chapter 17: operations scheduling
DESCRIPTION
Chapter 17: Operations Scheduling. Scheduling is the allocation of resources over time to perform a collection of tasks Resources Workers, Machines, Tools Tasks Operations that bring some physical changes to material in order to eventually manufacture products - PowerPoint PPT PresentationTRANSCRIPT
Chapter 17: Operations Scheduling• Scheduling is the allocation of resources over time to
perform a collection of tasks • Resources
– Workers, Machines, Tools• Tasks
– Operations that bring some physical changes to material in order to eventually manufacture products
– Setups such as walking to reach the workplace, obtaining and returning tools, setting the required jigs and fixtures, positioning and inspecting material, cleaning etc.
Job Shop
Batch production
ShopFlow C
usto
miz
atio
n
High
LowHighLow
Volume
Project
Production Systems
Continuous production
Job Shop
Batch production
ShopFlow C
usto
miz
atio
n
High
LowHighLow
Volume
Project
Production SystemsAircraft
Automobile
Oil refinery
Books
Custom-made machines and parts
Continuous production
Job Shop
Continuous production
Batch production
ShopFlow C
usto
miz
atio
n
High
LowHighLow
Volume
Production SystemsProject
Labor intensive
Capital intensive
Job Shop
Batch production
ShopFlow C
usto
miz
atio
n
High
LowHighLow
Volume
Production SystemsProject
More frequent Rescheduling
Less frequent Rescheduling
Continuous production
Infinite/Finite Scheduling
• Infinite - assumes infinite capacity– Loads without regard to capacity, levels the
load and sequence jobs– Job shop/batch production
• Finite - assumes finite (limited) capacity– Sequences jobs as part of the loading decision,
resources are never loaded beyond capacity– Flow shop/continuous production
Scheduling Job Shop/Batch Production
• Batch Production– many planning steps
• aggregate planning• master scheduling• material requirements planning (MRP)• capacity requirements planning (CRP)
• Scheduling determines– machine/worker/job assignments– resource/requirement matchings
Objectives in Scheduling• Conformance to prescribed deadlines
– Meet customer due dates, minimize job lateness, minimize maximum lateness, minimize number of tardy jobs
• Response time or lead time– Minimize mean completion time, minimize average time in
the system• Efficient utilization of resources
– Maximize machine or labor utilization, minimize idle time, maximize throughput, minimize the length of time the shop is open
• Costs– Minimize work-in-process inventory, minimize overtime
Responsibilities of Production Control Department
• Loading – Allocate orders to workers and machines, worker and
machines to work centers etc.• Sequencing
– Release work orders to shop & issue dispatch lists for individual machines
• Monitoring – Maintain progress reports on each job until it is complete
Loading
• Allocate orders to workers and machines, workers and machines to work centers, etc.
• Perform work on most efficient resources
• Use assignment method of linear programming to determine allocation
Assignment Method1. Perform row reductions
– Subtract minimum value in each row from all other row values
2. Perform column reductions– Subtract minimum value in each column from all other
column values3. Line Test
– Cross out all zeros in matrix using minimum number of horizontal & vertical lines. If number of lines equals number of rows in matrix, optimum solution has been found, stop.
4. Matrix Modification– Subtract minimum uncrossed value from all uncrossed values
& add it to all cells where two lines intersect. Go to Step 3.
Assignment ExampleCooker
Food 12 34Beans 105 610Peaches 62 46Tomatoes 76 56Corn 95 410
Row reduction Column reduction Line Test5 0 1 5 3 0 1 4 3 0 1 44 0 2 4 2 0 2 3 2 0 2 32 1 0 1 0 1 0 0 0 1 0 05 1 0 6 3 1 0 5 3 1 0 5
Number lines <> number of rows so modify matrix
Assignment Example
Cooker Food 12 34Beans 10 12 Peaches 00 21 Tom 03 20Corn 11 03
Modify matrix Line Test
1 0 1 2 1 0 1 20 0 2 1 0 0 2 10 3 2 0 0 3 2 01 1 0 3 1 1 0 3
# lines = # rows so at optimal solution
Cooker
Food 1 2 3 4Beans 10 5 6 10Peaches 6 2 4 6Tomatoes 7 6 5 6Corn 9 5 4 10
Orders completed in 6 hoursTotal number of hours = 21
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 to an objective
Sequencing Rules
• FCFS - first-come, first-served• SOT - shortest operating time• DDATE - earliest due date• STR - slack time remaining
– (due date - today’s date) - (remaining processing time)
• LCFS - last come, first served
Critical Ratio Rule
• CR = time remaining / work remaining
Jobs with the smallest CR are run first.
