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Sequence the jobs as C-B-E-D-A. Flow times are:
3
3 + 4 = 7
7 + 5 = 12
12 + 7 = 19
19 + 8 = 27
Average flow time = 13.6 days
Chapter 14—Operations Scheduling and Sequencing
Multiple Choice
Sequencing Problem A for Questions #1 to #4
The following five jobs, along with their processing time and due dates, are given below.
1. Using the shortest processing time (SPT) rule, the average flow time for the five jobs is _____.
a. less than or equal to 5 days
b. more than 5 but less than or equal to 10 days
c. more than 10 but less than or equal to 15 days
d. more than 15 but less than or equal to 20 days
2. Using the earliest due date (EDD) rule, the average flow time for the five jobs is _____.
a. less than or equal to 5 days
b. more than 5 but less than or equal to 10 days
c. more than 10 but less than or equal to 15 days
d. more than 15 but less than or equal to 20 days
Processing
Days Due
Job
Time (days)
From Today
A
8
12
B
4
9
C
3
6
D
7
7
E
5
20
Sequence the jobs C-D-B-A-E. Calculations are shown below:
Job
Flow time
Lateness
Tardiness
C
3
0
D
3 + 7 = 10
3
B
10 + 4 = 14
5
A
14 + 8 = 22
10
E
22 + 5 = 27
7
Average flow time = 15.2 days
2
3. Using the earliest due date (EDD) rule, the average lateness for the five jobs is _____.
a. less than or equal to 5 days
b. more than 5 but less than or equal to 10 days
c. more than 10 but less than or equal to 15 days
d. more than 15 but less than or equal to 20 days
4. Using the earliest due date (EDD) rule, the average tardiness for the five jobs is _____.
a. less than or equal to 5 days
b. more than 5 but less than or equal to 10 days
c. more than 10 but less than or equal to 15 days
d. more than 15 but less than or equal to 20 days
Sequencing Problem B for Questions #5 to #8
The table below includes processing times and due dates for five jobs.
Processing
Days Due
Job
Time (days)
From Today
A
16
24
B
23
30
C
22
40
D
8
28
E
10
18
Sequence the jobs as D-E-A-C-B. Flow times are:
8
8 + 10 = 18
18 + 16 = 34
34 + 22 = 56
56 + 23 = 79
Average flow time = 39 days
5. Using the shortest processing time (SPT) rule, the average flow time for the five jobs is _____.
a. less than or equal to 10 days
b. more than 10 but less than or equal to 20 days
c. more than 20 but less than or equal to 30 days
d. more than 30 but less than or equal to 40 days
6. Using the earliest due date (EDD) rule, the average flow time for the five jobs is _____.
a. more than 10 but less than or equal to 20 days
b. more than 20 but less than or equal to 30 days
c. more than 30 but less than or equal to 40 days
d. more than 40 days
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7. Using the earliest due date (EDD) rule, the average lateness for the five jobs is _____.
a. less than or equal to 10 days
b. more than 10 but less than or equal to 20 days
c. more than 20 but less than or equal to 30 days
d. more than 30 but less than or equal to 40 days
8. Using the earliest due date (EDD) rule, the average tardiness for the five jobs is _____.
a. less than or equal to 10 days
b. more than 10 but less than or equal to 20 days
c. more than 20 but less than or equal to 30 days
d. more than 30 but less than or equal to 40 days
Sequencing Problem C for Questions #9 to #11
A new surgical facility called Cut & Sew is opening in neighborhoods throughout the United
States. They are job shops that handle a variety of outpatient surgical procedures. Their process is
set up so that one doctor cuts and another sews. They have five patients to sequence for
tomorrow. Since the weather forecast is for a warm and sunny day, they would also like to play
golf tomorrow. They want to sequence their patients with the objective of minimizing the time
from the beginning of the first job until the finish of the last job. The patients and estimated times
are as follows:
Patient
Cut Time (hours)
Sew Time (hours)
A
2.3
2.8
B
2.5
3.0
C
2.0
1.5
D
0.6
1.0
E
3.6
2.6
9. Using Johnson’s rule to sequence these patients, the final patient sequence is _____
considering “A” as the first patient and “E” as the last.
a. A, B, C, D, E
10
0
57 + 22 = 79
39
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b. B, E, A, C, D
c. C, A, B, E, D
d. D, A, B, E, C
10. Using Johnson’s rule to sequence these patients, the makespan is _____.
a. less than or equal to 5 hours
b. more than 5 but less than or equal to 10 hours
c. more than 10 but less than or equal to 15 hours
d. more than 15 but less than or equal to 20 hours
11. Using Johnson’s rule to sequence the patients, and if your uncle is patient B, he will be
finished with surgery in _____.
a. less than or equal to 5 hours
b. more than 5 but less than or equal to 10 hours
c. more than 10 but less than or equal to 15 hours
d. more than 15 but less than or equal to 20 hours
Staff Scheduling Problem D for Questions #12 to #14
A movie theater requires the following minimum number of employees, each of whom is required
to have two consecutive days off.
