We introduce strong formulations for robust mixed 0–1 programming with uncertain objective coefficients. We focus on a polytopic uncertainty set described by a “budget constraint” for allowed uncertainty in the objective coefficients. We show that for a robust 0–1 problem, there is an α–tight linear programming formulation with size polynomial in the size of an α–tight linear programming formul...

One of the most complicated decision making problems for managers is the evaluation of bank performance, which involves various criteria. There are many studies about bank efficiency evaluation by network DEA in the literature review. These studies do not focus on multi-level network. Wu (Eur J Oper Res 207:856–864, 2010) proposed a bi-level structure for cost efficiency at the first time. In t...

Mixed integer programming is proposed as an approach for generating treatment plans for brachytherapy. Two related but distinct, mixed integer programming models are tested on data from eight prostate cancer patients. The results demonstrate that in some cases, "good" treatment plans can be obtained in less than five CPU minutes.

We discuss a mixed-integer nonlinear programming formulation for the problem of covering a set of points with a given number of slabs of minimum width, known as the bottleneck variant of the hyperplane clustering problem. We derive several linear approximations, which we solve using a standard mixed-integer linear programming solver. A computational comparison of the performance of the differen...