Integer Linear Programs - AMPL

← Back to document page

20______________________________________ ________________________________________ __________________Integer Linear ProgramsMany Linear programming problems require certain variables to have whole number,or Integer , values. Such a requirement arises naturally when the variables represent enti-ties like packages or people that can not be fractionally divided at least, not in a mean-ingful way for the situation being modeled. Integer variables also play a role in formulat-ing equation systems that model logical conditions, as we will show later in this some situations, the optimization techniques described in previous chapters are suf-ficient to find an Integer solution. An Integer optimal solution is guaranteed for certainnetwork Linear Programs , as explained in Section Even where there is no guarantee,a Linear programming solver may happen to find an Integer optimal solution for the par-ticular instances of a model in which you are interested.

Since the model has a combination of continuous (non-integer) and integer variables, it yields what is known as a ‘‘mixed-integer’’ program. To complete the model, we need to add constraints to assure thatTransand Useare related in the intended way. This is the ‘‘clever’’ part of the formulation; we simply

  Model, Mixed, Integre, A mixed