Day:
M
Tu
W
Th
F
Sa
Su
Minimum Personnel Required:
1
1
3
2
5
4
3
12. Using the staff scheduling method, the solution minimizes the number of employees required
to meet this demand with _____ number of employees.
a. 3 employees
b. 4 employees
c. 5 employees
d. 6 employees
Job
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13. Using staff scheduling method, the most overstaffed day is _____.
a. Friday only
b. Monday only
c. Tuesday only
d. Thursday only
14. Using staff scheduling method, the days on which demand equals staff capacity are _____.
a. Tuesday and Wednesday
b. Wednesday and Sunday
c. Thursday and Friday
d. Friday and Saturday
Staff Scheduling Problem E for Questions #15 to #17
A print shop has four jobs that have to be processed through their only five-color press. They
usually use the first come, first served (FCFS) rule of scheduling jobs. However, the customers
are waiting in the lobby for these jobs so the shop wants to minimize the average waiting time.
They are going to use the shortest processing time rule to do so. Processing times for each job are
as follows (assume this is the arrival order): Job A, 30 minutes; Job B, 17 minutes; Job C, 12
minutes; and Job D, 39 minutes.
15. Using the shortest processing time (SPT) rule to sequence these jobs, the final sequence
is_____, if A is the first person to arrive and D is the last.
a. A, B, C, D
b. C, B, A, D
c. C, D, B, A
d. A, B, D, C
16. Using the shortest processing time (SPT) rule to sequence these jobs, the average waiting
(flow) time is _____.
a. less than or equal to 20 minutes
b. more than 20 but less than or equal to 30 minutes
c. more than 30 but less than or equal to 40 minutes
d. more than 40 but less than or equal to 50 minutes
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a.
Shortest processing time (SPT) rule:
Order of jobs: C, B, A, D
b.
Average flow time: (12 + 29 + 59 + 98)/4 = 49.50
c.
First come, first served (FCFS):
Order of jobs: A, B, C, D
Completion (flow) times: A = 30; B = 30 + 17 = 47; C = 47 + 12 = 59; D = 59 + 39 = 98
Average waiting time: (30 + 47 + 59 + 98)/4 = 58.50
17. Using the first come, first served (FCFS) rule to sequence these jobs, the average waiting
(flow) time is _____.
a. more than 20 but less than or equal to 30 minutes
b. more than 30 but less than or equal to 40 minutes
c. more than 40 but less than or equal to 50 minutes
d. more than 50 minutes
18. Scheduling refers to specifying:
a.
the sequence in which jobs must be completed.
b.
the due date for each job.
c.
the start and completion times of jobs.
d.
the makespan of each job.
19. Triage by nurses in an emergency room would be an example of:
a.
scheduling.
b.
sequencing.
c.
appointments.
d.
work shifts.
20. Staff scheduling needs all of the following EXCEPT:
a.
flow time estimates.
b.
accurate forecasting.
c.
staffing levels required by time period.
d.
determining available personnel.
21. Which of the following is NOT a consideration when designing an appointment system?
a.
Determining the appointment time interval
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b.
Determining the appropriate sequencing rule
c.
Determining the length of each workday and the time off-duty
d.
Deciding on an overbooking policy
22. The time needed to process a given set of jobs is called:
a.
flow time.
b.
ready time.
c.
makespan.
d.
due date.
23. The numerical difference between the completion time and the due date is called:
a.
flow time
b.
lateness
c.
makespan
d.
tardiness
24. ScheduleAnywhere.com, an online software, helps clients do all the following EXCEPT:
a.
schedule employees from any computer with Internet access.
b.
decide how much to overbook for each day of the week.
c.
see who’s scheduled and who’s available.
d.
avoid scheduling conflicts.
25. The shortest processing time (SPT) rule:
a.
maximizes the number of jobs in the system.
b.
maximizes average flow time.
c.
minimizes resource utilization.
d.
minimizes work-in-process inventory.
