PERT 09 Penjadwalan Jangka Pendek (2) Assignment Method Pengurutan Pekerjaan Teori Keterbatasan
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1 PERT 09 Penjadwalan Jangka Pendek (2) Assignment Method Pengurutan Pekerjaan Teori Keterbatasan
2 Assignment Method Assigns tasks or jobs to resources Type of linear programming model Objective Minimize total cost, time etc. Constraints 1 job per resource (e.g., machine) 1 resource (e.g., machine) per job
3 Assignment Method - Four Steps 1 Subtract the smallest number in each row from every number in that row; then subtract the smallest number in every column from every number in that column 2 Draw the minimum number of vertical and horizontal straight lines necessary to cover all zeros in the table If the number of lines equals either the number of rows or the number of columns, then you can make an optimal assignment (Step 4) Otherwise: 3 Subtract the smallest number not covered by a line from every other uncovered number. Add the same number to any number(s) lying at the intersection of any two lines. Return to Step 2 4 Optimal assignments will always be at the zero locations of the table
4 Assignment Method Type Setter Example Job Typesetter A B C R-34 $11 $14 $ 6 S-66 $ 8 $10 $11 T-50 $9 $12 $7 Initial set-up
5 Step 1a & 1b Typesetter Job A B C Typesetter Job A B C R R S S T T Step 1a Step 1b
6 Step 2 Typesetter A B C Job R S T Smallest uncovered number
7 Step 3 Typesette r A B C Job R S T Make assignments
8 Sequencing Challenge Order release Job Packet Job XYZ Which job do I run next? Dispatch List Order Part Due Qty XYZ ABC Production Control Production
9 Sequencing Specifies order jobs will be worked Sequencing rules First come, first served (FCFS) Shortest processing time (SPT) Earliest due date (EDD) Longest processing time (LPT) Critical ratio (CR) Johnson s rule
10 Priority Rules for Dispatching Jobs FCFS EDD SPT LPT CR First come, first served The first job to arrive at a work center is processed first Earliest due date The job with the earliest due date is processed first Shortest processing time The job with the shortest processing time is processed first Longest processing time The job with the longest processing time is processed first Critical ratio The ratio of time remaining to required work time remaining is calculated, and jobs are scheduled in order of increasing ratio.
11 First Come, First Served Rule Process first job to arrive at a work center first Average performance on most scheduling criteria Appears fair & reasonable to customers Important for service organizations Example: Restaurants
12 Shortest Processing Time Rule Process job with shortest processing time first. Usually best at minimizing job flow and minimizing the number of jobs in the system Major disadvantage is that long jobs may be continuously pushed back in the queue.
13 Longest Processing Time Rule Process job with longest processing time first. Usually the least effective method of sequencing.
14 Earliest Due Date Rule Process job with earliest due date first Widely used by many companies If due dates important If MRP used Due dates updated by each MRP run Performs poorly on many scheduling criteria
15 Critical Ratio (CR) Ratio of time remaining to work time remaining Time remaining CR = Work days remaining = Due date - Today's date Work (lead) time remaining Process job with smallest CR first Performs well on average lateness
16 Advantages of the Critical Ratio Scheduling Rule Use of the critical ratio can help to: determine the status of a specific job establish a relative priority among jobs on a common basis relate both stock and make-to-order jobs on a common basis adjust priorities and revise schedules automatically for changes in both demand and job progress dynamically track job progress and location
17 Criteria to Evaluate Priority Rules Average completion time = ΣFlow times # Jobs Utilization= ΣProcess times ΣFlow times Average number of jobs in the system = ΣFlow times ΣProcess times Average job lateness Σ Late = Number times of jobs
18 Job Sequencing Example Job A B C D E Job Work Processing time in days Job Due Date (day)
19 FCFS Parameter Average completion time Utilization Average number of jobs in the system Average job lateness Value 15.4 days 36.4% 2.75 jobs 2.2 days Sequence A B C D E
20 SPT Parameter Average completion time Utilization Average number of jobs in the system Average job lateness Value 13 days 43.1% 2.32 jobs 1.8 days Sequence B D A C E
21 EDD Parameter Average completion time Utilization Average number of jobs in the system Average job lateness Value 13.6 days 41.2% 2.43 jobs 1.2 days Sequence B A D C E
22 LPT Parameter Average completion time Utilization Average number of jobs in the system Average job lateness Value 20.6 days 27.2% 3.68 jobs 9.6 days Sequence E C A D B
23 Summary Rule Average Completion Time (days) Utilization (%) Average Number of Jobs in the System Average Lateness (Days) FCFS SPT EDD LPT
24 Critical Ratio (CR) Job A B Job Work Processing time in days 6 2 Job Due Date (day) 8 6 Critical Ratio Sequence A C E C B D D E
25 Johnson s Rule Used to sequence N jobs through 2 machines in the same order Jobs (N = 3) Saw Drill Job A Job B Job C 1995 Corel Corp Corel Corp.
