15: CHAPTER SHORT-TERM SCHEDULING
TRUE/FALSE
1.
Delta uses mathematical short-term scheduling techniques and a high-tech nerve center to
manage the rapid rescheduling necessary to cope with weather delays and similar
disruptions.
True (Global company profile, moderate)
2.
Short-term scheduling is important to efficiency and to cost reduction, but its impact
is not of strategic importance.
False (The strategic importance of short-term scheduling, moderate)
3.
The benefits of effective scheduling include lower cost, faster delivery, and dependable
delivery.
True (The strategic importance of short-term scheduling, moderate)
4.
In forward scheduling, jobs are scheduled as late as possible within the time
allowed by the customer due dates.
False (Scheduling issues, moderate)
5.
One criterion for developing effective schedules is minimizing completion time.
True (Scheduling issues, easy)
6.
Scheduling optimization systems used in retail stores typically track customer traffic in 4hour time increments.
False (Scheduling services, difficult) {AACSB: Use of IT}
7.
Process-focused facilities and repetitive facilities generate forward-looking schedules, but
process- focused facilities do this with JIT and kanban while repetitive facilities generally
use MRP.
False (Scheduling issues, moderate)
8.
The work center master file contains data such as capacity and efficiency.
True (Scheduling process-focused facilities, moderate)
9.
The constant work-in-process (ConWIP) card aids input-output control by limiting the
amount of work in a work center.
True (Loading jobs, easy)
10. A Gantt load chart shows the loading and idle time of several departments, machines, or
facilities.
True (Loading jobs, moderate)
11.
Gantt charts are useful for scheduling jobs, but not for loading them.
False (Loading jobs, easy)
12.
The assignment method provides an optimum, one-to-one assignment of jobs to resources.
True (Loading jobs, easy)
1 3.
Earliest due date is a shop floor dispatching (sequencing) rule that relates the time
available to complete a job to the amount of work left to be completed.
False (Sequencing jobs, moderate)
407
1 4.
The critical ratio sequencing rule prioritizes the jobs based on the importance or
value of the customers who have placed the orders.
False (Sequencing jobs, moderate)
15.
Dispatching rules are typically judged by four effectiveness criteria: average
completion time, utilization, average number of jobs in the system, and average job
lateness.
True (Sequencing jobs, moderate)
16.
Johnson's rule (and its extensions) sequences a set of jobs through a set of operations
where the operations must be performed in a specific order.
True (Sequencing jobs, moderate)
17.
Finite capacity scheduling allows virtually instantaneous changes by operators,
which is the technique's primary advantage over rule-based scheduling.
True (Finite capacity scheduling, moderate)
18.
The word "finite" in finite capacity scheduling refers to the use of finite or limited
capacity rather than unlimited capacity.
True (Finite capacity scheduling, moderate)
19. The theory of constraints is fundamental to proper use of the assignment method of loading
jobs.
False (Theory of constraints, moderate)
20.
The theory of constraints is a body of knowledge that deals with anything that
limits an organization's ability to meet its goals.
True (Theory of constraints, easy)
21.
Substantial research has proved that the only successful method of dealing with
bottlenecks is to increase the bottleneck's capacity.
False (Theory of constraints, moderate)
22.
The first step in level material use is to combine orders into a few large batches in order
to utilize economies of scale.
False (Scheduling repetitive facilities, easy)
23.
In services, the scheduling emphasis is usually on staffing levels, not materials.
True (Scheduling services, easy)
24.
Because of the significance of labor in the scheduling of services, behavioral and
social issues, wage and hour law, and union contracts all complicate the scheduling
process.
True (Scheduling services, moderate)
25.
In manufacturing scheduling, physical inventories of goods can buffer variations in
demand, but service scheduling normally lacks that buffer because services are generally
consumed at the same time they are delivered.
True (Scheduling services, moderate)
408
2 6.
Some firms have developed arrangements to literally swap employees with each
other during their respective peak demand times.
True
(Scheduling
services,
moderate)
MULTIPLE CHOICE
27.
Which of the following statements regarding scheduling at Delta Airlines is false?
a. About one flight in twenty is disrupted by weather
events.
b. Schedule changes at one airport have a ripple effect that may have impacts in many
others. c.
Delta's high-tech computer and communications system is located in
Atlanta.
d. Delta's rapid rescheduling uses mathematical scheduling
models.
e. Delta's rapid rescheduling promotes air safety and limits traveler inconvenience, but
has not resulted in money savings for Delta.
e (Global company profile,
moderate)
28.
Which of the following best describes the strategic importance of short-term scheduling?
a. Effective scheduling, through lower costs, faster delivery, and more dependable
schedules, can provide a competitive advantage.
b. Effective scheduling is a tactical tool for increasing demand to meet
production.
c. Forward scheduling looks to future demand levels in order to increase customer
satisfaction. d. Aggregate planning is a tactical action, but short-term scheduling is
strategic because of its
immense impact on
costs.
e. Short-term scheduling matches capacity to demand during the short term, three to
eighteen months into the future.
a (The strategic importance of short-term scheduling,
moderate)
29.
The three components that can lead to competitive advantage through effective
scheduling are a.
aggregate planning, intermediate scheduling, and medium-term
planning
b.
forward scheduling, real-time scheduling, and backward
scheduling c. the item master file, the routing file, and the workcenter master file d.
lower costs, faster delivery, and more
dependable schedules
e. Gantt charts, Johnson's rule and the Pareto
principle
d (The strategic importance of short-term scheduling,
moderate)
30.
The sequence of decisions that affect
scheduling is a.
short
termintermediate termlong term
b. capacity planningaggregate planningmaster scheduleshort-term
schedules c. strategic decisionstactical decisionsoperational decisions
d.
forward decisionscurrent decisionsbackward
decisions
e. none of the
above
b
(Scheduling
issues,
moderate)
31.
Forward scheduling is the
scheduling of a.
the end items
or finished products
b. jobs as soon as the requirements are
known
c. the start items or component
parts
d. the final operation first beginning with the due
date e. jobs according to their profit contributions
b
(Scheduling
moderate)
issues,
409
3 2.
Short-term schedules are prepared
a. directly from the aggregate
plans b. directly from the
capacity plans
c. from inventory records for items that have been used up
d. from master schedules which are derived from aggregate
plans e. from the purchasing plans
d (Scheduling issues, moderate)
33. Which scheduling technique should be employed when due dates are important for a job
order?
a. forward
scheduling b.
loading
c. dispatching
d. backward
scheduling e. master
scheduling
d (Scheduling issues, moderate)
34.
