1. 9-1 Applications

2. 9-2 Outline Moulding shop scheduling (MSS) Construction site scheduling (CSS)

3. 9-3 MSS: Problem definition (1) 2 types of cast-iron (standard and special) For each cast-iron type: –available quantity every hour

4. 9-4 MSS: Problem definition (2) 3 moulding machines For each machine: –shifts –breaks (lunch, maintenance) –periods during which the machine can manufacture only some types of parts

5. 9-5 MSS: Problem definition (3) 30 types of parts For each part type: –cast-iron type –one or more possible machines For each (part, machine) pair: –production speed –cast-iron consumption –minimal and maximal batch size –maximal break duration (one break per batch allowed) –minimal production time before and after the break

6. 9-6 MSS: Problem definition (4) 200 orders for parts For each order: –part type –number of parts –due-date Optimization criterion –relaxation of due-dates –closer due-dates are more important than further due-dates

7. 9-7 MSS: Problem representation (1) Part type  Discrete resource –Produced by activities –Due-dates  minimal production constraints Machine  State resource –Part type produced at time t  state at time t –Default state 0 out of shifts and during breaks Cast-iron type  Energetic resource

8. 9-8 MSS: Problem representation (2) Minimal and maximal number of (ordered) batches for each (part, machine) pair Batch  3 Interval activities –BB before the break, B for the break, AB after the break –end(BB)  start(B) and end(B)  start(AB) –duration(BB) not in [1, minimal-duration-before-break  1] –duration(AB) not in [1, minimal-duration-after-break  1] –duration(B)  maximal-break-duration –batch-duration  duration(BB)  duration(AB) –batch-duration  maximal-batch-size / production-rate –batch-duration not in [1, (minimal-batch-size  1) / production-rate]

9. 9-9 MSS: Problem representation (3) Resource constraints –BB and AB require the machine in the "part type" state –BB and AB require the cast-iron at the given consumption rate –B requires the machine in the state 0 –AB produces the batch of parts (batch-duration  production-rate units of the part type) Redundant constraints –From start(BB) to end(AB), the state of the machine is either 0 or "part-type" –Counter of the minimal and maximal production of each part type each day

10. 9-10 MSS: Search procedure Select a batch with unbound start time or unbound duration –If the batch is optional: either confirm or cancel the batch –Else if the start time is unbound: either schedule (ASAP) or postpone the batch –Else (the duration is unbound): instantiate the duration Iterate

11. 9-11 MSS: Heuristics Heuristics applied in lexicographical order –Minimal earliest start time –Minimal latest start time –Minimal number of possible machines for the corresponding part –Highest user-defined priority

12. 9-12 MSS: Results 2200 lines of ILOG SCHEDULE source code –1400 lines for representing the problem –600 lines for reading the data –200 lines for solving the problem Executable –880K on an IBM RS600 –420K on a SUN-4 CPU time (for 300 non-zero activities and 40 resources) –In most cases: 10 seconds –When more: search is stopped and restarted with relaxed due-dates

13. 9-13 CSS: Problem definition Resource-constrained project scheduling problem with: –1 unary resource and 3 discrete resources –15 interval activities and 15 preemptable activities –15 activities with time-versus-capacity tradeoffs –10 activities with variable requirements over time –temporal constraints –periods during which a resource is not or not fully available –percentage constraints –synchronization constraints –40 preference constraints (10 levels of preferences)

14. 9-14 CSS: Problem representation Preemptive scheduling library developed in CLAIRE Based on the mixed edge finding technique for unary resources Based on time-tables for discrete resources

15. 9-15 CSS: Search procedure Select preferences Impose the selected preferences as constraints Search for a solution within a limited number of backtracks (blend of preemptive job-shop scheduling and resource-constrained project scheduling) Save the solution if one is found Iterate with a different set of preferences

16. 9-16 CSS: Results 2200 lines of CLAIRE source code (  2200 lines library) –1100 lines for representing the problem –300 lines for reading the data –800 lines for solving the problem 3000 lines for the graphical interface Executable –1130K on a PC under OS2 (with graphical interface) CPU time (for 30 activities and 4 resources) –"Good" schedules obtained in 5 to 10 iterations –15 seconds per iteration