Operations Scheduling

1
Operations Scheduling

• Typical Scheduling and Control Functions
• Job-shop Scheduling
• Shop-floor Control
• Principles of Work Center Scheduling

2
Work Center

• A work center is an area in a business in which
  productive resources are organized and work is
  completed
• Can be a single machine, a group of machines, or
  an area where a particular type of work is done

3
Capacity and Scheduling

• Infinite loading (Example MRP)
• Finite loading
• Forward scheduling
• Backward scheduling (Example MRP)

4
Types of Manufacturing Scheduling Processes and
Scheduling Approaches
Type of Process
Typical Scheduling Approach
Continuous process
Finite forward of process, machine limited
High-volume manufacturing
Finite forward of line, machine limited
Med-volume manufacturing
Infinite forward of process, labor and machine
limited
Low-volume manufacturing
Infinite forward of jobs, labor and some machine
limited
5
Typical Scheduling Process
6
Typical Scheduling and Control Functions

• Allocating orders, equipment, and personnel
• Determining the sequence of order performance
• Initiating performance of the scheduled work --
  dispatching
• Shop-floor control

7
Work-Center Scheduling Objectives

• Meet due dates
• Minimize lead time
• Minimize setup time or cost
• Minimize work-in-process inventory
• Maximize machine utilization

8
Scheduling n Jobs on One Machine
n jobs
One Machine
Scheduling Determine the order in which the n
jobs are to be processed.
9
Priority Rules for Job Sequencing

• 1. First-come, first-served (FCFS)
• 2. Shortest operating time first (SOT)
• 3. Earliest due date first (EDD)
• 4. Shortest slack time remaining first (STR)
• 5. Shortest average slack time remaining per
  operation first (STR/OP)

10
Priority Rules for Job Sequencing

• 6. Smallest critical ratio first (CR)
• Last come, first served (LCFS)
• 8. Random order or whim

11
Example First-Come First-Served
Suppose 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
12
Example Shortest Operating Time
Suppose you have the four jobs to the right
arrive for processing on one machine
What is the SOT schedule?
Do all the jobs get done on time?
No, Jobs A and B are going to be late
13
Example Earliest Due Date First
Suppose you have the four jobs to the right
arrive for processing on one machine
What is the earliest due date first schedule?
Do all the jobs get done on time?
No, Jobs C and B are going to be late
14
Example Critical Ratio Method
Suppose you have the four jobs to the right
arrive for processing on one machine
What is the CR schedule?
At Day 0 Job CR Next Job? A (5-0)/4
1.25 A B (10-0)/7 1.43 C (6-0)/3 2 D (4-0)/1
4
15
Example Critical Ratio Method (contd)
Repeat the same process after job A is done
What is the CR schedule?
Job A is done at Day 4 Job CR Next
Job? B (10-4)/7 0.86 C (6-4)/3 0.67 D (4-4)/1
0 D
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Example Critical Ratio Method (contd)
Continue this process until all jobs are scheduled
What is the CR schedule?
Job D is done at Day 5 Job CR Next Job? Last
Job B (10-5)/7 0.72 B C (6-5)/3 0.33 C
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Example Critical Ratio Method (contd)
What is the CR schedule?
Do all the jobs get done on time?
No, D,C, B are late
18
Example Last-Come First-Served
Suppose you have the four jobs to the right
arrive for processing on one machine
What is the LCFS schedule?
Answer Last-Come First-Served Schedule
Do all the jobs get done on time?

No, Jobs B and A are going to be late
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Evaluation of Performance

• Which of the methods is the best?
• Objective?
• Evaluate to minimize flow time
• FCFS 44 SOT 28 EDD 29 CR 43
• LCFS 31. SOT minimizes flow time is this
  generally true?