26 Johnson's Rule - Scheduling N Jobs on Two Machines All jobs are to be listed, and the time each requires on a machine shown. Select the job with the shortest activity time. If the shortest time lies with the first machine, the job is scheduled first; if with the second machine, the job is scheduled last. Once a job is scheduled, eliminate it. Apply steps 2-3 to the remaining jobs, working toward the center of the sequence.
27 Johnson s Rule Steps List jobs & activity times Machine? 2 Schedule LAST 1 Select job with shortest time Schedule FIRST Ties? No Eliminate job from list Yes Break arbitrarily Yes Jobs left? No Stop
28 Johnson s Rule - Example Job A B C D E Work Center 1 (Drill Press) Work Center 2 (Lathe)
29 Johnson s Rule - Example Step 1 A Step 2 B A Step 3 B C A Step 4 B D C A Step 5 B E D C A
30 Graphical Depiction of Job Flow Time => Work center 1 Work center 2 Time => B E D C A B E D C A B E D C A = Idle = Job completed
31 Limitations of Rule-Based Dispatching Systems Scheduling is dynamic; therefore, rules need to be revised to adjust to changes in process, equipment, product mix, etc. Rules do not look upstream or downstream; idle resources and bottleneck resources in other departments may not be recognized Rules do not look beyond due dates
32 Finite Scheduling System
33 Theory of Constraints Deals with factors limiting company s ability to achieve goals Types of constraints Physical Example: Machines, raw materials Non-physical Example: Morale, training Limits throughput in operations
34 Theory of Constraints A Five Step Process Identify the constraints Develop a plan for overcoming the identified constraints Focus resources on accomplishing the constraints identified in step 2 Reduce the effects of the constraints by off-loading work or by expanding capability Once one set of constraints is overcome, return to the first step and identify new constraints
35 Bottleneck Work Centers Bottleneck work centers have less capacity than prior or following work centers They limit production output 1995 Corel Corp.
36 Techniques for Dealing With Bottlenecks 1. Increase the capacity of the constraint 2. Ensure well-trained and cross-trained employees are available to operate and maintain the work center causing the constraint 3. Develop alternate routings, processing procedures, or subcontractors 4. Move inspections and tests to a position just before the constraint 5. Schedule throughput to match the capacity of the bottleneck
37 The 10 Commandments for Correct Scheduling 1. Utilization of a non-bottleneck resource is determined not by its own capacity but by some other constraint in the system 2. Activating a resource is not synonymous with utilizing a resource 3. An hour lost at a bottleneck is an hour lost of the whole system 4. An hour saved at a non-bottleneck is a mirage 5. The transfer batch may not, and many times should not, be equal to the process batch
38 The 10 Commandments for Correct Scheduling 6. The amount processed should be verifiable and not fixed 7. Capacity and priority need to be considered simultaneously, not sequentially 8. Damage from unforeseen problems can be isolated and minimized 9. Plant capacity should not be balanced 10. The sum of the local optimums is not equal to the global optimum
39 Repetitive Manufacturing - Advantages of Level Material Use Lower inventory levels, releasing capital for other uses Faster product throughput Improved component quality and hence improved product quality Reduced floor space requirements Improved communication among employees because they are closer together Smoother production process because large lots have not hidden the problems
40 Scheduling for Services Appointment systems - doctor s office Reservations systems - restaurant, car rental First come, first served - deli Most critical first - hospital trauma room
41 Cyclical Scheduling Plan a schedule equal in weeks to the number of people being scheduled Determine how many of each of the least desirable off-shifts must be covered each week Begin the schedule for one worker by scheduling the days off during the planning cycle (at a rate of 2 days per week on average)
42 Cyclical Scheduling - Continued Assign off-shifts for the first worker Repeat this pattern for each other worker, but offset by one week from the previous Allow each worker to pick his/her slot or line in order of seniority Mandate that any changes from the chosen schedule are strictly between the personnel wanting to switch
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