1. 15-1Scheduling Operations Scheduling Chapter 8

2. 15-2Scheduling The Hierarchy of Production Decisions The logical sequence of operations in factory planning corresponds to the sequencing of chapters in a production management text book.  All planning starts with the demand forecast.  Demand forecasts are the basis for the top level (aggregate) planning.  The Master Production Schedule (MPS) is the result of disaggregating aggregate plans down to the individual item level.  Based on the MPS, MRP is used to determine the size and timing of component and subassembly production.  Detailed shop floor schedules are required to meet production plans resulting from the MRP.

3. 15-3Scheduling Hierarchy of Production Decisions

4. 15-4Scheduling Detailed production schedule A detailed production schedule must include when and where each activity must take place in order to meet the master schedule.

5. 15-5Scheduling Scheduling Service Operations Vs Manufacturing Operations Scheduling service systems presents certain problems not generally encountered in manufacturing systems. This is primarily due to: 1. The inability to store services 2. The random nature of customer requests To avoid problems such as long delays, unsatisfied customers, service systems rely on appoinment systems and reservation systems.

6. 15-6Scheduling Goals of Production Scheduling  High Customer Service: on-time delivery  Low Inventory Levels: WIP and FGI  High Utilization: of machines and labor

7. 15-7Scheduling Measures to Evaluate Performance of a Scheduling Method  Service Level: Fraction of orders filled on before their due dates (used in make- to-order systems)  Fill Rate: Fraction of demand that are met from inventory without backorder (used in make-to-stock systems)  Job Flow Time: Time elapsed from the release of a job until it is completed.

8. 15-8Scheduling Measures to Evaluate Performance of a Scheduling Method  Lateness: Difference between completion time and due date of a job (may be negative).  Tardiness: The positive difference between the completion time and the due date of a job.  Makespan: The total length of the schedule (that is, when all the jobs have finished processing).

9. 15-9Scheduling Reducing WIP and Flow Time  Shorter flow time means:  Less WIP  Better responsiveness All of which reduce costs and improve sales revenue

10. 15-10Scheduling Measures to Evaluate Performance of a Scheduling Method  Production Rate  Utilization Keep in mind that high utilization means high return on investment. This is good provided that the equipment is utilized to increase revenue. Otherwise, high utilization only helps to increase inventory, not profits.

11. 15-11Scheduling Types of Production Systems  High Volume Systems (Mass Production) -Continous Production (petroleum refining, sugar refining) -Discrete Production (autos, personal computers, televisons)  Intermediate-Volume Systems (Batch production)  Low-Volume Systems (Job-Shops)

12. 15-12Scheduling High-Volume Systems  Flow system: High-volume system with Standardized equipment and activities Work Center #1Work Center #2 Output

13. 15-13Scheduling High-Volume Systems  High-volume systems are often referred to as flow systems; scheduling in these systems is referred to as flow-shop scheduling. Major aspects of system design include line balancing and flow system design.

14. 15-14Scheduling High-Volume Systems  Line balancing concerns allocating the required tasks to workstations so that they satisfy technical (sequencing) constraints and are balanced with respect to equal work times among stations.  It results in the maximum utilization of equipment and personnel as well as the highest possible rate of output.

15. 15-15Scheduling Intermediate-Volume Systems  Outputs are between standardized high- volume systems and made-to-order job shops  The volume of output is not large enough to justify continuous production.  Examples include canned foods, paint and cosmetics.

16. 15-16Scheduling Intermediate-Volume Systems The three basic issues in these systems are: 1.Run size, 2.Timing, and 3.Sequence of jobs  Economic run size: h’ is defined as h’= h(1- λ/P)

17. 15-17Scheduling Scheduling Low-Volume Systems  Loading - assignment of jobs to process centers  Sequencing - determining the order in which jobs will be processed  Job-shop scheduling  Scheduling for low-volume systems with many variations in requirements

18. 15-18Scheduling Gantt charts  Gantt charts are used as visual aid for loading and scheduling purposes.  The name was derived from Henry Gantt in the early 1900s.  The purpose of Gantt charts is to organize the use of resources in a time framework.  In most cases, a time scale is represented horizontally, and resources to be scheduled are listed vertically.

19. 15-19Scheduling Gantt Load Chart  Gantt chart - used as a visual aid for loading and scheduling Figure 15.2

20. 15-20Scheduling 20 Loading

21. 15-21Scheduling LOADING (The Assignment Problem)  In many business situations, management needs to assign - personnel to jobs, - jobs to machines, - machines to job locations, or - salespersons to territories.  Consider the situation of assigning n jobs to n machines.  When a job i (=1,2,....,n) is assigned to machine j (=1,2,.....n) that incurs a cost C ij.  The objective is to assign the jobs to machines at the least possible total cost.

22. 15-22Scheduling The Assignment Problem  This situation is a special case of the Transportation Model and it is known as the assignment problem.  Here, jobs represent “sources” and machines represent “destinations.”  The supply available at each source is 1 unit and demand at each destination is 1 unit.

