1.1. Consider a flexible flow shop environment. Whenever a job has to wait before it can start its processing at the next stage it is regarded as Work-In-Process (WIP), since it already has received processing on machines upstream. The costs associated with WIP are storage costs, amount of value already added, and so on. Explain why high WIP costs may postpone the starting times of jobs on certain machines.

1.2. Consider an airport terminal with a number of gates. Planes arrive and depart according to a fixed schedule. Upon arrival a plane has to be assigned to a gate in a way that is convenient for the passengers as well as for the airport personnel. Certain gates are only capable of handling narrowbody planes. Model this problem as a machine scheduling problem. (a) Specify the machines and the processing times. (b) Describe the processing restrictions and constraints, if any. (c) Formulate an appropriate objective function.

1.3. Consider the reservation system in a hotel. People call in to make reservations. Model the problem as a machine scheduling problem. (a) What are the machines? (b) Are all the machines identical? (c) What are the jobs and what are their processing times? (d) Formulate an appropriate objective for the hotel to optimize.