This is a report on how mixed integer programming works. It starts by showing the form of a mixed integer program with n variables and m constraints. They explain the branch and bound method which is the most widely used method for solving integer programs. It goes into some detail about how the variables have only two possible restrictions, one and zero. There’s also some mention of the branch...

We present a generic branch-and-bound algorithm for finding all the Pareto solutions of biobjective mixed-integer linear program. The main contributions are new algorithms obtaining dual bounds at node, checking node fathoming, presolve, and duality gap measurement. Our is predominantly decision space search method because branching performed on variables, akin to single objective problems, alt...

In this paper we consider the structural analysis problem for differential-algebraic systems with conditional equations. This consists, given a conditional differential-algebraic system, in verifying if the system is structurally solvable for every state, and if not in finding a state in which the system is structurally singular. We give an integer linear programming formulation for the problem...

This paper presents a branch-and-cut method for two-stage stochastic mixed-integer programming (SMIP) problems with continuous firststage variables. This method is derived based on disjunctive decomposition (D) for SMIP, an approach in which disjunctive programming is used to derive valid inequalities for SMIP. The novelty of the proposed method derives from branching on the first-stage continu...

Conflict analysis for infeasible subproblems is one of the key ingredients in modern SAT solvers. In contrast, it is common practice for today’s mixed integer programming solvers to discard infeasible subproblems and the information they reveal. In this paper, we try to remedy this situation by generalizing SAT infeasibility analysis to mixed integer programming. We present heuristics for branc...

in this paper, a mathematical method is proposed to formulate a generalized ordering problem. this model is formed as a linear optimization model in which some variables are binary. the constraints of the problem have been analyzed with the emphasis on the assessment of their importance in the formulation. on the one hand, these constraints enforce conditions on an arbitrary subgraph and then g...

The aim of this paper is to provide new efficient methods for solving general chance-constrained integer linear programs to optimality. Valid linear inequalities are given for these problems. They are proved to characterize properly the set of solutions. They are based on a specific scenario, whose definition impacts strongly on the quality of the linear relaxation built. A branch-and-cut algor...

Integer linear fractional programming problem with multiple objective MOILFP is an important field of research and has not received as much attention as did multiple objective linear fractional programming. In this work, we develop a branch and cut algorithm based on continuous fractional optimization, for generating the whole integer efficient solutions of the MOILFP problem. The basic idea of...

This study presents mixed integer programming (MIP) models for production lot-sizing problems with distribution costs using unit load devices such as pallets and containers. Problems that integrate production lot-sizing decisions and loading of the products in vehicles (bins) are also modelled, in which constraints such as weight limits, volume restrictions or the value of the cargo loaded in t...