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) ...

In this paper, a multi-period replacement model, based on a mixed integer nonlinear programming formulation, is developed for flexible automation investments. The model takes into account the costs, benefits and effective utilization of several types of flexibility. The decision variables pertain to the selection and optimal implementation sequence for new, CNC modules, the replacement schedule...

Euclidean norm computations over continuous variables appear naturally in the constraints or in the objective of many problems in the optimization literature, possibly defining non-convex feasible regions or cost functions. When some other variables have discrete domains, it positions the problem in the challenging Mixed Integer Nonlinear Programming (MINLP) class. For any MINLP where the nonli...

A branch and cut algorithm is developed for solving 0-1 MINLP problems. The algorithm integrates Branch and Bound, Outer Approximation and Gomory Cutting Planes. Only the initial Mixed Integer Linear Programming (MILP) master problem is considered. At integer solutions Nonlinear Programming (NLP) problems are solved, using a primal-dual interior point algorithm. The objective and constraints ar...

recently, lotfi et al. [10] established an equivalence model between the output-oriented dual ccr model and multiple objective linear programming (molp) and used an interactive method for finding target unit on efficiency frontier such that the decision maker preferences can be taken into account. however their method is not applicable for situations in which some outputs are undesirable and ne...

We consider the Module Allocation Problem with Non-Uniform communication costs (MAPNU), where a set of program modules must be assigned to a set of processors. The optimal assignment minimizes the sum of execution costs and communication costs between modules. This problem is naturally formulated as a quadratic 0-1 problem with linear constraints. In this paper, we compare two exact solution me...

Along with the increased competition in production and service areas, many organizations attempt to provide their products at a lower price higher quality. On other hand, consideration of environmental criteria conventional supplier selection methodologies is required for companies trying promote green supply chain management (GSCM). In this regard, multi-criteria decision-making (MCDM) techniq...