04 05 06 scheduling
TRANSCRIPT
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Operations Scheduling
Class04, 05, 06
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Scheduling
Work Center Typical Scheduling and Control Functions
Job-shop Scheduling
BatchShop Scheduling
Personnel Scheduling
Examples of Scheduling Rules
Shop-floor Control
Principles of Work Center Scheduling
Issues in Scheduling Service Personnel
SCHEDULING
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SCHEDULING
DETERMINATION OF WHEN LABOUR,
EQUIPMENTS AND FACILITIES ARE
NEEDED TO PRODUCE A PRODUCT OR
PROVIDE A SERVICE.
SCHEDULING IS THE LAST STAGE OF
PLANNING BEFORE PRODUCTION
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Typical Scheduling and Control
Functions
Allocating orders, equipment, and personnel.
Determining the sequence of orderperformance.
Initiating performance of the scheduled work.
Shop-floor control.
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Scheduling
Process-Focused
Manufacturing
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Scheduling and Shop-Floor
Decisions
MaterialRequirementsPlan (MRP)
CapacityRequirementsPlan (CRP)
Order-Processing orRouting Plans
PlannedOrder ReleasesReport
Work CenterLoading andOvertime Plan
Assignment ofOrders toWork Centers
MasterProduction
Schedule (MPS)
Product Designand
Process Plans
Day-to-Day Scheduling and Shop-Floor Decisions
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Work-Center Scheduling
Objectives
Meet due dates
Minimize lead time
Minimize setup time or cost
Minimize work-in-process inventory
Maximize machine utilization
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Pre-production Planning
Design the product in customer order
Plan the operations the product mustpass through ..... this is the routing plan
Work moves between operations on a
move ticket
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Common Shop Floor
Control Activities
The production control departmentcontrols and monitors order progress
through the shop.Assigns priority to orders
Issues dispatching lists
Tracks WIP and keeps systems updated
Controls input-output between work centers
Measures efficiency, utilization, andproductivity of shop
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Shop Floor Planning and Control
Input-Output Control
Gantt Chart Finite and Infinite Loading
Forward and Backward Scheduling
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Input-Output Control
Input-output control identifies problemssuch as insufficient or excessive
capacity or any issues that prevents theorder from being completed on time.
Input-output control report compares
planned and actual input, planned andactual output, and planned and actualWIP in each time period
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Input-Output Control Report
Week: -1 1 2 3 4Planned input: labor-hrs 100 50 40 100
Actual input: labor-hrs 50 40 30 80
Cumulative deviation -50 -60 -70 -90Planned output: labor-hrs 120 70 50 100
Actual output: labor-hrs 110 50 20 70
Cumulative deviation -10 -30 -60 -90Planned ending WIP: l-h 50 30 20 20
Actual ending WIP: l-h 70 10 0 10 20
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Gantt Charts
Gantt charts are useful tools to
coordinate jobs through shop; graphicalsummary of job status and loading ofoperations
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Assigning Jobs to Work Centers:
How Many Jobs/Day/Work Center
Infinite loadingAssigns jobs to work centers without regard to
capacity
Unless excessive capacity exists, long queuesoccur
Finite loading
Uses work center capacity to schedule orders Popular scheduling approach
Integral part of CRP
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Assigning Jobs to Work Centers:
Which Job Gets Built First?
Forward scheduling Jobs are given earliest available time slot in
operation
excessive WIP usually results
Backward scheduling Start with promise date and work backward
through operations reviewing lead times todetermine when a job has to pass througheach operation
Less WIP but must have accurate lead times
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Order-Sequencing Problems
Sequencing Rules
Criteria for Evaluating SequencingRules
Comparison of Sequencing Rules
Controlling Changeover Costs Minimizing Total Production Time
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Job Sequencing
The process of determiningwhich job to start first on which
machine / work center
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Priority Rules for Job Sequencing
(n Jobs on One machine)
1. First-come, first-served (FCFS)
2. Shortest operating time (SOT)
3. Earliest due date first (EDD)
4. Last come, first served (LCFS)
5. Longest Processing Time
6. Least slack time remaining (STR) first
7. Critical Ratio (CR)
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Schedule Performance
Measures
Meeting due dates of customers or
downstream operations.
Minimizing the flow time (the time a jobspends in the process).
Minimizing work-in-process inventory.
Minimizing idle time of machines or workers.
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Example of Job Sequencing:
First-Come First-ServedSuppose you have the four
jobs to the right arrive for
processing on one
machine.
