. the model, constructed as a multi-objective linearprogramming problem, provides flexibility for the decision maker (dm), andallows for the assignment of distinct weights to the constraints and the objectivefunction. the desired solutio...

Recent advances in symbolic dynamic programming (SDP) combined with the extended algebraic decision diagram (XADD) data structure have provided exact solutions for mixed discrete and continuous (hybrid) MDPs with piecewise linear dynamics and continuous actions. Since XADD-based exact solutions may grow intractably large for many problems, we propose a bounded error compression technique for XA...

This paper deals with linear fractional bilevel programming problem. The goals of objective functions are determined by optimizing individual objective function subject to the system constraints. Then the fractional objective functions are transformed into equivalent linear functions at the optimal solution point by using first order Taylor polynomial series. Since the objectives of the decisio...

1. Introduction. Nowadays, the bilevel optimization problems, arising in various applications [1, 2], seem to be one of the most attractive fields for many experts [1, 3, 4, 5]. Bilevel problems are such optimization problems, which – side by side with ordinary constraints such as equalities and inequalities [6] – include a constraint described as an optimization subproblem, called the lower-le...

This paper presents a quantitative and computational method to determine the optimal tax rate among generating units. To strike a balance between the reduction of carbon emission and the profit of energy sectors, the proposed bilevel optimization model can be regarded as a Stackelberg game between the government agency and the generation companies. The upper-level, which represents the governme...

Optimization problems involving two decision makers at two different decision levels are referred to as bilevel programming problems. In this work, we present a novel algorithm for the exact and global solution of two classes of bi-level programming problems, namely (i) bi-level mixed-integer linear programming problems (B-MILP) and (ii) bi-level mixed-integer quadratic programming problems (B-...