© 2006 Prentice Hall, Inc.15 – 1 Operations Management Chapter 15 – Short-Term Scheduling © 2006 Prentice Hall, Inc. PowerPoint presentation to accompany Heizer/Render Operations Management, 8e

© 2006 Prentice Hall, Inc.15 – 2 Strategic Importance of Short-Term Scheduling  Effective and efficient scheduling can be a competitive advantage  Faster movement of goods through a facility means better use of assets and lower costs  Additional capacity resulting from faster throughput improves customer service through faster delivery  Good schedules result in more reliable deliveries

© 2006 Prentice Hall, Inc.15 – 3 Scheduling Decisions Organization Managers Must Schedule the Following Arnold Palmer Hospital Operating room use Patient admissions Nursing, security, maintenance staffs Outpatient treatments University of Missouri Classrooms and audiovisual equipment Student and instructor schedules Graduate and undergraduate courses Lockheed-Martin factory Production of goods Purchases of materials Workers Hard Rock Cafe Chef, waiters, bartenders Delivery of fresh foods Entertainers Opening of dining areas Delta Airlines Maintenance of aircraft Departure timetables Flight crews, catering, gate, ticketing personnel Table 15.1

© 2006 Prentice Hall, Inc.15 – 4 Defining Scheduling  Scheduling deals with the assignment of activities to resources (and vice- versa) and timing of activities  Types of scheduling situations  Type I: Supply options (M) are fewer than demand options (N)  Type II: Supply options (M) are equal to demand options (N)  Type III: Supply options (M) exceed the number of demand options (N)

© 2006 Prentice Hall, Inc.15 – 5 Figure 15.1 Positioning Scheduling

© 2006 Prentice Hall, Inc.15 – 6 Objectives of Scheduling  Goals of scheduling  Type I: Supply options (M) are fewer than demand options (N)  Assign scarce supply to demand to minimize cost or maximize benefits  Type II: Supply options (M) are equal to demand options (N)  Assign supply to demand to minimize cost or maximize benefits for total process  Type III: Supply options (M) exceed the number of demand options (N)  Scheduling is done for limited capacity and excess capacity is outsourced.

© 2006 Prentice Hall, Inc.15 – 7 Scheduling Methods  Types of scheduling methods  Arbitrary approaches  Useful when there are no constraints of resources  Rule-based approaches  Useful when there are constraints of resources  Priorities-based approaches  Useful when there are constraints of resources and there are priorities among suppliers or customers

© 2006 Prentice Hall, Inc.15 – 8 Assignment Method (Type II Scheduling)  A special class of linear programming models that assign tasks or jobs to resources  Objective is to minimize cost or time  Only one job (or worker) is assigned to one machine (or project)

© 2006 Prentice Hall, Inc.15 – 9 Assignment Method 1.Create zero opportunity costs by repeatedly subtracting the lowest costs from each row and column 2.Draw the minimum number of vertical and horizontal lines necessary to cover all the zeros in the table. If the number of lines equals either the number of rows or the number of columns, proceed to step 4. Otherwise proceed to step 3. 3.Subtract the smallest number not covered by a line from all other uncovered numbers. Add the same number to any number at the intersection of two lines. Return to step 2. 4.Optimal assignments are at zero locations in the table. Select one, draw lines through the row and column involved, and continue to the next assignment.

© 2006 Prentice Hall, Inc.15 – 10 Assignment Example ABC Job R-34$11$14$ 6 S-66$ 8$10$11 T-50$ 9$12$ 7 Typesetter ABC Job R-34$ 5$ 8$ 0 S-66$ 0$ 2$ 3 T-50$ 2$ 5$ 0 Typesetter Step 1a - Rows ABC Job R-34$ 5$ 6$ 0 S-66$ 0$ 0$ 3 T-50$ 2$ 3$ 0 Typesetter Step 1b - Columns

© 2006 Prentice Hall, Inc.15 – 11 Assignment Example Step 2 - Lines ABC Job R-34$ 5$ 6$ 0 S-66$ 0$ 0$ 3 T-50$ 2$ 3$ 0 Typesetter Because only two lines are needed to cover all the zeros, the solution is not optimal Step 3 - Subtraction ABC Job R-34$ 3$ 4$ 0 S-66$ 0$ 0$ 5 T-50$ 0$ 1$ 0 Typesetter The smallest uncovered number is 2 so this is subtracted from all other uncovered numbers and added to numbers at the intersection of lines

© 2006 Prentice Hall, Inc.15 – 12 Assignment Example Because three lines are needed, the solution is optimal and assignments can be made Step 2 - Lines ABC Job R-34$ 3$ 4$ 0 S-66$ 0$ 0$ 5 T-50$ 0$ 1$ 0 Typesetter Start by assigning R-34 to worker C as this is the only possible assignment for worker C. Step 4 - Assignments ABC Job $ 3$ 4 R-34$ 3$ 4$ 0 $ 0$ 5 S-66$ 0$ 0$ 5 $ 1$ 0 T-50$ 0$ 1$ 0 Typesetter Job T-50 must go to worker A as worker C is already assigned. This leaves S-66 for worker B.

