**Summary**

This chapter provides an overview of Operations Research and its mathematical models for planning problems arising in the area of services. For a better understanding, a basic introduction into the field of Operations Research is given. Different examples from service areas are presented. Several methods for solving the mathematical problems are discussed. In addition, the optimization software called IBM ILOG CPLEX Optimization Studio is presented that can be used to determine an optimal solution for a mathematical problem. The use of simulation in the area of Operations Research is also discussed and the software AnyLogic is used to provide examples.

<math> <mrow> <mn>2</mn><mo>+</mo><mn>2</mn> <mo>=</mo><mn>4</mn> </mrow> </math>

**Review Section**

1. (Foundations) Explain the idealized planning process in your own words and use an example to illustrate the steps.

2. (Foundations) Give a generic formulation for a linear and a mixed integer linear program.

3. (Foundations) Explain the difference between an exact approach and a heuristic and give examples for both.

4. (Bin Packing) Find a sequence of items such that the two heuristics First Fit and Best Fit yield different bin assignments for those items. Try to use as few items as possible.

5. (Queuing) Consider a doctor’s practice operating under the walk-in policy just as in the example. Let us assume the following parameters: arrival rate &lambda 5 per hour (exponentially distributed inter-arrival times), service rate