Despite existing various integer programming for sequencing problems, there is not enoughinformation about practical values of the models. This paper considers the problem of minimizing maximumlateness with release dates and presents four different mixed integer programming (MIP) models to solve thisproblem. These models have been formulated for the classical single machine problem, namely sequ...

In this paper we provide a computation algorithm to get global solution for the maximum rank correlation estimator using mixed integer programming (MIP) approach. We construct new constrained optimization problem by transforming all indicator functions into binary parameters be estimated and show that it is equivalent original problem. also consider an application of best subset prediction can ...

Many optimisation problems contain substructures involving constraints on sequences of decision variables. Such constraints can be very complex to express with mixed integer programming (MIP), while in constraint programming (CP), the global constraint regular easily represents this kind of substructure with deterministic finite automata (DFA). In this paper, we use DFAs and the associated laye...

In this paper, a multi-product single machine scheduling problem with the possibility of producing defected jobs, is considered. We concern rework in the scheduling environment and propose a mixed-integer programming (MIP) model for the problem.  Based on the philosophy of just-in-time production, minimization of the sum of earliness and tardiness costs is taken into account as the objective fu...

The Chance-Constrained Stochastic Programming (CCSP) is one of the models for decision making under uncertainty. In this paper, we consider the special case of the CCSP in which only the righthand side vector is random with a discrete distribution having a finite support. The unit commitment problem is one of the applications of the special case of the CCSP. Existing methods for exactly solving...

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...

Abstract The paper considers the assignment of items to groups according their attribute values such that are as balanced possible. Although problem is in general NP -hard, we prove it can be solved pseudo-polynomial time if integer. We point out a relation partition and more multi-way number partitioning. Furthermore, introduce mixed-integer programming (MIP) formulation, variable reduction te...

Branch-and-bound is a widely used method in combinatorial optimization, including mixed integer programming, structured prediction and MAP inference. While most work has been focused on developing problem-specific techniques, little is known about how to systematically design the node searching strategy on a branch-and-bound tree. We address the key challenge of learning an adaptive node search...

Branch-and-bound methods for mixed-integer programming (MIP) are traditionally based on solving a linear programming (LP) relaxation and branching on a variable which takes a fractional value in the (single) computed relaxation optimum. In this paper we study branching strategies for mixed-integer programs that exploit the knowledge of multiple alternative optimal solutions (a cloud) of the cur...