© 2006 Prentice Hall, Inc.15 – 13 Assignment Example Step 4 - Assignments ABC Job $ 3$ 4 R-34$ 3$ 4$ 0 $ 0$ 5 S-66$ 0$ 0$ 5 $ 1$ 0 T-50$ 0$ 1$ 0 Typesetter From the original cost table Minimum cost = $6 + $10 + $9 = $25 ABC Job R-34$11$14$ 6 S-66$ 8$10$11 T-50$ 9$12$ 7 Typesetter

© 2006 Prentice Hall, Inc.15 – 14 Opportunity Loss: Assignment Example 2 ABC Job R-34$11$14$ 6 S-66$ 8$10$11 T-50$ 9$12$ 7 Typesetter ABC Job R S T Typesetter Opportunity Loss Table ABC Job R-34$ 4$ 1$ 9 S-66$ 7$ 5$ 4 T-50$ 5$ 2$ 7 Typesetter Assume sale price for units made on each Resource are: R-34 = $ 15 /unit; S-66 = $ 15 /unit; T-50 = $ 14 /unit; Opportunity Loss Table

© 2006 Prentice Hall, Inc.15 – 15 Opportunity Loss: Assignment Example 2 The table has profit margins that are earned for each unit made. To find the optimal assignment, use the method but subtract the highest score of each row not the least one. ABC Job R-34$ 4$ 1$ 9 S-66$ 7$ 5$ 4 T-50$ 5$ 2$ 7 Typesetter Opportunity Loss Table ABC Job R-34-$ 5-$ 8$ 0 S-66$ 0-$ 2-$ 3 T-50-$ 2-$ 5$ 0 Typesetter ABC Job R-34-$ 5-$ 6$ 0 S-66$ 0$ 0-$ 3 T-50-$ 2-$ 3$ 0 Typesetter Take smallest number from uncrossed cells and subtract it from all other uncrossed numbers in each column. Add the number to number on Intersection to get table 3. This is not an optimal solution – 2 lines through all zeros 1 2 3

© 2006 Prentice Hall, Inc.15 – 16 Opportunity Loss: Example 2 Assign A to T-50; B to S-66; C to R-34. The profit margin of the assignment is taken from first table: = $5 + $ 5 + $ 9 = $ 19 ABC Job R-34$ 4$ 1$ 9 S-66$ 7$ 5$ 4 T-50$ 5$ 2$ 7 Typesetter Opportunity Loss Table 1 ABC Job R-34-$ 3-$ 4$ 0 S-66$ 0$ 0-$ 1 T-50$ 0-$ 1$ 0 Typesetter2 ABC Job R-34-$ 5-$ 6$ 0 S-66$ 0$ 0-$ 3 T-50-$ 2-$ 3$ 0 Typesetter1 Largestuncrossednumber Subtract largest number from all unexposed numbers, to get Table 2

© 2006 Prentice Hall, Inc.15 – 17 Gantt Load Chart Method (Type III Scheduling) Day MondayTuesdayWednesdayThursdayFriday Work Center Metalworks Mechanical Electronics Painting Job 349 Job 408 ProcessingUnscheduled Center not available Job 350 Job 349 Job 295 Figure 15.3

© 2006 Prentice Hall, Inc.15 – 18 Gantt Staffing Chart (Type III Scheduling) Mon TueWedThu Fri SatSun Bill Off Off MaryOffOff Sue Off Off Will Off Off Bob Off Off MonOffOff Josh Off Off 1. Required Capacity Max available staff Max off duty staff Scheduled off-duty Extra staff needed Minus 3 Schedule

© 2006 Prentice Hall, Inc.15 – 19 Gantt Staffing Chart (Type III Scheduling) Mon TueWedThu Fri SatSun BillOffOff MaryOffOff Sue OffOff WillOff Off BobOff Off MonOffOff Josh Off Off 1. Required Capacity Max available staff Max off duty staff Scheduled off-duty Extra staff needed Minus 3 Schedule This solution shifts all temp staff requirement to weekends