26. The sequencing rule that minimizes the maximum number of jobs that are past due from a
given set of jobs is:
a.
shortest processing time (SPT).
b.
earliest due date (EDD).
c.
first come, first served (FCFS).
d.
least amount of work at the next process queue (LWNQ).
27. If the highest priority is to minimize the average job lateness, then the job sequence should
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begin with those jobs requiring:
a.
the shortest processing time.
b.
the smallest critical ratio.
c.
the least remaining operations.
d.
the longest processing time.
28. In a two-resource sequencing problem:
a.
the makespan is the same for any sequence of jobs.
b.
flow time is maximized.
c.
the goal is to minimize makespan.
d.
each job can be processed by either resource first.
29. A requirement of Johnson’s two-resource sequencing rule is:
a.
all jobs must begin at the same time.
b.
jobs must be processed through each work center in the same job sequence.
c.
only two jobs can be processed at a time through each work center.
d.
total processing time must be minimized.
30. Johnson’s sequencing rule is used to sequence:
a.
several jobs through five work centers.
b.
several jobs through one work center.
c.
two jobs through several work centers.
d.
several jobs through two work centers.
31. Which of the following is NOT a criterion for evaluating job sequencing rules?
a.
Average flow time
b.
Lateness
c.
Tardiness
d.
Sum of processing times
32. The chief disadvantage of the shortest processing time (SPT) rule is:
a.
it maximizes the average flow time.
b.
it maximizes the number of jobs in the system.
c.
long-duration jobs may have excessive completion times.
d.
average job lateness and average job tardiness are excessive.
9
33. Gantt charts can be used to:
a.
determine the appointment time interval.
b.
determine how to handle overbooking for each day of the week.
c.
display the two-resource sequencing solution using Johnson’s Rule.
d.
display minimizing maximum tardiness.
34. Which of the following is an example of a situation for which a Gantt chart would be
appropriate?
a.
Developing a factory layout
b.
Tracking inventory levels over time
c.
Monitoring job schedules
d.
Forecasting personnel requirements in a two-shift operation
True/False Questions
1. Scheduling refers to determining the order in which jobs or tasks are processed.
2. Scheduling applies to all aspects of the value chain.
3. Scheduling and sequencing methods used in manufacturing are more beneficial in low-
contact, than high-contact, service processes.
4. Scheduling problems occur almost exclusively in manufacturing.
5. Telling an umpire crew to work baseball games in Chicago, then Milwaukee, and then
Cleveland is an example of a sequence.
6. The time to rest and travel between games for baseball umpire crews is an important factor in
developing their schedule.
7. UPS, the world’s largest package delivery company, is highly dependent on scheduling but
not sequencing.
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8. Appointments can be viewed as a reservation of service time and capacity.
9. Indirectly, appointments reduce the cost of providing a service because the service provider is
idle less each workday.
10. Appointments systems usually overbook to maximize revenue when no-show percentage
reaches 10 percent or more.
11. Two examples of process-focused performance measures for sequencing rules are tardiness
and lateness.
12. Sequencing is not as much of a concern when several activities use a common resource.
13. Flow time is the amount of time a job spends in a shop or factory.
14. The makespan is the sum of flow times of a given set of jobs.
15. High flow times reduce work-in–process (WIP) inventory.
16. A lateness measure can only be zero (0) or a positive number.
17. Tardiness measures the amount of time by which the completion time exceeds the due date.
18. The shortest processing time (SPT) rule and the earliest due date (EDD) rule will always
provide the same sequence.
19. The shortest processing time (SPT) sequencing rule will maximize the average flow time.
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20. The earliest due date (EDD) rule minimizes the maximum of jobs past due but doesn’t
perform well on average flow time, work-in–process (WIP) inventory, or resource utilization.
21. For a single processor, a first come, first served (FCFS) rule minimizes the average flow time
because it considers both the job and customer criterion.
22. A tardiness measure can be either zero (0) or a positive number.
23. Since all jobs eventually get done, job sequencing has no effect on resource utilization.
24. In practice, whenever processing times of a set of jobs are almost equal, managers typically
use a first come, first served (FCFS) rule.
25. Like the shortest processing time (SPT) rule, the earliest due date (EDD) rule minimizes the
average flow time.
26. In sequencing a set of jobs on a single processor, different sequences will have different
makespans but the same average flow times.
