Endstri Mhendisliine Giri EM 111 BLM 15 retim

Endüstri Mühendisliğine Giriş EM 111 BÖLÜM 15 Üretim Çizelgeleme © 2006 Prentice Hall, Inc.

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

Scheduling Issues þ Scheduling deals with the timing of operations þ The task is the allocation and prioritization of demand þ Significant issues are þ The type of scheduling, forward or backward þ The criteria for priorities © 2006 Prentice Hall, Inc. 15 – 3

Scheduling Issues Figure 15. 1 © 2006 Prentice Hall, Inc. 15 – 4

Scheduling Decisions Organization Arnold Palmer Hospital University of Missouri Lockheed-Martin factory Hard Rock Cafe Delta Airlines Table 15. 1 © 2006 Prentice Hall, Inc. Managers Must Schedule the Following Operating room use Patient admissions Nursing, security, maintenance staffs Outpatient treatments Classrooms and audiovisual equipment Student and instructor schedules Graduate and undergraduate courses Production of goods Purchases of materials Workers Chef, waiters, bartenders Delivery of fresh foods Entertainers Opening of dining areas Maintenance of aircraft Departure timetables Flight crews, catering, gate, ticketing personnel 15 – 5

Forward and Backward Scheduling þ Forward scheduling starts as soon as the requirements are known þ Produces a feasible schedule though it may not meet due dates þ Frequently results in excessive work-inprocess inventory Now © 2006 Prentice Hall, Inc. Due Date 15 – 6

Forward and Backward Scheduling þ Backward scheduling begins with the due date and schedules the final operation first þ Schedule is produced by working backwards though the processes þ Resources may not be available to accomplish the Due Now Date schedule © 2006 Prentice Hall, Inc. 15 – 7

Scheduling Criteria 1. Minimize completion time 2. Maximize utilization of facilities 3. Minimize work-in-process (WIP) inventory 4. Minimize customer waiting time Optimize the use of resources so that production objectives are met © 2006 Prentice Hall, Inc. 15 – 8

Planning and Control Files Planning Files 1. An item master file contains information about each component 2. A routing file indicates each component’s flow through the shop 3. A work-center master file contains information about the work center Control Files Track the actual progress made against the plan © 2006 Prentice Hall, Inc. 15 – 9

Loading Jobs þ Assign jobs so that costs, idle time, or completion time are minimized þ Two forms of loading þ Capacity oriented þ Assigning specific jobs to work centers © 2006 Prentice Hall, Inc. 15 – 10

Gantt Charts þ Load chart shows the loading and idle times of departments, machines, or facilities þ Displays relative workloads over time þ Schedule chart monitors jobs in process þ All Gantt charts need to be updated frequently © 2006 Prentice Hall, Inc. 15 – 11

Gantt Load Chart Example Day Work Center Metalworks Monday Tuesday Job 349 Job 408 Painting Processing Friday Job 350 Mechanical Electronics Wednesday Thursday Job 408 Job 349 Job 295 Job 408 Unscheduled Job 349 Center not available Figure 15. 3 © 2006 Prentice Hall, Inc. 15 – 12

Gantt Schedule Chart Example Job Day Day 1 2 3 4 5 6 7 8 A B Start of an activity End of an activity Scheduled activity time allowed Actual work progress Maintenance Nonproduction time C Figure 15. 4 © 2006 Prentice Hall, Inc. Point in time when chart is reviewed Now 15 – 13

Assignment Method þ A special class of linear programming models that assign tasks or jobs to resources þ Objective is to minimize cost or time þ Only one job (or worker) is assigned to one machine (or project) © 2006 Prentice Hall, Inc. 15 – 14

Assignment Method þ Build a table of costs or time associated with particular assignments

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. © 2006 Prentice Hall, Inc. 15 – 16

