Read the following cases separately and identify the scheduling problem in each case using the || notation taught in the class. Provide a very short explanation about each parameter , and in your answer. Your answer for each case will be like:

Case 1: A pharmaceutical company has a team of engineers that work together. This team can work on only one single project at a time (not more than one project simultaneously). Research projects arrive dynamically (with known arrival times). The duration required to work on each research project is known. There is a payment of oney paid to the company if project is completed before its deadline . There is also a precedence relation between the chosen projects.

Case 2: In a production factory, there are 8 press machines with different capabilities. Each one of these machines can be used to manufacture a sub-category items processed in this factory. Each job arrive at this factory will be pressed by only of the machines and then will be shipped to an assembly centers. We know that every day 120 jobs arrive in the factory at different times (known). On each day, for some of the machines, a breakdown period is already scheduled for the maintenance. We are interested in scheduling of these jobs on machines such that the number of tardy jobs is minimized.

Case 3: In an immigration office, there are 10 employees processing the applications of immigrants. Each one of these employees assesses one part of the applications. For example, employee #1 only checks the proof of payments for the applications. Employee #2 only checks the completeness of the whole application package. Employee #3 only checks whether a specific application form is correctly filled out or not. There are similar activities for other employees. Each application must be processed consecutively by employees #1, #2, , #10 with the same order and no matter what the output of the evaluation by employees 1 to is, the application must be processed by the remaining employees to 10 as well. There are different types of application packages arriving at the immigration center every day. We are interested in scheduling the processing of application packages such that the sum of their completion times is minimized.