Which of the following is not an effectiveness criterion for scheduling?
a. minimizing customer waiting
time b. minimizing completion
time
c. minimizing WIP
inventory d. maximizing
utilization
e. maximizing flow time
e (Scheduling issues, moderate)
35.
The scheduling criterion minimize work-in-process inventory
a. results in the smallest flowtime of all scheduling criteria
b. is especially useful in problems solved with Johnson's rule
c. uses the average number of jobs in the system as the indicator of the level of
inventory d. is identical to the maximize utilization criterion
e. All of the above are true.
c (Scheduling issues, moderate)
36.
The four criteria for short-term
scheduling a. are of equal importance
b. include maximize completion time and minimize
utilization c. are applied simultaneously
d. may have different levels of importance, depending on
circumstances e.
All of the above are true.
d (Scheduling issues, moderate)
37.
Scheduling is rather straightforward in product-focused facilities
because a.
kanban automates the scheduling of the assembly
line
b. demand is reasonably stable, and capacities, set-up times, and run times are
generally known c. assembly line balancing assures the highest possible production
efficiency
d. finite capacity scheduling has made MRP much more realistic
e. All of the above are true.
b (Scheduling issues, moderate)
410
38.
Forward scheduling
a. begins with a delivery date, then offsets each operation one at a time, in
reverse order b. is well suited where the supplier is usually able to meet precise
delivery dates
c. tends to minimize work-in-process inventory
d. assumes that procurement of material and operations start as soon as requirements
are known e. produces a schedule only if it meets the due date
d (Scheduling issues, moderate)
39.
Which file contains important information regarding an item's flow through the shop?
a. item master file
b. work center master
file c. control files
d. routing file
e. None of the above provides information regarding an item's flow through the shop.
d (Scheduling process-focused facilities, moderate)
40. Which of these is not part of the planning files of a production planning and control
system?
a. a progress file
b. a work center master
file c. an item master file
d. a routing file
e. They are all part of the planning files.
a (Scheduling process-focused facilities, moderate)
41.
Which of the following files tracks work order progress?
a. work center master
files b. routing files
c. item master
files d. control
files
e. None of the above tracks work order progress.
d (Scheduling process-focused facilities, moderate)
42.
The production database containing information about each of the components that a firm
produces or purchases is the
a. routing file
b. work center master
file c. control file
d. item master file
e. none of the above
d (Scheduling process-focused facilities, moderate)
43.
The short-term scheduling activity called loading
a. assigns dates to specific jobs or operations steps
b. specifies the order in which jobs should be done at each
center c.
assigns jobs to work centers
d. assigns workers to jobs
e. assigns workers to machines
c (Loading jobs, easy)
411
4 4.
The assignment method
is
a. a method to highlight overloads in a given work center
b. a computerized method of determining appropriate tasks for an operation
c. a form of linear programming for optimally assigning tasks or jobs to
resources d. the same thing as the Gantt schedule chart
e. a method for achieving a balance between forward and backward scheduling
c (Loading jobs, moderate)
45.
A scheduling technique used to achieve optimum, one-to-one matching of tasks and
resources is a. the assignment method
b. Johnson's rule
c. the CDS algorithm
d. the appointment
method e.
the
reservation method
a (Loading jobs, moderate)
46.
Which of the following is an aid used to monitor jobs in
process?
a. a Gantt load chart
b. the assignment
method c.
a Gantt
schedule chart d.
Johnson's rule
e. none of the above
c (Loading jobs, moderate)
47.
A method of input-output control that uses a system of cards to limit the amount of work
at a work center and also to control lead time and monitor backlog is
a. the assignment method
b. backward
scheduling c. forward
scheduling
d. constant work-in-process or ConWIP
e. level material use
d (Loading jobs, easy)
48.
If an assignment problem consists of 6 workers and 7
projects, a.
one worker will not get a project
assignment
b. one worker will be assigned two projects
c. each worker will contribute work toward the seventh
project d. one project will not get a worker assigned
e. The problem cannot be solved by assignment method.
d (Loading jobs, moderate)
49.
If an assignment problem consists of 5 workers and 4
projects, a.
one worker will not get a project
assignment
b. one project will be assigned two workers
c. the fifth worker will split time among the four
projects d. one project will not get a worker
assigned
e. The problem cannot be solved by assignment method.
a (Loading jobs, moderate)
412
5 0.
Three jobs are to be assigned to three machines. Cost for each job-machine combination
appears in the table below. Perform the first two steps of the assignment method (subtract
the smallest number in each row and subtract the smallest number in each column; then
cover with straight lines). At
this point in the problem-solving process
Machine A
11
8
9
Job 1
Job 2
Job 3
Machine B
14
10
12
Machine C
6
11
7
a. the row for Job 1 contains the values 5, 6, and 0
b. calculations are complete, and the problem is ready for an optimal set of
assignments c. the column for Machine B indicates that it should be retired
d. Job 1 should be performed on Machine B
e. Job 1 should be performed on Machine A
a (Loading jobs, difficult) {AACSB: Analytic Skills}
51.
Orders are processed in the sequence in which they arrive if (the) rule sequences the
jobs. a.
earliest due date
b. slack time remaining
c. first come, first
served d. critical ratio
e. Johnson's
c (Scheduling jobs, moderate)
52.
Which of the following dispatching rules ordinarily gives the best results when the
criterion is lowest time for completion of the full sequence of jobs?
a. shortest processing time (SPT)
b. critical ratio (CR)
c. first in, first out (FIFO)
d. first come, first served (FCFS)
e. longest processing time
a (Scheduling jobs, moderate)
53.
Five jobs are waiting to be processed. Their processing times and due dates are given
below. Using the shortest processing time dispatching rule, in which order should the
jobs be processed?
a.
E b.
B c.
C d.
C e.
B
A,
C,
B,
D,
C,
B, C,
E, A,
D, A,
A, E,
E, A,
D,
D,
E,
B,
D,
d (Scheduling jobs, moderate) {AACSB: Analytic
Skills}
413
5 4.
Sequencing (or dispatching)
a. assigns dates to specific jobs or operations
steps b. assigns jobs to work centers
c. specifies the order in which jobs should be done at each
center d. assigns workers to jobs
e. assigns workers to machines
c (Scheduling jobs, moderate)
55.
Five jobs are waiting to be processed. Their processing times and due dates are given
below. Using the earliest due date dispatching rule, in which order should the jobs be
processed?
Job
A
B
C
D
E
Processing Time (days) Job due date (days)
4
7
2
4
8
11
3
5
5
8
a. C, E, A, D,
B b. A, B, C, D,
E c. B, D, A, E,
C d. C, B, A, E,
D
e. none of the
above
c (Scheduling jobs, moderate) {AACSB: Analytic
Skills}
56.
