In the 60-question afternoon session of the FE Exam, expect three questions on mathematical optimization and modeling. In addition, optimization can occur in almost any application area. In facility location, for example in addition to the median location algorithm, Steiner-Weber algorithm, and center-of-gravity algorithm, all reviewed in the Facility Location section of Chapter 4 (pages 4-3 to 4-4) the assignment algorithm covered in this chapter is used when locations are based on matchups. The shortest-route algorithm covered in this chapter is often applied to production planning and material handling problems. The max-flow algorithm covered in this chapter is often applied in material handling and logistics contexts, e.g., traffic planning. The minimal spanning tree has applications in facility planning. Linear programming and classical optimization, of course, can be applied in almost any context.

Mathematical Optimization and Modeling

There is a general procedure for any optimization problem:

General Optimization Procedure

• Isolate the decision variables and adopt symbols for them

• Express the objective as a function of the decision variables

• Express constraints as functions of the decision variables

• Examine the formulation to determine whether it fits a common model linear programming, one of the network models, etc.

• Simplify, e.g., by using equality constraints to eliminate variables, or ignoring inequality constraints known to be loose

• Solve

• Interpret the result. If the method yields the values of decision variables but not the value of the objective, it is nearly always beneficial to determine the objective value. Translate the results back to the context of the problem statement,...