Bi-level programming has been used widely to model interactions between hierarchical decision-making problems, and their solution is challenging, especially when the lower-level problem contains discrete decisions. The of such mixed-integer linear bi-level problems typically need decomposition, approximation or heuristic-based strategies which either require high computational effort cannot gua...

A standard trick in integer programming is to replace each bounded integer-constrained variable with a small number of binary variables, using the bit representation of the given variable. We show that, in the case of mixed-integer quadratic programs (MIQPs), this process can enable one to obtain stronger linear programming relaxations. Moreover, we give a simple sufficient condition under whic...

this paper presents a genetic algorithm (ga) for solving a generalized model of single-item resource-constrained aggregate production planning (app) with linear cost functions. app belongs to a class of pro-duction planning problems in which there is a single production variable representing the total production of all products. we linearize a linear mixed-integer model of app subject to hiring...

We propose mathematical programming models for solving problems arising from planning and running an energy production process based on burning biomasses. The models take into account different aspects of the problem: determination of the biomasses to produce and/or buy, transportation decisions to convey the materials to the respective plants, and plant design. Whereas the “running model” is l...

Lifting is a procedure for deriving strong valid inequalities for a closed set from inequalities that are valid for its lower dimensional restrictions. It is arguably one of the most effective ways of strengthening linear programming relaxations of 0–1 programming problems. Wolsey (1977) and Gu et al. (2000) show that superadditive lifting functions lead to sequence independent lifting of valid...