23. 15-23Scheduling The Assignment Problem The assignment model can be expressed mathematically as follows: Xij= 0, if the job j is not assigned to machine i 1, if the job j is assigned to machine i

24. 15-24Scheduling The Assignment Problem

25. 15-25Scheduling The Assignment Problem Example  Ballston Electronics manufactures small electrical devices.  Products are manufactured on five different assembly lines (1,2,3,4,5).  When manufacturing is finished, products are transported from the assembly lines to one of the five different inspection areas (A,B,C,D,E).  Transporting products from five assembly lines to five inspection areas requires different times (in minutes)

26. 15-26Scheduling The Assignment Problem Example  Ballston Electronics manufactures small electrical devices.  Products are manufactured on five different assembly lines (1,2,3,4,5).  When manufacturing is finished, products are transported from the assembly lines to one of the five different inspection areas (A,B,C,D,E).  Transporting products from five assembly lines to five inspection areas requires different times (in minutes)

27. 15-27Scheduling The Assignment Problem Example Under current arrangement, assignment of inspection areas to the assembly lines are 1 to A, 2 to B, 3 to C, 4 to D, and 5 to E. This arrangement requires 10+7+12+17+19 = 65 man minutes.

28. 15-28Scheduling The Assignment Problem Example  Management would like to determine whether some other assignment of production lines to inspection areas may result in less cost.  This is a typical assignment problem. n = 5 And each assembly line is assigned to each inspection area.  It would be easy to solve such a problem when n is 5, but when n is large all possible alternative solutions are n!, this becomes a hard problem.

29. 15-29Scheduling The Assignment Problem Example  Assignment problem can be either formulated as a linear programming model, or it can be formulated as a transportation model.  However, An algorithm known as Hungarian Method has proven to be a quick and efficient way to solve such problems.  This technique is programmed into many computer modules such as the one in WINQSB.

30. 15-30Scheduling The Assignment Problem Example WINQSB solution for this problem is as follows:

31. 15-31Scheduling Sequencing  Sequencing: Determine the order in which jobs at a work center will be processed.  Workstation: An area where one person works, usually with special equipment, on a specialized job.

32. 15-32Scheduling Common Sequencing Rules  FCFS. First Come First Served. Jobs processed in the order they come to the shop.  SPT. Shortest Processing Time. Jobs with the shortest processing time are scheduled first.  EDD. Earliest Due Date. Jobs are sequenced according to their due dates.  CR. Critical Ratio. Compute the ratio of processing time of the job and remaining time until the due date. Schedule the job with the largest CR value next.

33. 15-33Scheduling Sequencing n jobs on a Single Machine Priority rules: Simple heuristics such as FCFS, SPT, DD, CR are used to select the order in which jobs will be processed. CR= (Due Date – Current Time)/ Processing Time

34. 15-34Scheduling Example: Sequencing Rules Use the FCFS, SPT, and Critical Ratio rules to sequence the five jobs below. Evaluate the rules on the bases of average flow time, average number of jobs in the system, and average job lateness. (Due Date) Job Processing TimeTime to Promised Completion A 6 hours10 hours B 1216 C 9 8 D 1414 E 8 7

35. 15-35Scheduling Example: Sequencing Rules  FCFS RuleA > B > C > D > E Processing Due Flow JobTime Date Time Lateness A 6 10 6 0 B 12 16 18 2 C 9 8 27 19 D 14 14 41 27 E 8 7 49 42 49 141 90

36. 15-36Scheduling Example: Sequencing Rules  FCFS Rule Performance  Average flow time: 141/5 = 28.2 hours  Average number of jobs in the system: 141/49 = 2.88 jobs  Average job lateness: 90/5 = 18.0 hours

37. 15-37Scheduling Example: Sequencing Rules  SPT RuleA > E > C > B > D Processing Due Flow JobTime Date Time Lateness A 6 10 6 0 E 8 714 7 C 9 823 15 B 12 1635 19 D 14 1449 35 49 127 76

38. 15-38Scheduling Example: Sequencing Rules  SPT Rule Performance  Average flow time: 127/5 = 25.4 hours  Average number of jobs in the system: 127/49 = 2.59 jobs  Average job lateness: 76/5 = 15.2 hours

39. 15-39Scheduling Example: Sequencing Rules  Critical Ratio RuleE > C > D > B > A Processing Promised Flow JobTime Completion Time Lateness E (.875) 8 7 8 1 C (.889) 9 8 17 9 D (1.00) 14 14 31 17 B (1.33) 12 16 43 27 A (1.67) 6 10 49 39 49 14893

40. 15-40Scheduling Example: Sequencing Rules  Critical Ratio Rule Performance  Average flow time: 148/5 = 29.6 hours  Average number of jobs in the system: 148/49 = 3.02 jobs  Average job lateness: 93/5 = 18.6 hours

41. 15-41Scheduling Example: Sequencing Rules  Comparison of Rule Performance Average AverageAverage Flow Number of Jobs Job Rule Time in System Lateness FCFS 28.2 2.88 18.0 SPT 25.4 2.59 15.2 CR 29.6 3.02 18.6 SPT rule was superior for all 3 performance criteria.

