The mixed Chinese postman problem is a version of the well-known Chinese postman problem in which the underlying graph consists of both directed and undirected edges. We give an integer linear programming formulation for this problem and then show that the extreme points of its linear relaxation polyhedron are all half-integral. keywords: Chinese postman problem, half-integrality, graph, flow

We present an overview of noncommercial software tools for the solution of mixed-integer linear programs (MILPs). We first review solution methodologies for MILPs and then present an overview of the available software, including detailed descriptions of eight software packages available under open-source or other noncommercial licenses. Each package is categorized as a black-box solver, a calla...

We study a generic minimization problem with separable non-convex piecewise linear costs, showing that the linear programming (LP) relaxation of three textbook mixed-integer programming formulations each approximates the cost function by its lower convex envelope. We also show a relationship between this result and classical Lagrangian duality theory.

pumps are among the early instruments invented by humans to be taken advantage of in the use of water utilities. design and operation problem of pumping stations is a type of mixed integer non linear programming, in which gradient based optimization methods are not efficient for solving complex problems of this type. in this regard, such evolutionary optimization algorithms as genetic algorithm...

preventive maintenance scheduling of generating units is addressed as a long-term scheduling in power system studies aiming to increase the reliability incorporating cost reduction. it consists of knowing which generating units should be shut down for regular safety inspection. in this paper, a new formulation of preventive maintenance scheduling associated with cost reduction index (cri) is pr...

This survey presents tools from polyhedral theory that are used in integer programming. It applies them to the study of valid inequalities for mixed integer linear sets, such as Gomory’s mixed integer cuts.

A wide range of problems can be modeled as Mixed Integer Linear Programming (MILP) problems using standard formulation techniques. However, in some cases the resulting MILP can be either too weak or to large to be effectively solved by state of the art solvers. In this survey we review advanced MILP formulation techniques that result in stronger and/or smaller formulations for a wide class of p...

Mixed integer linear programming (MILP) is a powerful representation often used to formulate decision-making problems under uncertainty. However, it lacks a natural mechanism to reason about objects, classes of objects, and relations. First-order logic (FOL), on the other hand, excels at reasoning about classes of objects, but lacks a rich representation of uncertainty. While representing propo...