What is the FCFS schedule?
Do all the jobs get done on
time?
No, Jobs B, C,
and D are
going to be
late.
JOB (In order of
arrival)
Processing
Time(Days)Due date(Days)
A 3 4
B 5 7
C 4 6
D 2 5
Answer: FCFS Schedule
JOB (In order ofarrival)
ProcessingTime(Days)
Due date(Days) Flow Time Delay
A 3 4 0+3=3 0
B 5 7 3+5=8 1
C 4 6 8+4=12 6
D 2 5 12+2=14 9
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Example of Job Sequencing:
Shortest Operating TimeSuppose you have the four
jobs to the right arrive forprocessing on one machine.
What is the SOT schedule?
Do all the jobs get done on
time?
No, Jobs A,Cand B are goingto be late.
Answer: Shortest Operating Time Schedule
JOB (In order of
arrival)
Processing
Time(Days)Due date(Days)
A 3 4
B 5 7
C 4 6
D 2 5
JOB (In order ofarrival)
ProcessingTime(Days)
Due date(Days) Flow Time Delay
D 2 5 0+2=2 0
A 3 4 2+3=5 1
C 4 6 5+4=9 3
B 5 7 9+5=14 7
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Example of Job Sequencing:
Earliest Due Date FirstSuppose you have the four
jobs to the right arrive forprocessing on one machine.
What is the earliest due date
first schedule?
Do all the jobs get done on
time?
No, Jobs Cand B are
going to be
late.
JOB (In order of
arrival)
Processing
Time(Days)Due date(Days)
A 3 4
B 5 7
C 4 6
D 2 5
Answer: Earliest Due Date First
JOB (In order ofarrival)
ProcessingTime(Days)
Due date(Days) Flow Time Delay
A 3 4 0+3=3 0
D 2 5 3+2=5 0
C 4 6 5+4=9 3
B 5 7 9+5=14 7
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Example of Job Sequencing:
Last-Come First-Served
No, Jobs B andA are going tobe late.
Suppose you have the fourjobs to the right arrive forprocessing on one machine.
What is the LCFS schedule?
Do all the jobs get done on
time?
JOB (In order of
arrival)
Processing
Time(Days)Due date(Days)
A 3 4
B 5 7
C 4 6
D 2 5
Answer: Last-Come First-Served Schedule
JOB (In order of
arrival)
Processing
Time(Days) Due date(Days) Flow Time Delay
D 2 5 0+2=2 0
C 4 6 2+4=6 0
B 5 7 6+5=11 4
A 3 4 11+3=14 11
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Example of Job Sequencing:
Longest Processing Time
No, Jobs C, Aand D aregoing to belate.
Suppose you have the fourjobs to the right arrive forprocessing on one machine.
What is the LPT schedule?
Do all the jobs get done on
time?
JOB (In order of
arrival)
Processing
Time(Days)Due date(Days)
A 3 4
B 5 7
C 4 6
D 2 5
Answer: Longest Processing Time
JOB (In order of
arrival)
Processing
Time(Days) Due date(Days) Flow Time Delay
B 5 7 0+5=5 0
C 4 6 5+4=9 3
A 3 4 9+3=12 8
D 2 5 12+2=14 9
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Example of Job Sequencing:
Slack Time Remaining
No, Jobs C, Band D aregoing to belate.
Suppose you have the fourjobs to the right arrive forprocessing on one machine.
What is the STR schedule?
Do all the jobs get done ontime?
JOB (In order of
arrival)
Processing
Time(Days)Due date(Days)
A 3 4
B 5 7
C 4 6
D 2 5
Answer: Slack Time Remaining
JOB (In order of
arrival)
Processing
Time(Days) Due date(Days) Flow Time Delay
A 3 4 0+3=3 0
C 4 6 3+4=7 1
B 5 7 7+5=12 5
D 2 5 12+2=14 9
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Example of Job Sequencing:
Critical Ratio
No, Jobs A, B Cand D aregoing to belate.
Suppose you have the fourjobs to the right arrive forprocessing on one machine.
What is the CR schedule?
Do all the jobs get done ontime?
