1. © J. Christopher Beck 20051 Lecture 18: Timetabling with Workforce Capacity

2. © J. Christopher Beck 2005 2 Outline Adding Workforce Capacity to Timetabling Examples 9.4.1, 9.4.2 Bin Packing Example 9.4.3, 9.4.4

3. © J. Christopher Beck 2005 3 Workforce Capacity n activities Processing time of activity j is p j No pre-emption An infinite number of resources Each activity requires W j workers You only have W workers Find a schedule that minimizes makespan

4. © J. Christopher Beck 2005 4 Example W = 10 Find a lower bound on the makespan Find minimum makespan schedule activities12345678910 pjpj 36711203158 WjWj 31062173499

5. © J. Christopher Beck 2005 5 Special Case: Exam Scheduling (Example 9.4.2) All exams have the same duration One exam room with capacity W Course j has W j students All students in course j must write the exam at the same time Find a timetable for all n exams in the minimum amount of time

6. © J. Christopher Beck 2005 6 Special Case = Bin Packing … Each bin has capacity = W W1W1 W2W2 W3W3 W4W4 W5W5 W6W6 W7W7 W8W8 Pack the objects into the bins to minimize the number of that are used

7. © J. Christopher Beck 2005 7 Special Case = Bin Packing … Each bin has capacity = W W1W1 W2W2 W3W3 W4W4 W5W5 W6W6 W8W8 Pack the objects into the bins to minimize the number of that are used W7W7

8. © J. Christopher Beck 2005 8 Example 9.4.3 Find a lower bound on the number of bins Find an upper bound on the number of bins Find a solution – is it optimal? activities1…67…1213…18 WjWj 3017011051 W = 2100

9. © J. Christopher Beck 2005 9 Bin Packing Heuristics First Fit (FF) Order items arbitrarily Put item into lowest number bin that it will fit into First Fit Descending (FFD) Order items in descending order Put item into lowest number bin that it will fit into

10. © J. Christopher Beck 2005 10 Example 9.4.3 Find FF solution Find FFD solution Is either solution optimal? activities1…67…1213…18 WjWj 3017011051 W = 2100

11. © J. Christopher Beck 2005 11 Example 9.4.4 Find LB & UB Find FF solution Find FFD solution Find optimal solution activities1…67…1213…1819…30 WjWj 501252251248 W = 1000