Gomory mixed-integer (GMI) cuts are among the most effective cutting planes for general mixed-integer programs (MIP). They are traditionally generated from an optimal basis of a linear programming (LP) relaxation of a MIP. In this paper we propose a heuristic to generate useful GMI cuts from additional bases of the initial LP relaxation. The cuts we generate have rank one, i.e., they do not use...

We consider the problem of shipping a set of products from a single origin (the vendor) to a common destination (the buyer) with the objective of minimizing the sum of the inventory and transportation costs, when a set of shipping frequencies is given and products are assumed to be perishable. We provide a mixed integer linear programming model for the problem and propose the modification of kn...

Optimizing gate scheduling at airports is an old, but also a broad problem. The main purpose of this problem is to find an assignment for the flights arriving at and departing from an airport, while satisfying a set of constraints.A closer look at the literature in this research line shows thatin almost all studies airport gate processing time has been considered as a fix parameter. In this res...

We study the mixed-integer rounding (MIR) closures of polyhedral sets. The MIR closure of a polyhedral set is equal to its split closure and the associated separation problem is NP-hard. We describe a mixed-integer programming (MIP) model with linear constraints and a non-linear objective for separating an arbitrary point from the MIR closure of a given mixed-integer set. We linearize the objec...

Many real life optimization problems cannot be modeled adequately using linear programming. Other techniques such as integer programming and non-linear programming are typically used to solve these problems. However, these techniques provide limited view of the solution space and have serious limitations dealing with the stochastic nature of the constraints. This paper investigates the principl...

This paper addresses a class of two-stage robust optimization models with integer adversarial variables. We discuss the importance of this class of problems in modeling two-stage robust resource planning problems where some tasks have uncertain arrival times and duration periods. We apply Dantzig-Wolfe decomposition to exploit the structure of these models and show that the original problem red...

Heat Exchanger Network (HEN) synthesis is primarily formulated as a mixed integer non-linear programming (MINLP) problem based on method of stage-wise superstructure (SWS). Approaches to obtain an optimal HEN configuration can adopt deterministic algorithms. But, large scale problem, it difficult solve due the complexities arisen from nonlinearities SWS. To overcome model nonlinearities, stocha...

The purpose of the paper is to present a hybrid algorithm to solve a transportation optimization model with random demand parameters and network design variables. At first, the classical deterministic linear transportation model with network design 0-1 variables is introduced. Then, randomness is considered for demand parameters and modeled by here-and-now approach. The obtained scenario-based ...