27. When several products share common facilities, product sequencing affects cost.
28. In sequencing jobs in a flow shop with two resources, Johnson’s rule finds a sequence that has
the smallest makespan.
29. Rescheduling rarely occurs unless customers change their requested due dates.
30. Gantt charts can show what jobs are ahead of schedule, behind schedule, and on schedule.
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Case Study Questions (To reward students who attend class, listen and learn, and take good
class notes on the case discussion and/or student team presentation.)
1. Which one of the following statements about the Balloons Aloha case study on scheduling and
sequencing is TRUE?
a. The sequencing rule used did not impact average flow time but it did change tardiness.
b. The earliest due date (EDD) rule was the best sequencing rule to use for this case situation.
c. The shortest processing time (SPT) rule was the best sequencing rule to use for this case
situation.
d. Johnson’s rule was the best sequencing rule to use for this case situation.
Problems for Manual Grading, Take-Home Exams and Partial Credit (Also, review the OM
Instructor’s Manual for end-of-chapter questions/problems)
1. Differentiate between scheduling and sequencing.
2. What are the four steps involved in staff scheduling that attempt to match available personnel
with the needs of the organization?
3. What are the four decisions that are considered in designing an appointment system?
4. Give at least five examples of service organizations (and employee types) where, due to high
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variability in customer demand, staff-scheduling problems are prevalent.
5. Compare and contrast the advantages and disadvantages of the shortest processing time (SPT)
and the earliest due date (EDD) sequencing rules.
6. Explain the three categories of criteria used to evaluate job sequencing performance. For each
category, provide two example measures.
7. Explain why any sequence chosen in the single-machine scheduling problem will not change
makespan time.
M
W
F
2.
Find the job with the shortest processing time (on either resource).
Resource #2, sequence the job last.
4.
Repeat steps 2 and 3, using the next-shortest processing time and working inward from
8. Describe the algorithm that defines Johnson’s sequencing rule for the two-resource sequencing
problem.
2.
Sub-par labor performance
3.
Equipment (including power) failures
4.
Tooling (including set-up) problems
9. Short-term capacity fluctuations necessitate changes in schedules. List at least five factors
affecting short-term capacity.
PROBLEMS
10. A restaurant needs the following number of wait staff to serve its evening guests.
Day:
M
Tu
W
Th
F
Sa
Su
Minimum Number of Wait Staff
Needed:
5
2
1
4
6
7
2
How many employees are needed so that each has two consecutive days off? Construct a work
schedule for these employees.
13 employees are needed.
Employee
Mon
Tue
Thu
Fri
Sat
be to choose (Mon, Tue) or (Tue, Wed) as days off. For the twelfth employee the alternative
options would be to choose (Thu, Fri) or (Tue, Wed) as days off.
b.
Mon. overstaffed by 3; Wed. overstaffed by 3; Thu. overstaffed by 1; and Fri. overstaffed
by 1.
11. A young entrepreneur has just opened an electronics store. One of the many tasks that she
must address is work scheduling. She plans to stay open from 9 a.m. to 9 p.m., Monday through
Saturday. She expects her employees to stock the shelves and also be available for cashier check-
out when needed. All employees are full time and work four days with two consecutive days off
each week. She estimates the number of employees needed each day as follows:
Mo
n
Tue
Wed
Thu
Fri
Sat
Total
6
9
5
7
9
10
46
a.
Use the days-off scheduling procedure to determine the minimum number of employees
required.
b.
Based on your schedule found in part (a), which days are overstaffed and by how many
workers are they overstaffed?
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
Shortest processing time (SPT):
Order of jobs:
Completion (flow) times: C = 2; A = 2 + 4 = 6; F = 6 + 6 = 12; E = 12 + 9 = 21;
D = 21 + 16 = 37; B = 37 + 26 = 63
12. An airplane repair facility has a contract to repair cargo aircrafts for a regional airline. There
are 62 planes in the airline company’s fleet of planes. Because of the punishing workload, the
planes require a considerable amount of maintenance. The repair facility is trying to determine
how to schedule the needed repairs. They want to compare the shortest processing time (SPT)
rule and the first come, first served (FCFS) rule. Currently, the following planes need repair and
are in the repair facility (data given is in the order of plane arrival, only one plane is worked on at
a time, and the shop is open 24 hours a day, 7 days a week).
Plane
Estimated repair time
A342
4 hours
B554
26 hours
C222
2 hours
D876
16 hours
E211
9 hours
F887
6 hours
a.