20
Evaluation of Performance (contd)

• Other criteria
• Criterion Lateness (days) Jobs in Shop
• FCFS
• SOT
• EDD
• CR
• LCFS

21
Scheduling n Jobs on m Machines
n jobs
m machines in parallel
n jobs
n jobs
Stage 2
Stage 1
m (2 in this case) stages with one machine per
stage
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Johnsons Rule for 2 Machines

• Criterion Minimizing total flow time (from the
  beginning of the first job until the completion
  of the last one)
• Procedure
• List the operation time for each job on both
  machines (stages)
• Select the shortest time do the job first if the
  shortest time is for the first machine and the
  last otherwise. In the case of a tie, do the job
  first.
• Repeat the two steps until the schedule is
  complete

23
Example Johnsons Rule (Part 1)
Suppose you have the following five jobs with
time requirements in two stages of production.
What is the job sequence using Johnsons Rule?
Time in Hours Jobs Stage
1 Stage 2 A 1.50 1.25 B
2.00 3.00 C 2.50 2.00 D
1.00 2.00
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Example Johnsons Rule (Part 2)
First, select the job with the smallest time in
either stage.
Time in Hours Jobs Stage
1 Stage 2 A 1.50 1.25 B
2.00 3.00 C 2.50 2.00 D
1.00 2.00
That is Job D with the smallest time in the first
stage. Place that job as early as possible in
the unfilled job sequence below.
Drop D out, select the next smallest time (Job
A), and place it 4th in the job sequence.
Drop A out, select the next smallest time. There
is a tie in two stages for two different jobs.
In this case, place the job with the smallest
time in the first stage as early as possible in
the unfilled job sequence.
Then place the job with the smallest time in the
second stage as late as possible in the unfilled
sequence.
Job Sequence 1 2 3 4
Job Assigned D
A
B
C
25
More Complex Cases

• 1. Three stages Johnsons rule can be extended
  to generate an optimal solution
• 2. More than three stages Johnsons rule does
  not necessarily produce an optimal solution. The
  problem is typically considered as a multi-stage
  queuing system and analyzed using simulation

26
The Assignment Problem

• 1. Assign n things to n destinations the
  assignment will affect some performance
  measurement
• 2. Each must be assigned to one and only one.
• 3. Only one criterion can be used (minimizing
  cost, maximizing profit, minimizing production
  time, etc.)

27
The Assignment Method

• Subtract the smallest number in each row from all
  numbers in that row
• Subtract the smallest number in each column from
  all numbers in that column
• Draw the least possible number of lines through
  all the zeros. If the minimum number of line is
  the number of jobs, an optimal solution has been
  identified. Otherwise, go to the next step.
• Subtract the smallest number not covered by lines
  from all uncovered numbers and add it to the
  number at each intersection of lines. Then repeat
  step 3.

28
Example The Assignment Method
Suppose there are three jobs that can be run on
four machines and the following table contains
cost information for each assignment. How should
the jobs be assigned to minimize total cost?
Machine Jobs A B C D
1 12 16 14 10 2 9 8 13 7 3 15 12 9 11
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Example Assignment Method (contd)

• n jobs for n machines create a dummy with
  zero cost is necessary
• Apply the procedure see class demonstration
• Assign jobs at intersection with a zero entry

Machine Jobs A B C D
1 12 16 14 10 2 9 8 13 7 3 15 12 9 11 Dummy
0 0 0 0
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Shop-Floor Control Major Functions

• 1. Assigning priority of each shop order
• 2. Maintaining work-in-process quantity
  information
• 3. Conveying shop-order status information to the
  office

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Shop-Floor Control Major Functions

• 4. Providing actual output data for capacity
  control purposes
• 5. Providing quantity by location by shop order
  for WIP inventory and accounting purposes
• 6. Providing measurement of efficiency,
  utilization, and productivity of manpower and
  machines

32
Gantt Charts
33
Input/Output Control
34
Input/Output Control (contd)
Work Center

• Planned input should never exceed planned output
• Focuses attention on bottleneck work centers

35
Principles of Work Center Scheduling

• 1. There is a direct equivalence between work
  flow 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 steps
  back-to-back
• 4. A job once started should not be interrupted

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Principles of Job Shop Scheduling