JOB (In order
of arrival)
Processing
Time(Days)Due date(Days)
A 3 4
B 5 7
C 4 6
D 2 5
Answer: Critical Ratio (CR)
Critical ratio
1.333333
1.4
0.75
2.5
JOB (In
order ofarrival)
Critical ratio
Processing
Time(Days)
Due
date(Days)
Flow
Time Delay
C 0.75 4 3 0+4=4 1
A 1.33 3 4 4+3=7 3
B 1.4 5 7 7+5=12 5
D 2.5 2 5 12+2=14 9
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Sequencing Rules
For comparison between various ruleuse
Average flow time:
37/4 = 9.25 days
Average number of jobs in the system:
37/14 = 2.643 jobs Average job lateness:
18/4 = 4.5 days
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Scheduling on n jobs on Two Machines
Johnsons rule:Objective: To minimize the flow time from beginning of
the first job until the finish of the last.
1- List the operation time for each job on both machines.
2- Select the shortest operation time.
3- If shortest time is for the first machine, do the job first,
If it is for the second machine, do the job last
4- Repeat step-2 and 3 for remaining job until the
schedule is complete. Dont consider the job already
allotted.
Assumption: Processing of the jobs in Two machine in the order ofAB(First A and then B).
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Example of Job Sequencing:
Johnsons Rule (Part 1)Suppose you have the following six jobs with timerequirements in two stages of production. What is the
job sequence using Johnsons Rule?
Time in HoursJobs M/C-1 M/C-21 30 702 100 953 50 90
4 20 605 90 306 100 15
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Example of Job Sequencing:
Johnsons Rule (Part 1)
61
4 62
4 1 5 63
4 1 3 2 5 64
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Scheduling on n jobs on Three Machines
Johnsons rule:
The rule is applicable under the following condition.
Cond. 1- The smallest processing time of Machine-A
should be greater than or equal to largest processing
time on Machine-B.
OR
Cond. 2- The smallest processing time on Machine-C
should be greater than or equal to the largest processing
time on Machine-B
Rule: Assume Two fictitious machine X and Y
X= A+B and Y= B+C and Order XY
Assumption: Processing of the jobs in Three machine in the order ofABC(First A and then B and then C).
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Example of Job Sequencing:
Johnsons Rule (Part 2)Suppose you have the following Five jobs with timerequirements in Three stages of production. What is
the job sequence using Johnsons Rule?
Time in HoursJobs M/C-1 M/C-2 M/C-31 18 10 82 19 12 183 12 5 16
4 16 6 145 21 9 10
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Example of Job Sequencing:
Johnsons Rule (Part 2)
The smallest processing time on machine-A is 12 which is
greater than or equal to largest processing time on machine-B.
A B C X=A+B Y=B+C1 18 10 8 28 18
2 19 12 18 31 303 12 5 16 17 21
4 16 6 14 22 205 21 9 10 30 19
JOB
Processing Time
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Example of Job Sequencing:
Johnsons Rule (Part 2)
Time In Pro. Time Time Out Time In Pro. Time Time Out Time In Pro. Time Time Out
3 0 12 12 12 5 17 17 16 33
2 12 19 31 31 12 43 43 18 61
4 31 16 47 47 6 53 61 14 75
5 47 21 68 68 9 77 77 10 87
1 68 18 86 86 10 96 96 8 104
JOB
Machine-A Machine-B Machine-C
Idle Time for MachineC = 38 Hrs.
Total Operation Time = 104 Hours
Idle Time for MachineA = 18 Hrs.
Idle Time for MachineB = 62 Hrs.
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Scheduling on n jobs on m Machines
Johnsons rule:
The rule is applicable under the following condition.
Cond. 1- The smallest processing time of Machine-A1 should
be greater than or equal to largest processing time on
Machine-A2Am-1.
OR
Cond. 2- The smallest processing time on Machine-Am should
be greater than or equal to the largest processing time on
Machine-A2.Am-1Rule: Assume Two fictitious machine X and Y
X= A1+A2++Am-1 and Y= A2+A3++Am and Order
A1,A2Am
Assumption: Processing of the jobs in m machine in the order of A1,A2,.Am(First A1 and then A2 and then .Am).
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Example of Job Sequencing:
Johnsons Rule (Part 3)Suppose you have the following Five jobs with timerequirements in Four stages of production. What is the
job sequence using Johnsons Rule?
Time in HoursJobs M/C-1 M/C-2 M/C-3 M/C-41 18 10 8 82 19 12 10 183 12 5 11 16
4 16 6 9 145 21 9 7 10
Class Assignment Time10 Minutes
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ASSIGNMENT METHOD
(SPECIALISED LINEAR PROGRAMMING)
Application
1. n -Jobs to n -Machines2. Each job is assigned to one and only
one destination.