Flow time represents the time
a. an order spends waiting for processing at a work
center b. an order spends being processed at a work
center
c. an order spends moving from one work center to
another
d. to complete an order, including time spent in processing and in
waiting e.
none of the above
d
(Scheduling
jobs,
moderate)
57.
Which of the following dispatching rules tends to minimize job flow time?
a. FCFS: first come, first
served b.
SPT: shortest
processing time c.
EDD:
earliest due date
d.
LPT: longest processing
time e. FCLS: first come, last
served b (Scheduling jobs,
moderate)
58.
Average completion time for a schedule sequence at a work center is the
ratio of a.
total processing time to the number of jobs
b. total flow time to total processing
time c. total flow time to the number
of jobs
d. total processing time plus total late time to the number
of jobs e.
total flow time plus total late time to the
number of jobs
c
(Scheduling
moderate)
jobs,
414
59. Eight jobs have been sequenced at a single work center. Total processing time for the eight
jobs is
34 hours and total flow time for the sequence is 85 hours. For this schedule, utilization is
and average jobs in the system is
.
a. 100 percent; 10.625
b. low; .0941
c. 0.400 or 40 percent; 2.5
d. 0.235 or 23.5 percent;
4.25 e. maximized;
minimized
c (Sequencing jobs, moderate) {AACSB: Analytic Skills}
60.
Five welding jobs are waiting to be processed. Their processing times and due dates
are given below. Using the critical ratio dispatching rule, in which order should the
jobs be processed?
a. B, D, A, E,
C b. C, D, A, B,
E c. C, E, A, D,
B d. E, B, A, D,
C
e. none of the above
b (Scheduling jobs, moderate) {AACSB: Analytic Skills}
61.
Which critical ratio value implies that a job is already late?
a. more than
100 b. 1
c. less than 1
d. 10
e. none of the above
c (Scheduling jobs, moderate)
62.
The priority rule which sequences jobs using the smallest ratio of due date to
processing time is a. critical ratio
b. earliest due date
c. first come, first served
d. longest processing
time e. shortest
processing time
a (Scheduling jobs, moderate)
63. Which of the following is an advantage of the FCFS dispatching rule when used in
services?
a. FCFS is easy to update.
b. FCFS minimizes the average number of jobs in the
system. c.
FCFS minimizes the average lateness of
all jobs.
d. FCFS maximizes the number of jobs completed on
time. e. FCFS seems fair to customers.
e (Scheduling jobs, moderate)
415
6 4.
The most appropriate sequencing rule to use if the goal is to dynamically track the
progress of jobs and establish relative priority on a common basis is
a. shortest processing time
b. earliest due
date c. critical
ratio
d. longest processing time
e. Johnson's rule
c (Scheduling jobs, moderate)
65.
Use of the shortest processing time sequencing rule generally
results in a.
maximum average lateness
b. maximum utilization
c. maximum effectiveness
d. minimum average flow
time e. none of the above
d (Scheduling jobs, moderate)
66.
Which of the following dispatching rules is typically the best technique for taking first
those jobs with the most urgent needs?
a. shortest processing
time b. critical ratio
c. earliest due date
d. longest processing
time e. none of the
above
e (Scheduling jobs, moderate)
67.
When a set of jobs must pass through two workstations whose sequence is fixed,
rule most commonly applied.
a. critical ratio
b. earliest due date
c. first come, first
served d. slack time
remaining
e. Johnson's rule
e (Scheduling jobs, moderate)
68.
A recent advance in short-term scheduling that makes use of expert systems and
simulation in solving dynamic scheduling problems is
a. forward scheduling
b. backward
scheduling c. infinite
scheduling
d. finite capacity
scheduling e. progressive
scheduling
d (Finite capacity scheduling (FCS), moderate)
is the
416
6 9.
Five jobs are waiting for processing through two work centers. Their processing time (in
minutes) at each work center is contained in the table below. Each job requires work
center Alpha before work center Beta. According to Johnson's rule, which job should be
scheduled first?
Job
R
S
T
U
V
Alpha
20
25
50
15
55
Beta
10
35
20
35
75
a. R
b. S
c. T
d. U
e. V
d (Scheduling jobs, moderate) {AACSB: Analytic
Skills}
70.
Five jobs are waiting for processing through two work centers. Their processing time (in
minutes) at each work center is contained in the table below. Each job requires work
center Sigma before work center Delta. According to Johnson's rule, what sequence of
jobs will minimize the completion time for all jobs?
Job
R
S
T
U
V
Sigma
40
25
50
35
55
Delta
10
30
20
35
15
a. R-S-T-UV b. S-V-TR-U c. S-UT-V-R
d. V-R-U-ST
e. none of the
above
c (Scheduling jobs, moderate) {AACSB: Analytic
Skills}
71.
Which of the following are limitations of rules-based dispatching systems?
a. Rules need to be revised to adjust to changes in orders, product mix, and
so forth. b. Rules may not recognize idle resources.
c. Rules may not recognize bottleneck
resources
d. Rules may not be able to prioritize two jobs with identical due
dates. e.
All of the above are limitations.
e
(Scheduling
moderate)
jobs,
417
7 2.
Job
S
T
U
V
Five jobs are waiting for processing through two work centers. Their processing time (in
minutes) at each work center is contained in the table below. Each job requires work
center Alpha before work center Beta. According to Johnson's rule, what is the optimum
sequence of jobs and the minimum time for completion of all jobs?
Alpha
25
50
15
55
Beta
35
20
35
75
a. V-T-S-U-R;
225 b. U-R-T-SV; 175
c. R-S-T-U-V; 240
d. U-S-V-T-R; 200
e. none of the
above
d (Scheduling jobs, moderate) {AACSB: Analytic Skills}
73.
Conventional MRP uses time buckets that do not recognize capacity limits, and in fact
ignores capacity issues. A more realistic scheduling system that includes work center
capacities and other resource availabilities is
a. aggregate planning
b. the master production
schedule c.
finite capacity
scheduling
d. the assignment
method e.
level
material use
c (Finite capacity scheduling (FCS), moderate) {AACSB: Use of IT}
74.
Which of the following statements regarding finite capacity scheduling (FCS) is false?
a. Finite capacity scheduling allows delivery needs to be balanced against efficiency.
b. Finite capacity scheduling overcomes the disadvantages of systems based exclusively
on rules. c.
Finite capacity scheduling allows virtually instantaneous change by
operators.
d. Finite capacity scheduling software formalizes the same data needed in any manual
system. e.
None; all of the above are true.
e (Finite capacity scheduling (FCS), moderate) {AACSB: Use of IT}
75.