42. 15-42Scheduling Sequencing n jobs on two machines  Johnson’s Rule: technique for minimizing completion time for a group of n jobs to be processed on two machines or at two work centers.  Minimizes total idle time  Johnson’s Rule requires satisfying the following conditions:

43. 15-43Scheduling Johnson’s Rule Conditions  Job time must be known and constant  Job times must be independent of sequence  Jobs must follow same two-step sequence  Job priorities cannot be used  All units must be completed at the first work center before moving to second

44. 15-44Scheduling Johnson’s Rule Optimum Sequence 1. List the jobs and their times at each work center 2. Find the smallest processing time. If it belongs to the first operation of a job schedule that job next, otherwise schedule that job last. 3. Eliminate the job from further consideration 4. Repeat steps 2 and 3 until all jobs have been scheduled

45. 15-45Scheduling Johnson’s Algorithm Example  Data:  Iteration 1: min time is 4 (job 1 on M1); place this job first and remove from lists:

46. 15-46Scheduling Johnson’s Algorithm Example (cont.)  Iteration 2: min time is 5 (job 3 on M2); place this job last and remove from lists:  Iteration 3: only job left is job 2; place in remaining position (middle).  Final Sequence: 1-2-3  Makespan: 28

47. 15-47Scheduling Gantt Chart for Johnson’s Algorithm Example Short task on M1 to “load up” quickly. Short task on M2 to “clear out” quickly.

48. 15-48Scheduling 48 Example A group of six jobs is to be processed through a two-machine flow shop. The first operation involves cleaning and the second involves painting. Determine a sequence that will minimize the total completion time for this group of jobs. Processing times are as follows:

49. 15-49Scheduling 49 Select the job with the shortest processing time. It is job D, with a time of two hours. Since the time is at the first center, schedule job D first. Eliminate job D from further consideration. Job B has the next shortest time. Since it is at the second work center, schedule it last and eliminate job B from further consideration. We now have The remaining jobs and their times are

50. 15-50Scheduling http://www.baskent.edu.tr/~kilter 50 The shortest remaining time is six hours for job E at work center 1. Thus, schedule that job toward the beginning of the sequence (after job D). Thus, Job C has the shortest time of the remaining two jobs. Since it is for the first work center, place it third in the sequence. Finally, assign the remaining job (F) to the fourth position and the result is

51. 15-51Scheduling Scheduling Difficulties  Randomness in job arrival times  Variability in  Setup times  Processing times  Interruptions  Changes in the set of jobs  No method for identifying optimal schedule  Scheduling is not an exact science  Ongoing task for a manager

52. 15-52Scheduling Classic Dispatching Results  Optimal Schedules: Impossible to find for most real problems.  Dispatching: sorts jobs as they arrive at a machine.  Dispatching rules:  FIFO – simplest, seems “fair”.  SPT – Actually works quite well with tight due dates.  EDD – Works well when jobs are mostly the same size.  Many (100?) others.  Problems with Dispatching:  Cannot be optimal (can be bad).  Tends to be myopic.

53. 15-53Scheduling The Difficulty of Scheduling Problems  Dilemma:  Too hard for optimal solutions.  Need something anyway.  Classifying “Hardness”:  Class P: has a polynomial solution.  Class NP: has no polynomial solution.  Example: Sequencing problems grow as n!.  Compare e n /10000 and 10000n 10.  At n = 40, e n /10000 = 2.4  10 13, 10000n 10 = 1.0  10 20  At n = 80, e n /10000 = 5.5  10 30, 10000n 10 = 1.1  10 23  3! = 6, 4! = 24, 5! = 120, 6! = 720, … 10! =3,628,800, while 13! = 6,227,020,800 25!= 15,511,210,043,330,985,984,000,000 e n /10000 10000n 10

54. 15-54Scheduling The Difficulty of Scheduling Problems  NP stands for non polynomial, meaning that the time required to solve such problems is an exponential function of the number of jobs rather than a polynomial function.  The problems for which total enumeration is hopeless are known in mathematics as NP hard.

55. 15-55Scheduling Computation Times  Current situation: Suppose computer can examine 1,000,000 sequences per second and we wish to build a scheduling system that has response time of no longer than one minute. How many jobs can we sequence optimally?

56. 15-56Scheduling Effect of Faster Computers  Future Situation: New computer is 1,000 times faster, i.e. it can do 1 billion comparisons per second. How many jobs can we sequence optimally now?

57. 15-57Scheduling Implications for Real Problems  Violation of Assumptions: Most “real-world” scheduling problems violate the assumptions made in the classic literature:  There are always more than two machines.  Process times are not deterministic.  All jobs are not ready at the beginning of the problem.  Process time are sequence dependent.  Problem Difficulty: Most “real-world” production scheduling problems are NP-hard.  We cannot hope to find optimal solutions of realistic sized scheduling problems.  Polynomial approaches, like dispatching, may not work well.

58. 15-58Scheduling Implications for Real Problems (cont.)  Heuristic Approaches can be used to obtain “good” solutions for real-world problems.  Examples of most commonly used meta- heuristics include:  Simulated Annealing  Tabu Search  Genetic Algorithms