© 2006 Prentice Hall, Inc.15 – 20 Gantt Staffing Chart (Type III Scheduling) Mon TueWedThu Fri SatSun Bill Mary Sue Will Bob Mon Josh 1. Required Capacity 2. Max available staff 3. Max off duty staff 4. Actual off-duty 5. Extra staff needed

© 2006 Prentice Hall, Inc.15 – 21 Gantt Schedule Chart Example Figure 15.4 Job Day 1 Day 2 Day 3 Day 4 Day 5 Day 6 Day 7 Day 8 A B C Now Maintenance Start of an activity End of an activity Scheduled activity time allowed Actual work progress Nonproduction time Point in time when chart is reviewed

© 2006 Prentice Hall, Inc.15 – 22 Sequencing  Specifies the order in which jobs should be performed at work centers  Priority rules are used to dispatch or sequence jobs  FCFS: First come, first served  SPT: Shortest processing time  EDD: Earliest due date  LPT: Longest processing time

© 2006 Prentice Hall, Inc.15 – 23 Sequencing Example Job Job Work (Processing) Time (Days) Job Due Date (Days) A68 B26 C818 D315 E923 Apply the four popular sequencing rules to these five jobs

© 2006 Prentice Hall, Inc.15 – 24 Sequencing: FCFS Example Job Sequ- ence Job Work (Proce ssing) Time Wait Times Flow Time Job Due Date Job Lateness A60680 B26862 C D E FCFS: Sequence A-B-C-D-E

© 2006 Prentice Hall, Inc.15 – 25 Sequencing Example FCFS: Sequence A-B-C-D-E Average completion time = = 77/5 = 15.4 days Total flow time Number of jobs Utilization = = 28/77 = 36.4% Total job work time Total flow time Average number of jobs in the system = = 77/28 = 2.75 jobs/month Total flow time Total job work time Average job lateness = = 11/5 = 2.2 days Total late days Number of jobs

© 2006 Prentice Hall, Inc.15 – 26 Sequencing Example Job Sequence Job Work (Processing) Time Flow Time Job Due Date Job Lateness B2260 D35150 A61183 C E SPT: Sequence B-D-A-C-E

© 2006 Prentice Hall, Inc.15 – 27 Sequencing Example SPT: Sequence B-D-A-C-E Average completion time = = 65/5 = 13 days Total flow time Number of jobs Utilization = = 28/65 = 43.1% Total job work time Total flow time Average number of jobs in the system = = 65/28 = 2.32 jobs/months Total flow time Total job work time Average job lateness = = 9/5 = 1.8 days Total late days Number of jobs

© 2006 Prentice Hall, Inc.15 – 28 Sequencing Example Job Sequence Job Work (Processing) Time Flow Time Job Due Date Job Lateness B2260 A6880 D C E EDD: Sequence B-A-D-C-E

© 2006 Prentice Hall, Inc.15 – 29 Sequencing Example EDD: Sequence B-A-D-C-E Average completion time = = 68/5 = 13.6 days Total flow time Number of jobs Utilization = = 28/68 = 41.2% Total job work time Total flow time Average number of jobs in the system = = 68/28 = 2.43 jobs/ month Total flow time Total job work time Average job lateness = = 6/5 = 1.2 days Total late days Number of jobs

© 2006 Prentice Hall, Inc.15 – 30 Sequencing Example Job Sequence Job Work (Processing) Time Flow Time Job Due Date Job Lateness E99230 C A D B LPT: Sequence E-C-A-D-B

© 2006 Prentice Hall, Inc.15 – 31 Sequencing Example LPT: Sequence E-C-A-D-B Average completion time = = 103/5 = 20.6 days Total flow time Number of jobs Utilization = = 28/103 = 27.2% Total job work time Total flow time Average number of jobs in the system = = 103/28 = 3.68 jobs Total flow time Total job work time Average job lateness = = 48/5 = 9.6 days Total late days Number of jobs

© 2006 Prentice Hall, Inc.15 – 32 Summary Sequencing Examples Rule Average Completion Time (Days) Utilization (%) Average Number of Jobs in System per month Average Lateness (Days) FCFS SPT EDD LPT Summary of Rules

© 2006 Prentice Hall, Inc.15 – 33 Comparison of Sequencing Rules  No one sequencing rule excels on all criteria  SPT does well on minimizing flow time and number of jobs in the system  But SPT moves long jobs to the end which may result in dissatisfied customers  FCFS does not do especially well (or poorly) on any criteria but is perceived as fair by customers  EDD minimizes lateness

© 2006 Prentice Hall, Inc.15 – 34 Improving Performance of System  Changing setting of due dates  Changing process serial to parallel form BA C E D BA C E D