This paper discussed the scheduling problem of outpatients in a radiology center with an emphasis on priority. To more compatibility to real-world conditions, we assume that the elapsed times in different stages to be uncertain that follow from the specific distribution function. The objective is to minimize outpatients’ total spent time in a radiology center. The problem is formulated as a fle...

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-...

This paper develops an MILP model, named Satisfactory-Green Vehicle Routing Problem. It consists of routing a heterogeneous fleet of vehicles in order to serve a set of customers within predefined time windows. In this model in addition to the traditional objective of the VRP, both the pollution and customers’ satisfaction have been taken into account. Meanwhile, the introduced model prepares a...

We use logic-based Benders decomposition to minimize tardiness in single-facility scheduling problems with many jobs and long time horizons. Release dates and due dates are given. A mixed integer linear programming (MILP) based master problem allocates jobs to segments of the time horizon, and a constraint programming (CP) based subproblem schedules the jobs in each segment.

Linear programming problems with alternate solutions are challenging due to the choice of multiple strategiesresulting in the same optimal value of the objective function. However, searching for these solutions is atedious task, especially when using mixed integer linear programming (MILP), as previously applied tometabolic models. Therefore, judgment on plurality of optimal m...

This paper presents an efficient solution approach to tackle large-scale singlefloor process plant layout problems. Based on the mixed integer linear programming (MILP) model proposed by Papageorgiou and Rotstein [1], the final layout (i.e. coordinates and dimensions) is determined from an initial feasible solution by an iterative improvement procedure using mixed integer optimisation. The appl...

This paper addresses the globally optimal solution of the network-constrained unit commitment (NCUC) problem incorporating a nonlinear alternating current (AC) model of the transmission network. We formulate the NCUC as a mixed-integer quadratically constrained quadratic programming (MIQCQP) problem. A global optimization algorithm is developed based on a multi-tree approach that iterates betwe...

Given a mixed-integer linear programming (MILP) model and an optimal basis of the associated linear programming relaxation, the Gomory’s corner relaxation is obtained by dropping nonnegativity constraints on the basic variables. Although this relaxation received a considerable attention in the literature in the last 40 years, the crucial issue of evaluating the practical quality of the corner-r...

The paper focuses on the solution of the minimum loss reconfiguration problem of distribution networks, including embedded generation, by means of a mixed integer linear programming (MILP) model. The proposed model takes into account typical operating constraints of distribution networks (radial configuration, branch ampacity limits and bus voltage requirements). The accuracy of the results and...