1. Scheduling Operations Management - 5 th Edition Chapter 16 Roberta Russell & Bernard W. Taylor, III

2. 16-2 Lecture Outline   Objectives in Scheduling   Loading / Assignment   Sequencing   Monitoring   Theory of Constraints   Employee Scheduling

3. 16-3 What is Scheduling?  Last stage of planning before production occurs  Specifies when labor, equipment, facilities are needed to produce a product or provide a service

4. 16-4 Another Definition of Scheduling  Scheduling concerns the allocation of limited resources to tasks over time. It is a decision-making process that has as a goal the optimization of one or more objectives  Michael Pinedo – Scheduling: Theory, Algorithms, and Systems

5. 16-5 Scheduled Operations  Process Industry Linear programming Linear programming EOQ with non-instantaneous replenishment EOQ with non-instantaneous replenishment  Mass Production Assembly line balancing Assembly line balancing  Project Project -scheduling techniques (PERT, CPM) Project -scheduling techniques (PERT, CPM)  Batch Production Aggregate planning Aggregate planning Master scheduling Master scheduling Material requirements planning (MRP) Material requirements planning (MRP) Capacity requirements planning (CRP) Capacity requirements planning (CRP)

6. 16-6 Objectives in Scheduling  Meet customer due dates  Minimize job lateness  Minimize response time  Minimize completion time  Minimize time in the system  Minimize overtime  Maximize machine or labor utilization  Minimize idle time  Minimize work-in- process inventory

7. 16-7 Shop Floor Control  Loading Check availability of material, machines and labor Check availability of material, machines and labor  Sequencing Release work orders to shop and issue dispatch lists for individual machines Release work orders to shop and issue dispatch lists for individual machines  Monitoring Maintain progress reports on each job until it is complete Maintain progress reports on each job until it is complete

8. 16-8 Loading  Process of assigning work to limited resources  Perform work on most efficient resources  Use assignment method of linear programming to determine allocation

9. 16-9 Assignment Problem Example  WebStar, Inc. has 4 projects to complete  They have 4 programmers, each with varying degrees of expertise  On average, it costs $100 per hour  Assign a single worker to a single project in order to minimize total cost Processing PROJECT Estimates (hr)1234 Bryan105610 Kari6246 Noah7656 Chris95410

10. 16-10 Formulation  Indices i = project index i = project index j = worker index j = worker index n = total number of projects (and workers) n = total number of projects (and workers)  DATA COST ij = cost of having project i assigned to worker j COST ij = cost of having project i assigned to worker j  Variables x ij = indicates if project i assigned to worker j x ij = indicates if project i assigned to worker j totcost = total cost of assignments totcost = total cost of assignments

11. 16-11 Formulation, cont’d.  Objective min totcost = min totcost =  Constraints for i = 1, …, n for i = 1, …, n (assign only one worker to a project) for j = 1, …, n for j = 1, …, n (assign only one project to a worker) x ij binary x ij binary

12. 16-12 Another Example  Spring Weekend is coming up and Joe has 3 commitments to keep: Go out one night with his girlfriend Go out one night with his girlfriend Go out one night with his UConn friends Go out one night with his UConn friends Go out one night with his HS friends Go out one night with his HS friends  He has estimated his costs for each commitment as shown on the next slide  Help Joe decide which night he should spend with each group of friends

13. 16-13 Joe’s Costs Girlfriend UConn Friends HS Friends Thursday$30$50$100 Friday$40$60$90 Saturday$50$50$80

14. 16-14 Joe’s Dilemma Formulated  Let ??? ???  Objective Function ??? ???  Subject to ??? ???

