Top-T shirt company imprints T-shirts with cartoons and celebrity photographs. For each of their 4 pending contracts, the following table shows the number of days of production required, the earliest day the order can begin, and the day the order is due.

1 2 3 4 Production 10 3 16 8 Earliest 0 20 1 12 Due Date 12 30 20 21 The company wants to design an optimal schedule assuming that contracts can be processed in any sequence but that production cannot be interrupted once a job has started.

(a) Ignoring objective functions for the moment, formulate constraints of a single-

machine ILP to select an optimal start time for each contract.

(b) Evaluate each of the 8 objective function in principle 11.37 for the schedule with start times 2, 20, 23, and 12 for the four contracts, respectively.

(c) Extend your constraints of part

(a) to formulate an ILP to compute a minimum mean completion time schedule.

(d) Use class optimization software to solve your ILP of part (c).

(e) Without actually solving, list the other objective functions of 11.37 for which your schedule of part

(d) must be optimal.

(f) Extend your constraints of part

(a) to formulate an ILP to compute a minimum maximum lateness schedule.
(g) Use class optimization software to solve your ILP of part (f).
(h) Without actually solving, list the other objective functions of 11.37 for which your schedule of part (g) must be optimal.