The due dates are: 10, 12, 15, 18, 20.
1.2. : * Define the decision variables: $x_ij = 1$ if job $j$ is scheduled on machine $i$, and $0$ otherwise. * Define the objective function: Minimize $\max_j (C_j - d_j)$, where $C_j$ is the completion time of job $j$ and $d_j$ is the due date of job $j$. * Define the constraints: + Each job can only be scheduled on one machine: $\sum_i x_ij = 1$ for all $j$. + Each machine can only process one job at a time: $\sum_j x_ij \leq 1$ for all $i$. + The completion time of job $j$ is the sum of the processing times of all jobs scheduled on the same machine: $C_j = \sum_i p_ij x_ij$. The due dates are: 10, 12, 15, 18, 20
4.3. : * Multiple objective functions (e.g., makespan, lateness, and flowtime). * Goal: Schedule the jobs on the machines to optimize multiple objectives. * Define the objective function: Minimize $\max_j (C_j
3.3. : * A set of jobs, each with a processing time on each machine and a routing that specifies the order in which the machines must be visited. * Goal: Schedule the jobs on the machines to minimize the makespan. + The completion time of job $j$ is
2.1. : * Sort the jobs in arrival order. * Schedule each job on the first available machine.
4.2. : * Jobs arrive dynamically over time. * Goal: Schedule the jobs on the machines to minimize the maximum lateness.
| Job | Start Time | Completion Time | Lateness | | --- | --- | --- | --- | | 3 | 0 | 1 | 0 | | 1 | 1 | 4 | 0 | | 4 | 4 | 8 | 0 | | 2 | 8 | 11 | 1 | | 5 | 11 | 14 | 6 |