1. Production SchedulingP.C. Chang, IEM, YZU. 1 How to schedule ?? How to find 1. an efficient Heuristic? 2. the optimal solution?

2. Production SchedulingP.C. Chang, IEM, YZU. 2 Composite priority rule that is mixture of 3 basic priority rules: ATC ( apparent tardiness rule ) is comb. of: 1. Weighted Shortest Processing Time First 2. Earliest Due Date First 3. Minimal slack ATCS ( ATC with setups ) 4. Shortest Setup Time First

3. Production SchedulingP.C. Chang, IEM, YZU. 3 Composite dispatching: Apparent Tardiness Cost (ATC) ATC combines MS rule and WSPT rule k1=due date scaling par. (look-ahead parameter) k 1 function of Due Date Range factor:

4. Production SchedulingP.C. Chang, IEM, YZU. 4 Composite dispatching: Apparent Tardiness Cost with Setups (ATCS) ATCS combines MS rule, WSPT rule and SST rule: k1=due date scaling par. k2=setup time scaling par. k 1 and k 2 functions of: Due Date tightness Due Date Range Setup Time Severity

5. Production SchedulingP.C. Chang, IEM, YZU. 5 HW. Please solve the following problem using ATC and ATCS Rules. jpjpj djdj 159 2310 3712 4618 525 S ij 12345 105723 250465 374034 426302 535420

6. Production SchedulingP.C. Chang, IEM, YZU. 6 Dispatching rules: multiple passes drawback of priority rules: may yield bad solutions SOLUTION: Use multiple passes Multi-pass priority rule based methods: 1. Multi-priority rule procedures (repeat dispatching procedure with different disp. rules) 2. Sampling procedures (each job has a probability to be dispatched)

7. Production SchedulingP.C. Chang, IEM, YZU. 7 Weighted Problem..............................

8. Production SchedulingP.C. Chang, IEM, YZU. 8 WSPT – Weighted SPT WSPT Sort from small to large.

9. Production SchedulingP.C. Chang, IEM, YZU. 9 Example SPT rule: WSPT rule: jpjpj wjwj p j /w j 1313 2221 3732.333 4522.5 2 5 10 17 = 34 2*2 5*1 10*2 17*3 = 80 2 9 14 17 = 42 2*2 9*3 14*2 17*1 = 76 412 3 412 3

10. Production SchedulingP.C. Chang, IEM, YZU. 10 Dynamic WSPT Problem: Problem Min Total Completion Time

11. Production SchedulingP.C. Chang, IEM, YZU. 11 Heuristic HP [Hariri and Potts] HP procedure Step1: Step2: Step3: Step4: Step5: EWSPT

12. Production SchedulingP.C. Chang, IEM, YZU. 12 Ex. jrjrj pjpj wjwj 1410.4 2980.6 3190.3 43100.7 52120.8 3 1 10

13. Production SchedulingP.C. Chang, IEM, YZU. 13 Is HP an optimum? Why? …

14. Production SchedulingP.C. Chang, IEM, YZU. 14 Heuristic PPC Step1: Step2: Step3: Step4: Step5:

15. Production SchedulingP.C. Chang, IEM, YZU. 15 HW. Use to solve the problem jrjrj pjpj wjwj 1410.4 2980.6 3190.3 43100.7 52120.8

16. Production SchedulingP.C. Chang, IEM, YZU. 16 For Another Tardiness Problems…

17. Production SchedulingP.C. Chang, IEM, YZU. 17 I.Smith Rule Baker p.26

18. Production SchedulingP.C. Chang, IEM, YZU. 18 EX. jpjpj djdj 1416 27 318 4621 539 42 8 15 21 153 SPT

19. Production SchedulingP.C. Chang, IEM, YZU. 19 II.Hodgson’s Algorithm Baker p.27 Sule p.37 [Minimize the number of tardy jobs.]

20. Production SchedulingP.C. Chang, IEM, YZU. 20 EX.1 jpjpj djdj 112 257 338 4913 5711 Stage 1 Step1. InitializeE={1-2-3-5-4}L=ψ Step2. Job 3 is the 1 st late job Step3. Job 2 is removed from E.E={1-3-5-4}L={2} Stage 2 Step1. Job 4 is the 1 st late job Step2. Job 4 is removed from E.E={1-3-5}L={2-4} Stage 3 Step1. No jobs in the E are late.An optimal sequence is 1-3-5-2-4(N T =2)

21. Production SchedulingP.C. Chang, IEM, YZU. 21 EX.2 jpjpj djdj 11015 2 25 3827 41232 52240 Step1. Select the 1 st job, T temp =T+10=10 < d 1, so S={1}, T= T temp =10 Step2. Examine job 2. T temp =10+15=25 ≦ d 2, so S={1,2} T= T temp =25 Step3. For job 3. T temp =25+8=33 > d 3, find job 2 with Max P in S ∵ d2>d3,so remove it, T=25-15=10, T temp =10+8=18 < d 3, so S={1,3}, T=T temp =18 Step4. For job 4 T temp =18+12=30 < d 4, so S={1,3,4} T= T temp =30 Step5. For job 5 T temp =52 > d 5, find job 4 with Max P in S, but d 4 <d 5, so job 5 is not selected. Step6. The Max number of jobs can be processed on time is three. And the sequence is {1,3,4}

22. Production SchedulingP.C. Chang, IEM, YZU. 22 III.Wilkerson-Irwin Baker p.30 N : Set of all jobs S : Scheduled set Q : Unscheduled set S ∪ Q = N ji S Q

23. Production SchedulingP.C. Chang, IEM, YZU. 23 Test two exception : or when Use SPT rule

24. Production SchedulingP.C. Chang, IEM, YZU. 24 S Q : the index of the last job on the schedule list : the index of the pivot job : the index of the first job on the unscheduled list

25. Production SchedulingP.C. Chang, IEM, YZU. 25 Test 0: Place all the jobs on the unscheduled list in EDD order Test 1:or if then jobandand repeat test 1,other wise test2 Test 2:and unscheduled list, and, and proceed to test 3 Test 3:or if and go to test 1&2 otherwise test 4 Test 4:and jump, remove

26. Production SchedulingP.C. Chang, IEM, YZU. 26 EX. j Pj=tjPj=tj djdj 156 278 369 4410 Stage 1-test 1: Stage 2- test 1: test 1 fail test 2: test 2 success 3 2 1 4… remove

27. Production SchedulingP.C. Chang, IEM, YZU. 27 EX. Stage 3-test 3: Stage 3’-test 1: fail test 2: success test 3:fail test 4:success stageScheduled listUnscheduled listDecision result 1Empty0-122-3-4 2151233-4 31-3113244jump 3‘151-42-3 41-494233 Final sequence is 1-4-3-2 Job 1 enter Scheduled list 2 vs. 4 2 vs. 3 3 vs. 4 4 Enter 2 leave

28. Production SchedulingP.C. Chang, IEM, YZU. 28 HW. Using Wilkerson & Irvine to solve n/1/ jtjtj djdj 1210 2714 3518 4620 5423