Which of the following statements regarding finite capacity scheduling (FCS) is false?
a. Finite capacity scheduling is well suited for dynamic scheduling environments.
b. Finite capacity scheduling overcomes the disadvantages of systems based exclusively
on rules. c.
Finite capacity scheduling is very powerful, but does not allow for rapid
changes.
d. Finite capacity scheduling often gets its data from the output of an MRP system.
e. None; all of the above are true.
c (Finite capacity scheduling (FCS), moderate) {AACSB: Use of IT}
418
7 6.
The theory of constraints has its
origins in a. linear programming
theory
b. the theory of economies of scale
c. material requirements planning
d. the theory of finite capacity planning
e. Goldratt and Cox's book, The Goal: A Process of Ongoing Improvement
e (Theory of constraints, easy)
77.
Which of the following techniques is not a technique for dealing with a bottleneck?
a. Schedule throughput to match capacity of the
bottleneck. b. Increase capacity of the constraint.
c. Have cross-trained employees available to keep the constraint at full operation.
d. Develop alternate routings.
e. All are tools for dealing with bottlenecks.
e (Theory of constraints, easy)
78.
An appliance manufacturer assembles icemakers in large batches. The operations
manager would like to significantly reduce the batch size. What would you suggest?
a. Use the SPT rule.
b. Use forward
scheduling. c. Use Gantt
charts.
d. Use finite scheduling.
e. Develop level material use schedules.
e (Repetitive facilities, moderate)
79. Which of the following is not tracked by scheduling optimization systems used in retail
stores?
a. cars parked in the parking
lot b. individual store sales
c.
transactions d.
units sold
e. customer traffic
e (Scheduling services, moderate)
80.
In drum, buffer, rope, what provides the schedule, i.e. the pace of production?
a. drum
b.
buffer c.
rope
d. all three of the above in
combination e. none of the above
a (Scheduling services, moderate)
81.
Which of the following is true regarding services scheduling?
a. The critical ratio sequencing rule is widely used for fairness to
customers. b. The emphasis is on staffing levels, not materials.
c. Reservations and appointments are often used to manipulate the supply of services.
d. Labor use can be intensive, and labor demand is usually
stable. e.
All of the above are true.
b (Scheduling services, moderate)
419
FILL-IN-THE BLANK
82.
scheduling begins with the due date and schedules the final operation first
and the other job steps in reverse order.
Backward (Scheduling issues, moderate)
83.
In the sequence of decisions that affect scheduling,
of the master schedule (or master production schedule).
short-term schedules (Scheduling issues, moderate)
84.
Because facility capacity, set-up time, and run time are usually known, scheduling
is often straightforward in
facilities.
product-focused or continuous (Scheduling issues, easy)
85.
is the assignment of jobs to work or processing centers.
Loading (Loading jobs, easy)
86.
is an input-output control system that uses cards to manage the amount of
work in a work center.
ConWIP or continuous work-in-process (Scheduling process-focused facilities,
moderate)
87.
are used to schedule resources and allocate time.
Gantt charts (Loading jobs, moderate)
88.
The
is a special class of linear programming models that involves
assigning tasks or jobs to resources.
assignment method (Loading jobs, moderate)
89.
determines the order in which jobs should be done at each work center.
Sequencing (Sequencing jobs, easy)
90.
determine the sequence of jobs in process-oriented facilities.
Priority rules (Sequencing jobs, easy)
91.
The priority rule that appears fair to customers in service systems is
first come, first served (Sequencing jobs, easy)
92.
An approach to sequencing that can handle the situation where jobs must pass through two
or more work centers in a fixed sequence is _.
Johnson's rule (Sequencing jobs in work centers, moderate)
93.
uses computerized short-term scheduling to overcome the disadvantages
of rule- based systems by providing the user with interactive computing and graphical
output.
Finite capacity scheduling (Finite capacity scheduling (FCS), moderate) {AACSB: Use
of IT}
94.
The
is a body of knowledge that deals with anything that limits an
organization's ability to achieve its goals.
theory of constraints (Theory of constraints, moderate)
is (are) the immediate follower
.
420
9 5.
Rerouting work, changing work sequence, and accepting idleness at other workstations
are some techniques for dealing with a .
bottleneck (Theory of constraints, moderate)
96.
In "drum, buffer, rope,"
is the resource, usually inventory, necessary to keep
the constraint operating at capacity.
buffer (Theory of constraints, moderate)
97.
means frequent, high-quality, small lot sizes that contribute to justin-time production.
Level material use (Repetitive facilities, moderate)
98.
In drum, buffer, rope, the
acts like kanban signals.
rope (Theory of constraints, moderate)
SHORT ANSWERS
99. Briefly describe how "the unexpected" makes short-term scheduling at Delta Airlines a
challenge.
Also describe how Delta meets that challenge, and achieves competitive advantage
through short- term scheduling.
The unexpected refers to delays and cancellations that are largely weather-related.
These
events require rapid rescheduling in order to keep operations going and to keep
passengers from becoming too inconvenienced. Delta's solution involves a high-tech
nerve center of computers and communications gear, and uses mathematical
models to reroute and reschedule as quickly as possible. (Global company profile,
easy)
100. What makes short-term scheduling of strategic importance?
Effective scheduling lowers cost by making greater use of facilities. Faster
throughput leads to faster delivery to customers. Good scheduling contributes to
realistic schedules and therefore to more dependable delivery. These three elements
can create competitive advantage, and therefore make short-term scheduling of
strategic importance. (The strategic importance of short-term scheduling, moderate)
101. Explain, in your own words, how backward scheduling and forward scheduling scheduling differ.
Forward starts the schedule as soon as the requirements are known.
Backward scheduling begins with the due date, scheduling the final operation first
and proceeding in the reverse order. (Scheduling issues, moderate)
102. How does short-term scheduling vary among the different process choices? Specifically,
compare short-term scheduling at process-oriented, work cells, repetitive, and productfocused facilities. All three process choices produce forward-looking schedules.
Process-focused facilities and work cells use MRP; their scheduling problems are
ongoing because their product mix is so variable. Repetitive facilities schedule with
line balancing and pull techniques; their scheduling problems are most challenging
when assembly lines are new or when models change. Continuous processes have
rather straightforward scheduling because they make relatively few products, and
facility capacity and setup times and run times are usually known. (Scheduling
issues, moderate)
421
103. Identify the types of planning files used in scheduling decisions. Which are used in
manual systems, and which are used in automated systems?
The three types are item master files, routing files, and work center master files. All
three are
used in both manual and in automated systems. (Scheduling issues, moderate)
104. What is input-output control?
Input-output control is a technique that allows operations personnel to manage
facility work flow by tracking work added to a work center and its completed work.
