This paper considers a new canonical duality theory for solving mixed integer quadratic programming problem. It shows that this well-known NP-hard problem can be converted into concave maximization dual problems without duality gap. And the dual problems can be solved, under certain conditions, by polynomial algorithms.

The wellknown CLSP problem is generalized including sequence dependent setup times and overtimes and modeling it as a quadratic mixed 0-1 integer programming problem called Capacitated Lot Sizing Problem with Sequence Dependent Setups and Overtimes. We develop a heuristics based on Lagrangean relaxation and tabu search for solving the problem. At the end, some computational results are presented.

We show how to implement the cross-validation technique used in machine learning as a slice model. We describe the formulation in terms of support vector machines and extend the GAMS/DEA interface to allow for efficient solutions of linear, mixed integer and simple quadratic slice models under GAMS.

Technical and market uncertainties during product launch planning can have a significant impact in the companies decision-making process, particularly in today’s business context of the pharmaceutical industry. This paper addresses this planning problem, considering both types of uncertainty and integrating process design and capacity decisions under limited resources. A Mixed Integer Linear Pr...

This paper proposes a framework for modeling and controlling systems described by interdependent physical laws, logic rules, and operating constraints, denoted as mixed logical dynamical (MLD) systems. These are described by linear dynamic equations subject to linear inequalities involving real and integer variables. MLD systems include linear hybrid systems, finite state machines, some classes...

We present a matheuristic, an integer programming based heuristic, for the Liner Shipping Network Design Problem. The heuristic applies a greedy construction heuristic based on an interpretation of the liner shipping network design problem as a multiple quadratic knapsack problem. The construction heuristic is combined with an improvement heuristic with a neighborhood defined by the solution sp...

This paper considers the solution of Mixed Integer Nonlinear Programming (MINLP) problems. Classical methods for the solution of MINLP problems decompose the problem by separating the nonlinear part from the integer part. This approach is largely due to the existence of packaged software for solving Nonlinear Programming (NLP) and Mixed Integer Linear Programming problems. In contrast, an integ...

A mathematical programming approach to deal with the global configuration of resource constraints is presented. A specialized parametric programming algorithm to obtain the pareto set for the biobjective problem that appears to deal with the global configuration for 0-1-Integer Linear Programing problems is presented and implemented. Computational results for Multiconstrained Knapsack problems ...

This paper proposes a framework for modeling and controlling systems described by interdependent physical laws, logic rules, and operating constraints, denoted as Mixed Logical Dynamical (MLD) systems. These are described by linear dynamic equations subject to linear inequalities involving real and integer variables. MLD systems include constrained linear systems, finite state machines, some cl...