A short introduction to Integer Programming (IP). Problems leading to IP models. Some modelling tricks and reformulations. Geometry of linear IP. TUM matrices. Brief notes on polyhedral analysis. Separation theory. Chvatal cut hierarchy, Gomory cuts, Disjunctive cuts, RLT cut hierarchy. Iterative methods: Branch-and-Bound, Cutting Plane, Branch-and-Cut, Branch-and-Price. Lower bounds: Lagrangia...

 We present a new mathematical model for a permutation flowshop scheduling problem with sequence-dependent setup times considering minimization of two objectives, namely makespan and weighted mean total earliness/tardiness. Only small-sized problems with up to 20 jobs can be solved by the proposed integer programming approach. Thus, an effective multi-objective immune system (MOIS) is ...

Facility location decisions play a prominent role in strategic planning of many firms, companies and governmental organizations. Since in many real-world facility location problems, the data are subject to uncertainty, in this paper, we consider the P-center problem under uncertainty of demands. Using Bertsimas and Sim approach, we develop a robust model of the problem as an integer programming...

data envelopment analysis (dea) has been widely studied in the literature since its inception with charnes, cooper and rhodes work in 1978. the methodology behind the classical dea method is to determine how much improvements in the outputs (inputs) dimensions is necessary in order to render them efficient. one of the underlying assumptions of this methodology is that the units consume and prod...

This paper is about modeling and solving mixed integer programming (MIP) problems. In the last decade, the use of mixed integer programming models has increased dramatically. Fifteen years ago, mainframe computers were required to solve problems with a hundred integer variables. Now it is possible to solve problems with thousands of integer variables on a personal computer and obtain provably g...

in this paper a new method is proposed for path planning of planar manipulators amid obstacles through mathematical programming in a way that the robot’s links avoid collision with obstacles throughout their motion from an initial to a goal configuration. after inputting the workspace geometry, the shortest feasible path for the robot’s end-effector is planned toward its goal position using gen...

Mathematical modeling of supply chain operations has proven to be one of the most complex tasks in the field of operations management and operations research. Despite the abundance of several modeling proposals in the literature; for vast majority of them, no effective universal application is conceived. This issue renders the proposed mathematical models inapplicable due largely to the fact th...

Here, we consider single vendor-buyer model with multi-product and multi-customer and multi-facility location-production-distribution problem. It is assumed that the players of the supply chain are coordinated by sharing information. Vendor manufactures produce different products at different plants with limited capacities and then distribute the products to the consumers according to determini...

A design problem of cross-docking distribution networks is addressed as a new research area in logistics management. This paper presents a new mathematical model for the location of cross-docking facilities and vehicle routing scheduling problems in distribution networks. For this purpose, a two-phase mixed-integer programming (MIP) is formulated. Then, a new heuristic-based simulated annealing...