(Loading jobs, moderate)
105. What are the options available to operations personnel to manage facility work flow?
Options available to manage facility work flow include correcting performances,
increasing capacity, and increasing or reducing input to the work center by routing
work to or from other work centers, increasing or decreasing subcontracting, and
producing less or more. (Loading jobs, moderate)
106. What is the assignment method?
The assignment method is a special class of linear programming models that
involves assigning tasks or jobs to resources. (Loading jobs, moderate)
107. Identify the disadvantages of the Gantt load chart.
It does not account for production variability, such as unexpected breakdowns or
human errors that require reworking a job, and it must be updated regularly to
account for new jobs and revised time estimates. (Loading jobs, moderate)
108. What is the difference between a Gantt load chart and a Gantt scheduling chart?
The Gantt load chart indicates a planned allocation of capacitythe allocation of
the capacity of a department or work center to a particular job or order. The Gantt
schedule chart indicates, for each job or order, the relative adherence to the
particular time schedule, i.e., what fraction of total time to be expended on an order
has been expended. (Loading jobs, moderate)
109. What does Johnson's rule do?
Johnson's rule is an approach that minimizes processing time for sequencing a group
of jobs through two work centers while minimizing total idle time in the work
centers. (Sequencing jobs, moderate)
110. In retail outlets, customers are usually processed on a first come, first served basis.
Why? Is the express lane in the supermarket an exception? Craft a sequencing rule to
explain express lane behavior.
All customers are considered equally important, and not one should be given a higher
priority than another. Most students will write a rule like "FCFS, except for
very short processing times"; "8 items or less" is a proxy for processing time.
(Sequencing jobs, moderate) {AACSB: Reflective Thinking}
111. What is the primary disadvantage of the shortest processing time dispatch rule? Is this a
problem if there can be no new jobs arriving after the sequence is set?
As new jobs arrive, new short-duration jobs will push back existing long-duration
jobs in priority in favor of short-duration jobs. If newly arriving jobs must wait for
a new sequence to be built, this is less problematic. (Sequencing jobs, moderate)
422
112. Consider the arrival of patients into a public health clinic. Some patients are ill; some are
injured; some are elderly; and some are very young. Some cases may be life-threatening,
while others are inconsequential. How do the basic dispatch rules fall short in this
situation? Design a dispatch rule for scheduling these patients.
First come, first served is inappropriate because it ignores the urgency of treating
the most serious cases. There is no "due date" on which to base lateness or critical
ratio sequences. Most students will write a "priority" rule that behaves like triage
assigning an urgency code to each patient, and taking highest urgency cases first.
Student rules may have more than one part; for example, patients may be sorted by
urgency code, and by treatment time within urgency code. They may also create a
separate code for contagious cases. (Sequencing jobs, moderate) {AACSB: Reflective
Thinking}
113. What are the criteria by which we evaluate sequencing rules?
There are a number of criteria for evaluating job sequencing rules. Criteria
discussed in the text include average job completion time, average number of jobs in
the system, and average job lateness. Additional criteria include: average wait time,
average total completion time, and variance in completion times. (Sequencing jobs,
moderate)
114. What are some limitations of rule-based scheduling systems? What alternatives are there
to rules- based scheduling systems?
Three limitations are (1) Rules need to be revised to adjust to changes in process,
equipment,
product mix, etc.; (2) Rules do not look at upstream or downstream, and (3)
Rules do not look beyond due dates. Finite capacity scheduling is one recently
developed option. (Sequencing jobs, easy)
115. Describe finite capacity scheduling in a sentence or two. What is its role in short-term
scheduling?
Finite capacity scheduling (FCS) removes a shortcoming of MRP, which is that it
ignores the capacity of time buckets. FCS makes short-term scheduling more realistic
because it accounts for the finite capacity of time buckets. FCS can allow almost
instantaneous change, and may involve an expert system or simulation system as
planning tools. Short-term scheduling is evolving into finite capacity scheduling.
(Finite capacity scheduling (FCS), moderate)
{AACSB: Use of IT}
116. Describe the theory of constraints in a sentence.
The theory of constraints is the body of knowledge that deals with anything that
limits an organization's ability to achieve its goals. (Theory of constraints, easy)
117. Identify, in proper sequence, the steps in the process of recognizing and managing
constraints.
The five-step process of the theory of constraints
includes: Step 1: Identify the constraints.
Step 2: Develop a plan for overcoming them.
Step 3: Focus resources on accomplishing
step 2.
Step 4: Off-load work from the constraint or expand capability at the
constraint. Step 5: Once one set of constraints is overcome, go back to step
1 and identify new constraints. (Theory of constraints, moderate)
118. Explain the importance of a bottleneck operation in a production sequence.
A bottleneck operation is one that limits output in the production sequence.
Consequently, to increase throughput of the facility, the bottleneck operations must
be maximized. (Theory of constraints, moderate)
423
119. What techniques exist for dealing with bottlenecks? Which of these leads to increased
capacity?
Which of these leads to more throughput without adding capacity? Do any of these
techniques fail to increase throughput?
Five techniques are available to deal with the constraint. They are:
1. Increase the capacity of the constraint. This obviously increases capacity.
2. Have well-trained and cross-trained employees keep the bottleneck at full
operation. This increases capacity.
3. Develop alternate routings. This makes better use of existing capacity.
4. Move inspection and testing points to positions that precede the bottleneck,
to avoid wasting bottleneck capacity on bad items. This makes better use of
existing capacity.
5. Schedule throughput to match the bottleneck's capacity. There's no more
throughput, but there may be lower costs at other work centers. (Theory of
constraints, difficult)
120. In repetitive manufacturing, what are the advantages of level material use? Does level
material use have any role in intermittent process facilities?
The five advantages are:
1. Lower inventory levels to release capital for other uses.
2. Increase the rate of product throughput.
3. Improve component quality and hence improve product quality.
4. Reduce floor-space requirements.
5. Move employees closer together to improve communication.
6. The production process is smoothed because large lots have not "hidden" the
problems. Intermittent (job shop) facilities have so many additional sources of
variation (materials, requirements, work center order, etc.) that there is little role
for level material use. (Repetitive facilities, moderate)
121. Explain, in your own words, what is meant by "level material use." In what types of
facilities is it appropriate? Explain.
It means frequent, high quality, small lot sizes that contribute to just-in-time
production. It is appropriate in repetitive processing, not in intermittent processing,
because repetitive processing has much more predictable material and processing
needs. (Repetitive facilities, moderate)
122. In what ways does the problem of scheduling service systems differ from that of
scheduling manufacturing systems?
Scheduling services differs from scheduling manufacturing systems in five ways:
1. In manufacturing, emphasis is on materials, whereas in services it is on staffing
levels.