3. Only one criterion to be used ( MinimumCost or Maximum profit or Minimum
time etc.)
Procedure
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ProcedureHungarian Assignment Method
1. PERFORM ROW REDUCTIONS BYSUBTRACTING THE MINIMUM VALUE IN EACHROW FROM OTHER ROW VALUES
2. PERFORM COLUMN REDUCTIONS BYSUBTRACTING THE MINIMUM VALUE IN EACHCOLUMN FROM ALL OTHER COLUMN VALUES
3. THE RESULTING TABLE IS ANOPPORTUNITY COST MATRIX. CROSS OUT ALLZEROS IN THE MATRIX USING THE MINIMUMNUMBER OF HORIZONTAL OR VERTICAL LINES.
Procedure
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4. IF THE NUMBER OF LINES EQUALS THE
NUMBER OF ROWS / COLUMN THE MATRIX, AN
OPTIMUM SOLUTION HAS BEEN REACHED
AND ASSIGNMENTS CAN BE MADE WHERETHE ZEROS APPEAR.
OTHERWISE, MODIFY THE MATRIX BY
SUBTRACTING THE MINIMUM UNCROSSED
VALUE FROM ALL OTHER UNCROSSEDVALUES AND ADDING THIS SAME AMOUNT TO
ALL CELLS WHERE TWO LINES INTERSECT.
ALL OTHER VALUES IN THE MATRIX REMAIN
UNCHANGED
ProcedureHungarian Assignment Method
Procedure
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5. REPEATSTEPS3 AND 4 UNTIL AN OPTIMUMSOLUTION IS REACHED
6. ASSIGNMENT
a. Locate a row /column contains only one zeroelement. Assign the job to that and cross out the
zeros if any in the column corresponding to the
assigned cell.
b. Repeat for each row, which contains only one
zero.
c. If no row/column with single zero, then select
arbitrarily any cell and complete the assignment.
d. Determine the total cost with reference to the
original cost table.
ProcedureHungarian Assignment Method
Example of Assignment
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Example of Assignment
Problem
A B C D
1 45 40 51 67
2 57 42 63 553 49 52 48 64
4 41 45 60 55
JobWorker
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A B C D1 5 0 11 27
2 15 0 21 13 Step-1
3 1 4 0 16
4 0 4 19 14
Worker Job
Example of Assignment Problem
1- PERFORM ROW REDUCTIONS BY SUBTRACTING THE
MINIMUM VALUE IN EACH ROW FROM OTHER ROW
VALUES
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A B C D
1 5 0 11 14
2 15 0 21 0 Step-2
3 1 4 0 3
4 0 4 19 1
Worker Job
Example of Assignment Problem
2- PERFORM COLUMN REDUCTIONS BYSUBTRACTING THE MINIMUM VALUE IN EACH
COLUMN FROM ALL OTHER COLUMN VALUES
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Example of Assignment Problem
3- THE RESULTING TABLE IS AN OPPORTUNITY COST MATRIX.CROSS OUT ALL ZEROS IN THE MATRIX USING THE MINIMUMNUMBER OF HORIZONTAL OR VERTICAL LINES.
4- IF THE NUMBER OF LINES EQUALS THE NUMBER OF ROWS /COLUMN THE MATRIX, AN OPTIMUM SOLUTION HAS BEEN
REACHED AND ASSIGNMENTS CAN BE MADE WHERE THE ZEROSAPPEAR
A B C D
1 5 0 11 14
2 15 0 21 0 Step-33 1 4 0 3
4 0 4 19 1
WorkerJob
& 4
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A B C D
1 5 0 11 142 15 0 21 0 Step-4
3 1 4 0 3
4 0 4 19 1
Worker Job
Example of Assignment Problem
5- Assignment
Step-5&6
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1 2 3 4 5
A 10 3 3 2 8
B 9 7 8 2 7
C 7 5 6 2 4
D 3 5 8 2 4
E 9 10 9 6 10
JOBMACHINIST
Assignment Problem
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Scheduling
Product-Focused
Manufacturing
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Product-Focused
Scheduling
Two general types of product-focused
production: Batch - large batches of several
standardized products produced
Continuous - few products producedcontinuously.... minimal changeovers
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Scheduling Decisions
If products are produced in batches on thesame production lines: How large should production lot size be for
each product?
When should machine change overs bescheduled?
If products are produced to a delivery
schedule:At any point in time, how many productsshould have passed each operation if timedeliveries are to be on schedule?