due date - today’s date remaining processing time
=
Performance Measures• Completion time
– Epoch at which the job is completed• Makespan
– Completion time of the last job processed• Lateness
– Lateness of job j – = (completion time of job j)-(due date of job j)
• Tardiness– Tardiness of job j = max(0, lateness of job j)
Sequencing Rule Example
A 510(10-1) - 5 = 4(10-1)/5 = 1.80B 1015(15-1)-10 = 4(15-1)/10 = 1.40C 25(5-1)-2 = 2 (5-1)/2 = 2.00D 812(12-1)-8 = 3 (12-1)/8 = 1.37E 68(8-1)-6 = 1 (8-1)/6 = 1.16
120 possible sequences for 5 jobs
Processing Due CriticalJob Time Date Slack Ratio
First-Come First-Served
A 5 10B 10 15C 2 5D 8 12E 6 8
Average
Start Processing Completion DueSequenceTime Time Time Date Tardiness
Earliest Due Date
C 2 5E 6 8A 5 10D 8 12E 10 15
Average
Start Processing Completion DueSequenceTime Time Time Date Tardiness
Slack Time Remaining
E 6 8C 2 5D 8 12A 5 10B 10 15
Average
Slack for each job A - 4, B - 4, C - 2, D - 3, E - 1
Start Processing Completion DueSequenceTime Time Time Date Tardiness
Critical Ratio
E 6 8D 8 12B 10 15A 5 10C 2 5
Average
CR for each job A - 1.80, B - 1.40, C - 2.00, D - 1.37, E - 1.16
Start Processing Completion DueSequenceTime Time Time Date Tardiness
Shortest Operating Time
C 2 5A 5 10E 6 8D 8 12B 10 15
Average
Start Processing Completion DueSequenceTime Time Time Date Tardiness
Summary
FCFS 18.60 9.6 3 23DDATE 15.00 5.6 316STR 16.40 6.8 416CR 20.80 11.2 426SOT 14.80 6.0 316
* Best values** Guaranteed best values
Average Average No. of MaximumRule Completion Time Tardiness Jobs Tardy Tardiness
** **
*
**
*
**
Johnson’s Rule: Sequencing Jobs Through a Two Machine Flow Shop to Minimize Makespan
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 & all jobs are
sequenced.
Johnson’s Rule Example
A 6 8B 11 6C 7 3D 9 7E 5 10
Machine Machine Job Center 1 Center 2
Johnson’s Rule Example
A 6 8B 11 6
D 9 7E 5 10
Machine Machine Job Center 1 Center 2
C
Johnson’s Rule Example
A 6 8B 11 6
D 9 7
Machine Machine Job Center 1 Center 2
CE
Johnson’s Rule Example
B 11 6
D 9 7
Machine Machine Job Center 1 Center 2
CAE
Johnson’s Rule Example
D 9 7
Machine Machine Job Center 1 Center 2
CBAE
Johnson’s Rule Example Machine Machine
Job Center 1 Center 2
CBDAE
Johnson’s Rule Example
E 5 10A 6 8D 9 7B 11 6C 7 3
Machine Machine Job Center 1 Center 2
CBDAEEach triplet above shows the start, processing, and stopping times of an operation. Johnson’s rule guarantees that the above schedule gives the best value (41) of makespan.