2. Service systems do not store inventories of services.
3. Services are labor intensive, and demand for this labor can be highly variable.
4. Legal considerations constrain scheduling decisions.
5. Behavioral, social, seniority, and status issues occur in service
scheduling. (Scheduling services, moderate)
123. Identify some scheduling optimization systems that are used at retail stores. Describe
what these systems do.
Workbrain, Cybershift, and Kronos. These systems track individual store sales,
transactions, units sold, and customer traffic in 15-minute increments to create work
schedules.
(Scheduling services, difficult) {AACSB: Use of IT}
424
PROBLEMS
124. A practitioner of family medicine begins her day with five patients needing urgent care.
She does a very brief assessment of what each patient appears to need and estimates the
time required of each. None of the cases is life-threatening, and so she determines to take
the five in the order that they arrived at the clinic. The data for these patients, in the order
they arrived, is Patient A, 30 minutes; Patient B, 40 minutes; Patient C; 10 minutes; Patient
D, 50 minutes; and Patient E, 15 minutes.
a. If it is now 8:00 a.m., at what time will the doctor be finished with all five of these
emergencies?
b. How much time will the five patients have collectively spent waiting?
c. How much less time would have been spent waiting if the doctor had taken the
patients according to shortest processing time?
(a) Using first come, first served, all five patients will be finished in 145 minutes, or
at 10:25 a.m. (b)Total flow time is 455 minutes, of which 145 is for processing, and
the remaining 310 is waiting time. (c) If the doctor had used shortest processing time,
the total flow time would have been 330 minutes, of which 185 is waiting time. In
both cases, the doctor finished all patients at 10:25 a.m. A supporting table for each
rule appears below.
(Sequencing jobs, moderate) {AACSB: Analytic Skills}
425
125. The emergency room at a hospital estimates the following requirements for registered
nurses (RNs)
for the late night shift each week. Nurses work four consecutive days, then have off
three days.
Sunday
3
Monday
4
Tuesday
2
Wednesday Thursday
2
3
Friday
6
Saturday
4
Perform cyclical scheduling on the data. (Note that you must identify three-day
patterns of minimum requirements). How many RNs are required? How much extra
capacity is required?
RN-1
RN-2
RN-3
RN-4
RN-5
RN-6
RN-7
RN-8
Capacity
Sunday
3
2
1
b
-
Monday
4
e
3
d
2
1
0
Tuesday
d
d
d
2
c
1
b
5
5
2
Wednesday Thursday Friday
d
e
6
d
3
5
d
d
4
2
2
3
c
c
2
1
1
c
b
b
1
1
2
3
7
Saturday
4
3
2
c
1
b
5
Days off are shaded. Seven full-time RNs are needed; an eighth works Friday only. A
total of
29 shifts are used, while only 24 are required; thus 5 shifts represent excess capacity.
This solution is not unique, as there are two instances where an arbitrary set of days
was selected for minimum sum. (Scheduling services, moderate) {AACSB: Analytic
Skills}
426
126. Jack's Refrigeration Repair is under contract to repair, recondition, and/or refurbish
commercial and industrial icemakers from restaurants, seafood processors, and similar
organizations. Jack currently has five jobs to be scheduled, shown in the order in which
they arrived.
Job
V
W
X
Y
Z
Processing Time (hours) Due (hours)
20
50
10
35
50
90
15
35
55
75
a. Complete the following table. (Show your supporting calculations
below). b. Which dispatching rule has the best score for flow time?
c. Which dispatching rule has the best score for work-in-process (jobs in the system)?
d. Which dispatching rule has the best score for lateness?
e. What dispatching rule would you select? Support your decision.
Dispatching
FCFS
SPT
EDD
CR
Job Sequence
Average
Average
Average
(a) A summary of calculations appears in the table below.
Dispatching Job Sequence Average
Average
Average
FCFS
V, W, X, Y, Z
75
2.50
27
SPT
W, Y, V, X, Z
65
2.17
16
EDD
W, Y, V, Z, X
66
2.23
17
CR
Z, X, Y, V, W
114
3.80
61
(b,c,d) SPT is best on all three criteria: flow time, work-in-process, and lateness.
(e) Most students will select SPT as quite obvious, but EDD is a close second in all
criteria. Supporting calculations for each priority rule appear in the tables below.
SPT
W
Y
V
X
Z
Machine1
10
15
20
50
55
Due Date
35
35
50
90
75
Flow Time Late
10
0
25
0
45
0
95
5
150
75
Average # jobs in system = 2.17
427
FCFS
V
W
X
Y
Z
Machine1
20
10
50
15
55
Due Date
50
35
90
35
75
Flow Time Late
20
0
30
0
80
0
95
60
150
75
Average # jobs in system = 2.5
EDD
W
Y
V
Z
X
Machine1
10
15
20
55
50
Due Date Flow Time Late
35
10
0
35
25
0
50
45
0
75
100
25
90
150
60
Average # jobs in system = 2.23
CR
Z
X
Y
V
W
Machine1
55
50
15
20
10
Due Date
75
90
35
50
35
CR
Flow Time Late
1.36
55
0
1.8
105
15
2.33
120
85
2.5
140
90
3.5
150
115
Average # jobs in system = 3.80
(Sequencing jobs, moderate) {AACSB: Analytic Skills}
428
127. The operations manager of a body and paint shop has five cars to schedule for repair. He
would like to minimize the throughput time (makespan) to complete all work on these
cars. Each car requires body work prior to painting. The estimates of the times required
to do the body and paint work on each are as follows:
Car
A
B
C
D
E
Body Work (Hours)
8
9
7
3
12
Paint (Hours)
7
4
9
4
5
a. Chart the progress of these five jobs through the two centers on the basis of the
arbitrary order
A BCDE.
b. After how many hours will all jobs be completed?
Body Work
Paint
c. Use Johnson's rule to sequence these five jobs for minimum total duration. Show your
work in determining the job sequence.
d. The optimal sequence is
.
e. Chart the progress of the five jobs in this optimal
sequence. f. After how many hours will all jobs be
completed?
SEE NEXT PAGE FOR SOLUTION.