Assignment Method 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 – 17

Assignment Example Typesetter Job R-34 S-66 T-50 Step 1 a - Rows Typesetter Job R-34 S-66 T-50 © 2006 Prentice Hall, Inc. A $ 5 $ 0 $ 2 B $ 8 $ 2 $ 5 A B C $11 $ 8 $ 9 $14 $10 $12 $ 6 $11 $ 7 Step 1 b - Columns C $ 0 $ 3 $ 0 Typesetter Job R-34 S-66 T-50 A B C $ 5 $ 0 $ 2 $ 6 $ 0 $ 3 $ 0 15 – 18

Assignment Example Step 2 - Lines Typesetter Job R-34 S-66 T-50 A B C $ 5 $ 0 $ 2 $ 6 $ 0 $ 3 $ 0 Because only two lines are needed to cover all the zeros, the solution is not optimal © 2006 Prentice Hall, Inc. The smallest uncovered number is 2 so this is subtracted from all other uncovered numbers and added to numbers at the intersection of lines Step 3 - Subtraction Typesetter Job R-34 S-66 T-50 A $ $ $ 3 0 0 B $ $ $ 4 0 1 C $ $ $ 0 5 0 15 – 19

Assignment Example Step 2 - Lines Typesetter Job R-34 S-66 T-50 A $ $ $ 3 0 0 B $ $ $ 4 0 1 C $ $ $ 0 5 0 Because three lines are needed, the solution is optimal and assignments can be made © 2006 Prentice Hall, Inc. Start by assigning R-34 to worker C as this is the only possible assignment for worker C. Job T-50 must go to worker A as worker C is already assigned. This leaves S-66 for worker B. Step 4 - Assignments Typesetter Job R-34 S-66 T-50 A B C $ 3 $ 0 $ 4 $ 0 $ 1 $ 0 $ 5 $ 0 15 – 20

Assignment Example From the original cost table Minimum cost = $6 + $10 + $9 = $25 Step 4 - Assignments Typesetter Job R-34 S-66 T-50 © 2006 Prentice Hall, Inc. A $11 $ 8 $ 9 B $14 $10 $12 C $ 6 $11 $ 7 Typesetter Job R-34 S-66 T-50 A B C $ 3 $ 0 $ 4 $ 0 $ 1 $ 0 $ 5 $ 0 15 – 21

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

Sequencing Example Apply the four popular sequencing rules to these five jobs Job A B C D E © 2006 Prentice Hall, Inc. Job Work (Processing) Time (Days) 6 2 8 3 9 Job Due Date (Days) 8 6 18 15 23 15 – 23

Sequencing Example FCFS: Sequence A-B-C-D-E Job Sequence Job Work (Processing) Time Flow Time Job Due Date A 6 6 8 0 B 2 8 6 2 C 8 16 18 0 D 3 19 15 4 E 9 28 23 5 28 77 © 2006 Prentice Hall, Inc. Job Lateness 11 15 – 24

Sequencing Example FCFS: Sequence A-B-C-D-E Total flow time Jobtime Work Average completion = = 77/5 = 15. 4 days Job (Processing) Number Flowof jobs Job Due Job Sequence Time Date Lateness Total job work time = 28/77 A Utilization = 6 Total flow time 6 8 = 36. 4% 0 B 2 8 6 2 Total flow time Average number of = 77/28 = 2. 75 jobs. Cin the system =8 Total job work 16 time 18 0 D 3 19 days 15 4 Total late Average job lateness = = 11/5 = 2. 2 days Number of jobs E 9 28 23 5 28 © 2006 Prentice Hall, Inc. 77 11 15 – 25

Sequencing Example SPT: Sequence B-D-A-C-E Job Sequence Job Work (Processing) Time Flow Time Job Due Date B 2 2 6 0 D 3 5 15 0 A 6 11 8 3 C 8 19 18 1 E 9 28 23 5 28 65 © 2006 Prentice Hall, Inc. Job Lateness 9 15 – 26

