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

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

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:

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

Production SchedulingP.C. Chang, IEM, YZU. 5 HW. Please solve the following problem using ATC and ATCS Rules. jpjpj djdj S ij

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)

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

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

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

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

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

Production SchedulingP.C. Chang, IEM, YZU. 12 Ex. jrjrj pjpj wjwj

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

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

Production SchedulingP.C. Chang, IEM, YZU. 15 HW. Use to solve the problem jrjrj pjpj wjwj

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

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

Production SchedulingP.C. Chang, IEM, YZU. 18 EX. jpjpj djdj SPT

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

Production SchedulingP.C. Chang, IEM, YZU. 20 EX.1 jpjpj djdj Stage 1 Step1. InitializeE={ }L=ψ Step2. Job 3 is the 1 st late job Step3. Job 2 is removed from E.E={ }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 (N T =2)

Production SchedulingP.C. Chang, IEM, YZU. 21 EX.2 jpjpj djdj 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}

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

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

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

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

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

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 1Empty jump 3‘ Final sequence is Job 1 enter Scheduled list 2 vs. 4 2 vs. 3 3 vs. 4 4 Enter 2 leave

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