15. 16-15 Sequencing  Prioritize jobs assigned to a resource  If no order specified use first-come first-served (FCFS)  Many other sequencing rules exist  Each attempts to achieve an objective

16. 16-16 Sequencing Rules  FCFS - first-come, first-served  LCFS - last come, first served  DDATE - earliest due date  CUSTPR - highest customer priority  SETUP - similar required setups  SLACK - smallest slack  CR - critical ratio  SPT - shortest processing time  LPT - longest processing time

17. 16-17 Critical Ratio Rule CR considers both time and work remaining CR = = If CR > 1, job ahead of schedule If CR < 1, job behind schedule If CR = 1, job on schedule time remainingdue date - today’s date work remainingremaining processing time

18. 16-18 Sequencing Jobs Through One Process  Flowtime (completion time) Time for a job to flow through the system Time for a job to flow through the system  Makespan Time for a group of jobs to be completed Time for a group of jobs to be completed  Tardiness Difference between a late job’s due date and its completion time Difference between a late job’s due date and its completion time

19. 16-19 Sequencing Jobs Through Two Serial Process Johnson’s Rule 1.List time required to process each job at each machine. Set up a one-dimensional matrix to represent desired sequence with # of slots equal to # of jobs. 2.Select smallest processing time at either machine. If that time is on machine 1, put the job as near to beginning of sequence as possible. 3.If smallest time occurs on machine 2, put the job as near to the end of the sequence as possible. 4.Remove job from list. 5.Repeat steps 2-4 until all slots in matrix are filled and all jobs are sequenced.

20. 16-20 Johnson’s Rule JOBPROCESS 1PROCESS 2 A68 B116 C73 D97 E510 C E A B D

21. 16-21 Johnson’s Rule (cont.) ABCDE EADBC Process 1 (sanding)511203138 EADBC Process 2 (painting) 51523303741 Idle time Completion time = 41 Idle time = 5+1+1+3=10

22. 16-22 Guidelines for Selecting a Sequencing Rule  SPT most useful when shop is highly congested  Use SLACK for periods of normal activity  Use DDATE when only small tardiness values can be tolerated  Use LPT if subcontracting is anticipated  Use FCFS when operating at low-capacity levels  Do not use SPT to sequence jobs that have to be assembled with other jobs at a later date

23. 16-23 Monitoring  Work package Shop paperwork that travels with a job Shop paperwork that travels with a job  Gantt Chart Shows both planned and completed activities against a time scale Shows both planned and completed activities against a time scale  Input/Output Control Monitors the input and output from each work center Monitors the input and output from each work center

24. 16-24 Theory of Constraints  Not all resources are used evenly  Concentrate on the “bottleneck” resource  Synchronize flow through the bottleneck  Use process and transfer batch sizes to move product through facility

25. 16-25 TOC Scheduling Procedure   Identify bottleneck   Schedule job first whose lead time to the bottleneck is less than or equal bottleneck processing time   Forward schedule the bottleneck machine   Backward schedule the other machines to sustain the bottleneck schedule   Transfer in batch sizes smaller than the process batch size

26. 16-26 Employee Scheduling  Labor is very flexible resource  Scheduling workforce is complicated repetitive task  Assignment method can be used  Heuristics are commonly used

27. 16-27 Employee Scheduling Heuristic 1.Let N = no. of workers available D i = demand for workers on day i X = day working O = day off 2.Assign the first N - D 1 workers day 1 off. Assign the next N - D 2 workers day 2 off. Continue in a similar manner until all days are have been scheduled 3.If number of workdays for full time employee < 5, assign remaining workdays so consecutive days off are possible 4.Assign any remaining work to part-time employees 5.If consecutive days off are desired, consider switching schedules among days with the same demand requirements

28. 16-28 DAY OF WEEKMTWTHFSASU MIN NO. OF WORKERS REQUIRED3343453 HomerMargeBartLisaMaggie Employee Scheduling

29. 16-29 DAY OF WEEKMTWTHFSASU MIN NO. OF WORKERS REQUIRED3343453 HomerOXXOXXX MargeOXXOXXX BartXOXXOXX LisaXOXXXXO MaggieXXOXXXO Completed schedule satisfies requirements but has no consecutive days off Employee Scheduling (cont.)

30. 16-30 Employee Scheduling (cont.) DAY OF WEEKMTWTHFSASU MIN NO. OF WORKERS REQUIRED3343453 HomerOOXXXXX MargeOOXXXXX BartXXOOXXX LisaXXXOXXO MaggieXXXXOXO Revised schedule satisfies requirements with consecutive days off for most employees