429
(a,b) Arbitrary order:
Body A
B
C
D
Paint
A
5
10 15
E
B
20
25
C
30
D
35 40
E
45
50
(c,d) The sequence of jobs is Car E, Car D, Car A, Car C, Car B. Makespan = 43 as
per the
(c) Johnson's method sequence of steps
(e,f)
(Sequencing jobs, moderate) {AACSB: Analytic Skills}
430
128. The president of a consulting firm wants to minimize the total number of hours it will
take to complete four projects for a new client. Accordingly, she has estimated the time it
should take for each of her top consultants -- Charlie, Gerald, Johnny, and Rick -- to
complete any of the four projects, as follows:
Charlie
Gerald
Johnny
Rick
Project
13
13
15
17
16
15
11
17
11
10
20
12
18
12
15
22
a. In how many different ways can she assign these consultants to these projects?
b. What is the total number of hours required by the following arbitrary
assignment? CharlieB; GeraldA; JohnnyD; RickC
c. What is the optimal assignment of consultants to projects? (Use the assignment method;
SHOW
YOUR WORK!)
d. For the optimal schedule, what is the total number of hours it will take these
consultants to complete these projects?
e. What is the significance, if any, of the fact that Gerald is the best performer at all four
projects? (a) 4!, or 24 ways. (b) 16+13+15+12=56 hours. (c) Table appears below. (d)
48 hours. (e) Each person must get exactly one assignment. Note that Gerald does not
get the assignment at which he is absolutely most productive (Project C). The
optimum assignment is about opportunity cost, not absolute high or low values.
Project A
Charlie
Gerald
Johnny
Rick
1
0
0
0
Project B
0
0
1
0
Project C
Project D
0
0
0
1
(Loading jobs, moderate) {AACSB: Analytic Skills}
431
0
1
0
0
129. The following jobs are waiting to be processed at your work center, which cleans valve
body castings. Job numbers are assigned sequentially upon arrival in the facility (a
missing number means that job does not require your work center). All dates are
specified as days from present.
Job
101
102
104
107
108
Due Date
43
34
37
32
37
Duration (days)
10
12
11
7
15
a. In what sequence should the jobs be processed according to the FCFS
scheduling rule? b. In what sequence should the jobs be processed according to
the EDD scheduling rule? c. In what sequence should the jobs be processed
according to the SPT scheduling rule?
d. In what sequence should the jobs be processed according to the LPT
scheduling rule?
e. In what sequence should the jobs be processed according to the critical ratio
scheduling rule?
FCFS: 101, 102, 104, 107,
108
EDD: 107, 102, 104 and 108 (tie),
101
SPT: 107, 101, 104, 102,
108
LPT: 108, 102, 104, 101,
107
CR: 108 (2.47), 102 (2.67), 104 (3.36), 101 (3.40), 107
(6.14) (Sequencing jobs, moderate) {AACSB: Analytic
Skills}
130. Lockport Marine Services, Inc. wishes to assign a set of jobs to a set of machines. The
following table provides data on the cost of production of each job when performed on a
specific machine. a. Determine the set of assignments that maximizes production value.
b. What is the total production value of your
assignments?
Job
1
2
3
4
A
27
30
31
29
Machine
B
C
29
28
29
27
25
29
31
25
D
30
26
26
28
(a) The optimal set of assignments is Job 1Machine A, Job 2Machine D, Job
3Machine
B, and Job 4Machine C. (b) The total production value is 103.
Machine A Machine B Machine C Machine D Row Total
Job 1
Job 2
Job 3
Job 4
Column Total
Total Cost
1
0
0
0
1
0
0
1
0
1
0
0
0
1
1
103
(Loading jobs, moderate) {AACSB: Analytic Skills}
432
0
1
0
0
1
1
1
1
1
4
131. At Morgan's Transformer Rebuilding, a set of five jobs is ready for dispatching to a
machine center. The processing times and due dates for the jobs are given in the table
below. Use shortest processing time to sequence the jobs, and calculate the average
completion time, the average job lateness, and the average number of jobs in the machine
center.
The optimal sequence is C-E-B-A-D. The average completion time is 31.6 days. The
average lateness is 4 days. The average jobs in system is 2.548. Details appear in the
table below.
Total
158
Average
31.6
Average number of jobs in system
2.548
(Sequencing jobs, moderate) {AACSB: Analytic
Skills}
20
4
132. At Morgan's Transformer Rebuilding, five jobs are ready now for dispatching to a machine
center.
The processing times and due dates for the jobs are given below. Use earliest due date to
sequence the jobs, and calculate the average completion time, the average job lateness, and
the average number of jobs in the machine center.
The EDD sequence is E-C-B-A-D. Average completion time is 32 days. Average
lateness is 3.8 days. Average number of jobs is 2.58
E
C
B
A
D
EDD
9
7
13
15
18
Time
15
20
28
38
50
Due Date
Slack
6
9
13
16
15
29
23
44
32
62
Total
160
Average
32
Average number of jobs in system
Flow time Late days
0
0
1
6
12
19
3.8
2.58
(Sequencing jobs, moderate) {AACSB: Analytic Skills}
433
133.
Use Johnson's rule to determine the optimal sequencing for the five jobs to be
processed on two machines in a fixed order (Machine 1 before Machine 2). The
processing times are given in the table below.
a. What is the optimal sequence?
b. What is the total flow time for this sequence?
Job
L
M
N
O
P
Machine 1
10
8
14
13
10
Machine 2
11
17
9
7
8
(a,b) The optimal sequence is M-L-N-P-O, and the total flow time is 62. Details are
contained in the solution table below.
(Sequencing jobs, moderate) {AACSB: Analytic Skills}
134. A manufacturer has the following jobs waiting on a single work center. The firm has not
decided which dispatching rule to apply in order to prioritize the jobs and fix them into
the schedule. Processing time in 15-minute time blocks and due date for each job are in
the table below.
Job 1
Job 2
Job 3
Job 4
Job 5
Job 6
5
4
3
7
3
5
Time Due Date
17
20
16
9
6
7
a. Complete the following table. Show your supporting calculations below.
b. Which dispatching rule has the best score for flow time? for work in process
(jobs in the system)? for lateness?
c. Is there ANY sequence that can avoid all lateness? Explain or provide an example.
Dispatching
Average
Average
EDD
SPT
LPT
SEE NEXT PAGE FOR SOLUTION.
434
(a) The results appear in the table below. A supporting table for each dispatch
rule also follows.
(b,c,d) SPT is best for flow time, and for average jobs in system; EDD is best for
lateness.
(e) Lateness is unavoidable with any dispatch rule; the sum of processing times is 27
but the longest due date is only 20 days away.