• 5. Speed of flow is most efficiently achieved by
  focusing on bottleneck work centers 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 to what
  the worker can actually do

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Principles of Job Shop Scheduling

• 9. When seeking improvement in output, look for
  incompatibility between engineering design and
  process execution
• 10. Certainty of standards, routings, and so
  forth is not possible in a job shop, but always
  work towards achieving it

38
Scheduling in Services

• The differences in scheduling between
  manufacturing and service
• Personnel scheduling
• consecutive days off
• Scheduling daily work times
• Scheduling hourly work times

39
Daily Scheduling of Telephone Operator Workshifts

Topline profile
Scheduler program assigns tours so that the
number of operators present each half hour
adds up to the number required
Tour
12 2 4 6 8 10
12 2 4 6 8 10
12
12 2 4 6 8 10
12 2 4 6 8 10
12
40
Weekly Workshift Schedule(5 consecutive work
days)

Schedule matrix, x day off Operator Su
M Tu W Th
F Sa 1 x
x
... 2 x
x
3
... x x
4
... x
x
5
x x
6
x x
7
x x
8 x

x Total 6 6
5 6 5
5 7 Required 3 6
5 6 5
5 5 Excess 3 0
0 0 0
0 2
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First Hour Principle

• Start with one time unit (hour, day, etc)
• Add, if necessary, to meet the exact requirement

Day Su M Tu W Th F Sa Total Required 3
6 5 6 5 5 5 Assigned 3 3 0 0 0
2 3 11 On duty 8 11 11 9 6 5 5 Excess 5
5 6 3 1 0 2 Is this optimal?
Total number of workers 11
42
Linear Programming Model

43
Question Bowl
44
Question 1

• A Work Center may be which of the following?
• A single machine
• A group of machines
• An area where a particular type of work is
  performed
• All of the above
• None of the above

Answer d. All of the above
45
Question 2

• When work is assigned to a work center simply
  based on what is needed over time, we would refer
  to this as which of the following scheduling
  systems?
• A finite loading of work
• An infinite loading of work
• Forward scheduling
• All of the above
• None of the above

Answer b. An infinite loading of work
46
Question 3

• Typical scheduling and controlling of operations
  include which of the following functions?
• Allocating orders at work centers
• Allocating equipment at work centers
• Allocating personnel at work centers
• All of the above
• None of the above

Answer d. All of the above
47
Question 4

• Typical scheduling and controlling of operations
  include which of the following functions?
• Determining the job sequences
• Dispatching
• Expediting late and critical orders
• All of the above
• None of the above

Answer d. All of the above
48
Question 5

• Which of the following are standard measures of
  schedule performance used to evaluate priority
  rules?
• Meeting due dates
• Maximizing job flow time
• Maximizing work-in-process inventory
• All of the above
• None of the above

Answer a. Meeting due dates (Correct answer can
also include minimizing WIP inventory, idle time,
and job flow time.)
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Question 6

• Which priority rule uses the calculation of the
  difference between the due date and the current
  date divided by the remaining processing time?
• STR
• SOT
• DDate
• FCFS
• None of the above

Answer e. None of the above (Correct answer can
is CR or critical ratio.)
50
Question 7

• The major functions of a shop-floor control are
  which of the following?
• Conveying shop-order status
• Measuring efficiency
• Assigning priorities
• Maintaining WIP quantity information
• All of the above

Answer e. All of the above (Correct answer can
also include providing quantity by location and
actual output data.)
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Question 8

• Which of the following are Tools of Shop-Floor
  Control?
• Daily dispatch lists
• Scrap reports
• Rework reports
• All of the above
• None of the above

Answer d. All of the above (Correct answer can
also include all status and exception reports and
input/output control reports.)
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Question 9

• Which of the following is a Principle of
  Work-Center Scheduling?
• There is a direct equivalence between work flow
  and cash flow
• Certainty of routings are very possible in a shop
• Reschedule only once a week
• All of the above
• None of the above

Answer a. There is a direct equivalence between
work flow and cash flow (There are nine other
principles.)
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End Q A