In what order should the planes be repaired using the shortest processing time rule (use first
letter of plane)?
b.
What is the average time (in hours) in the shop using the shortest processing time (SPT)
rule?
c.
What is the average time (in hours) in the shop using the first come, first served (FCFS)
rule?
1
2
3
4
5
6
7
8
9
a.
First come, first served (FCFS):
Order of jobs: A, B, C, D, E
Completion (flow) times: A = 4; B = 4 + 9 = 13; C = 13 + 5 = 18;
D = 18 + 8 = 26; E = 26 + 11 = 37
Average flow time:
(4 + 13 + 18 + 26 + 37)/5 = 98/5 = 19.6 hours
b.
Average job lateness (difference between flow time and time to completion):
(- 4 -17 + 1 + 18 + 25)/5 = 23/5 = 4.6 hours
c.
Shortest processing time (SPT):
Order of jobs: A, C, D, B, E
Completion (flow) times: A = 4; C = 4 + 5 = 9; D = 9 + 8 = 17; B = 17 + 9 = 26;
E = 26 + 11 = 37
Average flow time:
(4 + 9 + 17 + 26 + 37)/5 = 18.6 hours
d.
Average job lateness (difference between flow time and time to completion):
13. A print shop has five large commercial printing jobs to finish. They are trying to decide
whether to use the shortest processing time (SPT) or the first come, first served (FCFS)
sequencing rule. Data on estimated processing time (in hours) and time to promised completion
(in hours) is as follows (jobs shown in order of arrival):
Job
Processing time
Time to promised completion
A
4
8
B
9
30
C
5
17
D
8
8
E
11
12
a.
What is the average flow time in hours using the FCFS rule?
b.
What is the average job lateness in hours using the FCFS rule?
c.
What is the average flow time in hours using the SPT rule?
d.
What is the average job lateness in hours using the SPT rule?
(2 + 6 + 12 + 21 + 37 + 63)/6 = 141/6 = 23.5 hours
c.
First come, first served (FCFS):
Order of jobs: A, B, C, D, E, F
Completion (flow) times: A = 4; B = 4 + 26 = 30; C = 30 + 2 = 32;
D = 32 + 16 = 48; E = 48 + 9 = 57; F = 57 + 6 = 63
Average time in shop:
(4 + 30 + 32 + 48 + 57 + 63)/6 = 234/6 = 39.0 hours
18
14. At the end of each month, a research and development team writes status reports for the
projects worked on during the month. The team leaders, Andrew and Julie, submit the reports to
the R&D director on the first Monday of each month. It is late Friday evening and to their
surprise, they discover that the month ends on Sunday, and the reports are due on Monday
morning. They decide to come to work early Saturday morning, so they can finish the reports
before Monday morning. They split the work as follows: Andrew will write and edit the reports,
while Julie collates data and draws all the necessary graphs. 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 (in hours) are as follows:
Projects
Andrew
Julie
A
4
2
B
3
5
C
5
1
D
7
3
E
8
6
a.
What is the order of the projects using Johnson’s rule?
b.
How many hours will it take them to finish all the reports?
c.
How many hours is Andrew idle?
d.
How many hours is Julie idle?
a.
Order of jobs using Johnson’s rule: B, E, D, A, C
b.
Andrew:
B (3), E(11), D (18), A (22), C (27)
Julie:
B (8), E(17), D (21), A (24), C (28)
(time in parentheses is cumulative hours to complete)
It will take 28 hours to complete all of the reports
c.
d.
15. A company is faced with seven tasks that have to be processed through two work centers,
work center I and then center II. Assume work center I works continuously and that they are
using Johnson’s rule. Work centers need not change over to new jobs at the same time. Data
appears below in hours:
Task
Work Center I
Work Center II
A
2.58
3.47
B
1.66
5.84
C
2.71
2.41
D
5.52
1.99
E
3.38
7.62
F
5.22
1.73
G
2.89
1.11
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a.
What is the sequence of tasks?
b.
What is the time in hours to complete all the tasks in both work centers?
c.
What is the total idle time (in hours) for work center I?
d.
What is the total idle time (in hours) for work center II?
b.
Work center I: B (1.66); A (4.24); E (7.62); C (10.33); D (15.85);
F (21.07); G (23.96)
(time in parentheses is cumulative hours to complete)
It will take 25.83 hours to complete all tasks
d.
Work center II’s idle time: 1.66 hours (wait for task B)