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.
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 Presentation
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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
• 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.
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.
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