Sequencing Example SPT: Sequence B-D-A-C-E Total flow time Job Work Average completion time = = 65/5 = 13 days Job (Processing) Number Flow of jobs Job Due Job Sequence Time Date Lateness Total job work time = 28/65 B Utilization = 2 Total flow time 2 6 = 43. 1% 0 D 3 5 15 0 Total flow time Average number of = 65/28 = 2. 32 jobs. Ain the system =6 Total job work 11 time 8 3 C 8 19 days 18 1 Total late Average job lateness = = 9/5 = 1. 8 days Number of jobs E 9 28 23 5 28 © 2006 Prentice Hall, Inc. 65 9 15 – 27

Sequencing Example EDD: Sequence B-A-D-C-E Job Sequence Job Work (Processing) Time Flow Time Job Due Date B 2 2 6 0 A 6 8 8 0 D 3 11 15 0 C 8 19 18 1 E 9 28 23 5 28 68 © 2006 Prentice Hall, Inc. Job Lateness 6 15 – 28

Sequencing Example EDD: Sequence B-A-D-C-E Total flow time Jobtime Work Average completion = = 68/5 = 13. 6 days Job (Processing) Number Flowof jobs Job Due Job Sequence Time Date Lateness Total job work time = 28/68 B Utilization = 2 Total flow time 2 6 = 41. 2% 0 A 6 8 8 0 Total flow time Average number of = 68/28 = 2. 43 jobs. Din the system =3 Total job work 11 time 15 0 C 8 19 days 18 1 Total late Average job lateness = = 6/5 = 1. 2 days Number of jobs E 9 28 23 5 28 © 2006 Prentice Hall, Inc. 68 6 15 – 29

Sequencing Example LPT: Sequence E-C-A-D-B Job Sequence Job Work (Processing) Time Flow Time Job Due Date E 9 9 23 0 C 8 17 18 0 A 6 23 8 15 D 3 26 15 11 B 2 28 6 22 28 103 © 2006 Prentice Hall, Inc. Job Lateness 48 15 – 30

Sequencing Example LPT: Sequence E-C-A-D-B Total flow time Jobtime Work Average completion = = 103/5 = 20. 6 days Job (Processing)Number Flow Job of jobs Due Sequence Time Date Lateness Total job work time = 28/103 EUtilization = 9 Total flow time 9 23 = 27. 2% 0 C 8 17 18 0 Total flow time Average number of = = 103/28 = 3. 68 jobs in A the system 6 Total job work 23 time 8 15 D 3 26 days 15 11 Total late Average job lateness = = 48/5 = 9. 6 days Number of jobs B 2 28 6 22 28 © 2006 Prentice Hall, Inc. 103 48 15 – 31

Sequencing Example Summary of Rules Rule Average Completion Time (Days) FCFS 15. 4 36. 4 2. 75 2. 2 SPT 13. 0 43. 1 2. 32 1. 8 EDD 13. 6 41. 2 2. 43 1. 2 LPT 20. 6 27. 2 3. 68 9. 6 © 2006 Prentice Hall, Inc. Average Number Average Utilization of Jobs in Lateness (%) System (Days) 15 – 32

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

Sequencing N Jobs on Two Machines: Johnson’s Rule þ Works with two or more jobs that pass through the same two machines or work centers þ Minimizes total production time and idle time © 2006 Prentice Hall, Inc. 15 – 34

Johnson’s Rule 1. List all jobs and times for each work center 2. Choose the job with the shortest activity time. If that time is in the first work center, schedule the job first. If it is in the second work center, schedule the job last. 3. Once a job is scheduled, it is eliminated from the list 4. Repeat steps 2 and 3 working toward the center of the sequence © 2006 Prentice Hall, Inc. 15 – 35

Johnson’s Rule Example Job Work Center 1 (Drill Press) Work Center 2 (Lathe) A

Johnson’s Rule Example Job Work Center 1 (Drill Press) Work Center 2 (Lathe) A 5 2 B 3 6 C 8 4 D 10 7 E 7 12 Time WC 1 0 3 10 B E WC 2 Time 0 1 5 28 D C E 7 9 10 11 12 13 B © 2006 Prentice Hall, Inc. 20 B 3 B E D C A 33 A D C A 17 19 21 22 23 25 27 29 31 33 35 E D C A 15 – 39