EDD
Job 5
Job 6
Job 4
Job 3
Job 1
Job 2
Time
3
5
7
3
5
4
Due Date
6
7
9
16
17
20
Slack
3
2
2
13
12
16
Total
Average
Average number of jobs in system
SPT
Job 3
Job 5
Job 2
Job 1
Job 6
Job 4
Time
3
3
4
5
5
7
Due Date
16
6
20
17
7
9
Average umber of jo s in system
b
n
LPT
Time
Due Date
Job 4
7
9
Job 6
5
7
Job 1
5
17
Job 2
4
20
Job 5
3
6
Job 3
3
16
Average umber of jo s in system
b
n
Flow time
3
8
15
18
23
27
94
15.67
3.481
Late
0
1
6
2
6
7
22
3.667
Slack Flow
13
3
3
6
16
10
12
15
2
20
2
27
Total
81
Average
13.5
3
Late
0
0
0
0
13
18
31
5.167
Slack Flow
2
7
2
12
12
17
16
21
3
24
13
27
Total
108
Average
18
4
Late
0
5
0
1
18
11
35
5.83
(Sequencing jobs in work centers, moderate) {AACSB: Analytic Skills}
435
135. Bob Dresser operates a major appliance warranty service center. His operation has two
check stations that are required at the end of every repair task performed by his
appliance repair staff. These are the Functionality Review (FR) and the Overall Scan
(OS). The FR must be performed successfully before the OS is begun. On Friday
morning, six repair jobs are completed, awaiting these two inspection activities.
Processing times are given in minutes.
Job
A
B
C
D
E
F
FR
50
35
25
20
15
10
OS
30
55
20
35
10
25
a. What is the optimal sequence of jobs for the objective of minimizing the total flow time?
b. Show your work, and document the
sequence. c. Chart the solution to this
problem.
d. What jobs are being processed at time period 90?
e. What is the total flow time of this problem?
FR
OS
(a) The optimal sequence is F-D-B-A-C-E. (b) Supporting work appears in the table
below.
(c) The schedule appears in the chart below. (d) At hour 50, B is in the first center,
and D is in the second. (e) Total flow time for the schedule is 185.
d) Job A is being processed at FR (Machine 1), while Job B is being
processed at OS (Machine 2) (Sequencing jobs, moderate) {AACSB: Analytic
Skills}
436
136. Machines A, B, C, and D have been in use for several years, while machine E is new. The
following table provides data on the value of production of each job when performed on a
specific machine.
a. Determine the set of assignments that maximizes production
value. b. What is the total production value of your
assignments?
c. Which machine should be retired (i.e., gets no assignment)?
d. If they do retire one machine, will they be as profitable without it as with it? Explain.
Job
1
2
3
4
A
27
30
33
29
B
29
32
25
31
Machine
C
28
31
29
24
D
30
34
26
28
E
40
46
37
28
(a) The optimal assignment is Job 1D, Job 2E, Job 3A, and Job 4B. (b) The
cost of this assignment is 140. (c) C gets no assignment, and should be the machine
retired.
A
Job 1
0
Job 2
0
Job 3
1
Job 4
0
Job 5
0
Column Total
1
Total Cost
140
B
0
0
0
1
0
1
C
0
0
0
0
1
1
D
1
0
0
0
0
1
E
0
1
0
0
0
1
Row
1
1
1
1
1
5
(d) Taking away what was arguably the least productive machine still reduces the
options of the firm, and alters the opportunity costs. They cannot be better off
without the machine.
Column Total
1
Total Cost 140
1
1
(Loading jobs, moderate) {AACSB: Analytic Skills}
1
Row Total
1
1
1
1
4
437
137. A firm that specializes in desktop publishing for local charities has agreed to take on the
following jobs. The firm has not decided which dispatching rule to apply in order to
prioritize the jobs and fix them into the schedule.
Time Due
20 Date
15
7
25
31
43
Job 1
Job 2
Job 3
Job 4
Job 5
Job 6
25
20
16
50
33
55
a. Complete the following table. Show your supporting calculations
below. b. Which dispatching rule has the best score for flow time?
c. Which dispatching rule has the best score for work-in-process (jobs in the system)?
d. Which dispatching rule has the best score for lateness?
Dispatching
FCFS
EDD
SPT
LPT
Average
Average
(a) The table of results appears below. A supporting table for each dispatch rule also
follows.
Dispatching
Average
Average
Average
FCFS
1-2-3-4-5-6
67.2
2.86
34.8
EDD
3-2-1-5-4-6
63.8
2.71
32.2
SPT
3-2-1-4-5-6
62.8
2.67
31.2
LPT
6-5-4-1-2-3
101.7
4.33
70.5
(b,c,d) The SPT rule is best for flow time, for average jobs in system, and for lateness.
FCFS
Job 1
Job 2
Job 3
Job 4
Job 5
Job 6
Time
20
15
7
25
31
43
Average jo in syste
bs
m
Due Date
25
20
16
50
33
55
Slack Flow time Late
5
20
0
5
35
15
9
42
26
25
67
17
2
98
65
12
141
86
Total
403
209
Average
67.17
34.8
3
2.858
438
EDD
Job 3
Job 2
Job 1
Job 5
Job 4
Job 6
Time
7
15
20
31
25
43
Due Date
Slac Flow time
16
9
7
20
5
22
25
5
42
33
2
73
50
25
98
55
12
141
Total
383
Average
63.83
Average number of jobs in
2.716
system
SPT
Time Due Date
Slack Flow time
Job 3
7
16
9
7
Job 2
15
20
5
22
Job 1
20
25
5
42
Job 4
25
50
25
67
Job 5
31
33
2
98
Job 6
43
55
12
141
Total
377
Average
62.83
Average n
umber of jo s in system
b
2.674
Late
LPT
Job 6
Job 5
Job 4
Job 1
Job 2
Job 3
Late
Time
43
31
25
20
15
Due Date
Slac Flow time
55
12
43
33
2
74
50
25
99
25
5
119
20
5
134
7
16
9
141
Total
610
Average
101.67
Average number of jobs in
4.326
system
(Sequencing jobs, moderate) {AACSB: Analytic Skills}
0
2
17
40
48
86
193
32.1
7
Late
0
2
17
17
65
86
187
31.1
7
0
41
49
94
114
125
423
70.5
439
138. Use Johnson's rule to determine the optimal sequencing for the five jobs to be processed
on two machines in a fixed order (Machine 1 before Machine 2). The processing times in
hours are given in the table below.
a. What is the optimal sequence?
b. What is the total flow time for this sequence?
c. Which job is the first to be scheduled? Is it scheduled to be the first job or the last?
Explain.
Job
A
B
C
D
E
F
G
Machine 1 Machine 2
10
11
8
17
14
10
13
7
10
8
25
9
6
15
(a,b) The optimal sequence is G-B-A-C-F-E-D, and the total flow time is 93 hours, as
shown
(c) Job G is the first job to be scheduled. The smallest of all processing times is 6
hours, for Job G. Because this occurs at Machine 1, Job G is scheduled into the
first position. (Sequencing jobs, moderate) {AACSB: Analytic Skills}
440