• Let b = b + f0 where 0 < f0 < 1. • Let aj = aj + fj where 0 ≤ fj < 1. p • Then fj xj + (fj − 1)xj + gj yj = k + f0, where k is some integer. fj ≤f0 fj >f0 j=1

This document contains a “recipe” for coding a mixed-integer program (MIP) in Python via the modeling framework Pyomo. We first recap what a MIP is (Section 1) and then discuss …

Integer (Linear) Programming Integer linear program (ILP): a linear program with the additional constraint that variables must take integer values

A mixed integer linear program (MILP, MIP) is of the form min cT x Ax = b ≥ 0 xi ∈ Z ∀i ∈ I If all variables need to be integer, it is called a (pure) integer linear program (ILP, IP) If all variables …

This approach works as follows. We solve the LP relaxation of the (mixed) integer program. If we obtain an optimal solution in which all the variables (or, in the case of a mixed integer program, …

This chapter describes the use of mixed-integer programming in optimizing complex systems, such as those arising in biology, medicine, transportation, telecommunications, sports, and …

Thus, as we understand it today, mixed integer programming problems are those which contain decision variables which may be assigned integer or continuous real numeric values. Two …