Write Nooz’s problem as an integer program. Modeling logical constraints that include only two binary variables. Step 1. Graph the feasible region as restricted to the two variables. Step 2. Add linear equalities and or inequalities so that the feasible region of the IP is the same as that given in Step 1. Constraint 1.

An integer programming problem is a mathematical optimization or feasibility program in which some or all of the variables are restricted to be integers. In many settings the term refers to integer linear programming (ILP), in which the objective function and the constraints (other than the integer constraints) are linear .

2.4 IP Formulation We put the objective function and the constraints together to obtain the formulation below: Maximize 0:10xOR +0:04xAc +0:06xIT +0:12xFi +0:08xMa +0:03xOB +0:04xIC +0:05xRu Subject to 9xOR +7xAc +5xIT +8xFi +5xMa +3xOB +7xIC +10xRu • 40 xj 2 f0;1g So if we have a solution where xOR = 1, xAc = 1, xIT = 1, xFi = 1, xMa = 1 and ...

IPs. In Section 9.2, we explain how to formulate integer programming models. We also dis-cuss how to solve IPs on the computer with LINDO, LINGO, and Excel Solver. In Sections 9.3–9.8, we discuss other methods used to solve IPs. 9.1 Introduction to Integer Programming An IP in which all variables are required to be integers is called a pure ...

The purpose of this chapter is to show some interesting integer programming applications and to describe some of these solution techniques as well as possible pitfalls.

IP Reference guide for integer programming formulations. This document is intended as a compact (or relatively compact) guide to the formulation of integer programs. For more detailed explanations, see the PowerPoint tutorial on integer programming.

Goals of lectures on Integer Programming. Lectures 1 and 2 –Introduce integer programming –Techniques (or tricks) for formulating combinatorial optimization problems as IPs Lectures 3 and 4. –How integer programs are solved (and why they are hard to solve). •Rely on solving LPs fast •Branch and bound and cutting planes Lecture 5.

Integer programming example In the planning of the monthly production for the next six months a company must, in each month, operate either a normal shift or an extended shift (if it produces at all).

0 xj 1 and xj is integer. Here, we address different logical constraints that can be transformed into integer programming constraints. If item i is selected, then item j is also selected. Either item i is selected or item j is selected, but not both. Item i is selected or item j is selected or both.

polynomial-time algorithms for solving integer programs. Solving the associated convex relaxation (ignoring integrality constraints) results in an lower bound on the optimal value.