Integer-programming models arise in practically every area of application of mathematical programming. To develop a preliminary appreciation for the importance of these models, we introduce, in this section, three areas where integer programming has played an important role in supporting managerial decisions.

• What is Integer Programming (IP)? • How do we encode decisions using IP? – Exclusion between choices – Exclusion between constraints • How do we solve using Branch and Bound? – Characteristics – Solving Binary IPs – Solving Mixed IPs and LPs

Jul 1, 2014 · In a second step, the search of an optimal learning path in H is considered as a binary integer programming problem which we propose to solve using an exact method based on the well-known...

Binary Programming Model IP with all integer variables restricted to 0 or 1. The model can be classified as a pure-binary programming model or mixed-binary programming model.

In order to model fixed costs using integer variables and linear constraints, we create new variables. In this case, we create binary variables w. 1, w. 2, and w. 3. We will then create linear constraints (on the next slide) that ensures that w. 1, w. …

Integer programs: a linear program plus the additional constraints that some or all of the variables must be integer valued. We also permit “ x. j. ∈{0,1},” or equivalently, “x. j. is . binary” This is a shortcut for writing the constraints: 0 ≤ x. j ≤ 1 and xj integer.

learning path in H is considered as a binary integer programming problem which we propose to solve using an exact method based on the well-known branch-and-bound algorithm. The method detailed in the paper takes into account the prerequisite and gained competencies as constraints of the optimization problem by

binary, bivalent, logical, or 0–1 variables. • Binary variables are of great importance because they occur regularly in many model formulations. • But can be also used as auxiliary variables…

Jan 1, 2014 · All modern integer programming solvers use intersection graphs to model logical conditions among the binary variables of integer programming formulations.

Such problems are called pure (mixed) 0-1 programming problems or pure (mixed) binary integer programming problems. The use of integer variables in production when only integral quantities can be produced is the most obvious use of integer programs. In this section, we will look at some less obvious ones.