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Batch Scheduling
EOQ for Production Lot Size How many units of a single product should be
included in each production lot to minimizeannual inventory carrying cost and annual
machine changeover cost?
DAnnual Demand
SOrdering or Set up cost
CCarrying / Holding cost
drate at which units are used out of inventoryDemand rate
prate at which units are supplied to inventoryProduction rate
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Example: EOQ for Production
LotsCPC, Inc. produces four standard electronicassemblies on a produce-to-stock basis. Theannual demand, setup cost, carrying cost, demand
rate, and production rate for each assembly areshown on the next slide.
a) What is the economic production lot size foreach assembly?
b) What percentage of the production lot of powerunits is being used during its production run?
c) For the power unit, how much time will passbetween production setups?
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Example: EOQ for Production
LotsAnnual Setup Carry Demand Prod.Demand Cost Cost Rate Rate
Power Unit 5,000 $1,200 $6 20 200
Converter 10,000 600 4 40 300
Equalizer 12,000 1,500 10 48 100Transformer 6,000 400 2 24 50
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Example: EOQ for Production
Lots Economic Production Lot SizesEOQ = (2DS/C[p/(p-d)]
1EOQ = (2(5,000)(1,200)/6[200/(200-20)] 1,490.7
2EOQ = (2(10,000)(600)/4[300/(300-40)] 1,860.5
3EOQ = (2(12,000)(1,500)/10[100/(100-48)] 2,631.2
4EOQ = (2(6,000)(400)/2[50/(50-24)] 2,148.3
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Example: EOQ for Production
Lots
% of Power Units Used During
Production
d/p = 20/200 = .10 or 10%
Time Between Setups for Power UnitsEOQ/d = 1,490.7/20 = 74.535
days
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Batch Scheduling
Limitations of EOQ Production Lot Size
Uses annual ballpark estimates ofdemand and production rates, not the mostcurrent estimates
Not a comprehensive scheduling techniqueonly considers a single product at a time
Multiple products usually share the samescarce production capacity
Sh Fl C t l
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Shop-Floor Control
Major Functions
1. Assigning priority of each shop order.
2. Maintaining work-in-process quantityinformation.
3. Conveying shop-order status information tothe office.
Shop-Floor Control:
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Shop Floor Control:
Major Functions (Continued)
4. Providing actual output data for capacitycontrol purposes.
5. Providing quantity by location by shop orderfor WIP inventory and accounting purposes.
6. Providing measurement of efficiency,utilization, and productivity of manpower andmachines.
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Input/Output Control
Input Output
Planned input should never exceedplanned output.
Focuses attention on bottleneck workcenters.
WorkCenter
Principles of Work Center
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Principles of Work Center
Scheduling
1. There is a direct equivalence between workflow and cash flow.
2. The effectiveness of any job shop should be
measured by speed of flow through the shop.
3. Schedule jobs as a string, with process stepsback-to-back.
4. A job once started should not be interrupted.
Principles of Job Shop
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Principles of Job Shop
Scheduling (Continued)
5. Speed of flow is most efficientlyachieved by focusing on bottleneck workcenters and jobs.
6. Reschedule every day.
7. Obtain feedback each day on jobs that
are not completed at each work center.
8. Match work center input information towhat the worker can actually do.
Principles of Job Shop
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Principles of Job Shop
Scheduling (Continued)
9. When seeking improvement in output,
lookfor incompatibility between engineeringdesign and process execution.
10. Certainty of standards, routings, and soforth is not possible in a job shop, butalways work towards achieving it.
At the end of each month a research and development team writes status
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At the end of each month, a research and development team writes statusreports for the projects worked on during the month. The team leaders, Andrewand Julie, submit the reports to the R&D director on the first Monday of eachmonth. It is late Friday evening and to their surprise, they have discovered that
the month ends on Sunday and the reports are due on Monday morning. Theyhave decided to come to work early Saturday morning, so they can finish thereports before Monday morning. They split the work as follows: Andrew willwrite and edit the reports while Julie collates data and draws all the necessarygraphs. Assume that Julie starts her work on a report as soon as Andrew is
finished with it and that Andrew works continuously. Times for the reports (inhours) are as follows:
Projects Andrew Julie
A 4 2B 3 5
C 5 1D 7 3E 8 6
What is the order of the projects using Johnson's rule?
How many hours will it take them to finish all the reports?
How many hours is Andrew & Julie idle?
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Thank You