In this chapter we will introduce six case studies:

1. production, at least-cost, of a commodity from machines that have minimum and maximum machine capacity constraints (Section 15.1),

2. optimal routing in a data communications network (Section 15.2),

3. least absolute value estimation (Section 15.3),

4. optimal margin pattern classification (Section 15.4),

5. choosing the widths of interconnects between latches and gates in integrated circuits (Section 15.5), and

6. the optimal power flow problem in electric power systems (Section 15.6).

The first and third case studies will draw from the previous formulations in Sections 12.1 and 9.1, respectively. The sixth case study combines the formulations from Sections 15.1 and 6.2. These three case studies will be introduced briefly, concentrating on the extensions from the previous formulations. They further illustrate the idea of incremental model development. The second, fourth, and fifth case studies introduce new material and will be developed in more detail. All six of these case studies will turn out to be optimization problems with both equality and inequality constraints. The first three have linear constraints, while the last three have non-linear constraints. Transformations will be applied to the fourth and fifth to deal with the non-linear constraints.

Least-cost production with capacity constraints

This case study generalizes the least-cost production case study from Section 12.1.

Motivation

Recall the least-cost production case study discussed in Section 12.1.