Monitoring with Gantt Chart
1 2 3 4 5 6 8 9 10 11 12 Days
1
2
3
Today’s Date
Job 32B
Job 23C
Job 11C Job 12A
Faci
lity
Key:
PlannedActivity
CompletedActivity
Behind schedule
Ahead of schedule
On schedule
Gantt Chart shows both planned and completed activities against a time scale
Employee Scheduling
• Labor is very flexible resource• Scheduling workforce is a complicated
repetitive task• An objective is to create a consecutive days
off schedule that uses the fewest workers. • Heuristics are commonly used.
Employee Scheduling Heuristic
1. Consider the first worker and the unassigned workload.
2. Assign the worker to all days except the two consecutive days with the lowest unassigned workload.
3. If there are unassigned workload, consider the next worker and repeat step 2. Else, stop.
Employee Scheduling Example
Number of Workers RequiredM Tu W Th F S Su
3 3 4 3 4 5 3
Employee Scheduling Example
Number of Workers RequiredM Tu W Th F S Su
3 3 4 3 4 5 3Worker 1 3 3 4 3 4 5 3
Employee Scheduling Example
Number of Workers RequiredM Tu W Th F S Su
3 3 4 3 4 5 3Worker 1 3 3 4 3 4 5 3
Employee Scheduling Example
Number of Workers RequiredM Tu W Th F S Su
3 3 4 3 4 5 3Worker 1 3 3 4 3 4 5 3Worker 2 3 3 3 2 3 4 2
Employee Scheduling Example
Number of Workers RequiredM Tu W Th F S Su
3 3 4 3 4 5 3Worker 1 3 3 4 3 4 5 3Worker 2 3 3 3 2 3 4 2
Employee Scheduling Example
Number of Workers RequiredM Tu W Th F S Su
3 3 4 3 4 5 3Worker 1 3 3 4 3 4 5 3Worker 2 3 3 3 2 3 4 2Worker 3 2 2 3 2 2 3 1
Employee Scheduling Example
Number of Workers RequiredM Tu W Th F S Su
3 3 4 3 4 5 3Worker 1 3 3 4 3 4 5 3Worker 2 3 3 3 2 3 4 2Worker 3 2 2 3 2 2 3 1
Employee Scheduling Example
Number of Workers RequiredM Tu W Th F S Su
3 3 4 3 4 5 3Worker 1 3 3 4 3 4 5 3Worker 2 3 3 3 2 3 4 2Worker 3 2 2 3 2 2 3 1Worker 4 2 1 2 1 1 2 1
Employee Scheduling Example
Number of Workers RequiredM Tu W Th F S Su
3 3 4 3 4 5 3Worker 1 3 3 4 3 4 5 3Worker 2 3 3 3 2 3 4 2Worker 3 2 2 3 2 2 3 1Worker 4 2 1 2 1 1 2 1
Employee Scheduling Example
Number of Workers RequiredM Tu W Th F S Su
3 3 4 3 4 5 3Worker 1 3 3 4 3 4 5 3Worker 2 3 3 3 2 3 4 2Worker 3 2 2 3 2 2 3 1Worker 4 2 1 2 1 1 2 1Worker 5 1 0 1 1 1 1 0
Employee Scheduling Example
Number of Workers RequiredM Tu W Th F S Su
3 3 4 3 4 5 3Worker 1 3 3 4 3 4 5 3Worker 2 3 3 3 2 3 4 2Worker 3 2 2 3 2 2 3 1Worker 4 2 1 2 1 1 2 1Worker 5 1 0 1 1 1 1 0
Employee Scheduling Example
Remark:The resulting schedule provides consecutive days
off to 4 workers among 5. Still, it’s better than two schedules shown next.
Employee Scheduling ExampleDay of week M T W Th F Sa SuMin # workers 3 3 4 3 4 5 3Worker 1 O X X 0 X X XWorker 2 O X X 0 X X XWorker 3 X O X X O X XWorker 4 X O X X X X OWorker 5 X X O X X X OIMPROVED SCHEDULEDay of week M T W Th F Sa SuMin # workers 3 3 4 3 4 5 3Worker 1 O O X X X X XWorker 2 O O X X X X XWorker 3 X X O O X X XWorker 4 X X X O X X OWorker 5 X X X X O X O
Reading
• Reading: Chapter 17 pp. 668-74, 678-81• Chapter end problems: 4,6,12,13