Chapter 16 – Scheduling
16-1
CHAPTER 16
SCHEDULING
Teaching Notes
Scheduling techniques are designed to disaggregate the master production schedule into time-phased daily
or hourly activities. A detailed production schedule must include when and where each activity must take
place to meet the master schedule.
Scheduling involves the following major activities:
1. Short-run machine, labor, and production scheduling.
2. Short-run capacity planning.
3. Routing (determining where the work is going to be done).
4. Dispatching (issuing the order to begin work).
5. Expediting late, critical jobs.
6. Controlling the progress of orders and monitoring the process to determine that operations are
running according to plan.
7. Determining the sequence of activities (determining when the work is to be done).
8. Revising the schedule based on changes in order status of jobs, material and/or capacity
1. Job arrival patterns (static vs. dynamic). A dynamic arrival pattern means that more jobs will
2. Ratio of workers to machines (machine limited vs. labor limited environment).
3. Priority rules for scheduling.
4. Flow patterns of jobs through the plant.
a. Flow shop: All jobs follow the same pattern of flow through the plant. In a flow shop, routing
5. Evaluation of the scheduling technique (maximization of service level, or minimization of
6. Number and types of machines in the plant (as the number and types of machines increase, the
scheduling environment gets more complicated).
7. Facility layout (different layouts lead to different types of scheduling problems).
Chapter 16 – Scheduling
Scheduling decisions are based on the following critical factors:
1. Material availability.
2. Capacity availability (worker or machine).
3. Bottleneck vs. nonbottleneck operations.
4. Job priorities.
5. Queue of work before each work station.
A major portion of the chapter is devoted to production scheduling. I generally emphasize production
scheduling because it has more “meat” than other areas of scheduling and because it enables students to
get a better grasp on what scheduling involves and some of the tools available.
It is important to spend at least a few moments to establish the basic differences in scheduling needs
among high volume, intermediate volume and job shop systems. It is also important to compare and
contrast the scheduling needs of service operations and the scheduling needs of manufacturing operations.
Answers to Discussion and Review Questions
1. Job shops are intended to handle a wide range of processing requirements; jobs tend to follow
many different paths through the shop, and often differ significantly with respect to processing
2. The main decision areas of job shop scheduling are loading and sequencing. Loading deals with
3. Gantt charts are visual aids used by managers for loading and scheduling purposes. A time scale
is represented horizontally on the chart, and resources to be scheduled are listed vertically on the
4. The assignment model assumes a one-for-one matching is possible, that costs for each
combination are known and fixed, and that in general, each machine or worker is capable of
5. a. FCFS: Process jobs in order of arrival.
b. SPT: Process jobs according to processing times, shortest ones first.
6. Priority rules are simple heuristics used to select the order in which jobs waiting will be processed.
Priority rules allow for the fact that jobs are not equally important, i.e., different processing
Chapter 16 – Scheduling
7. Service systems usually must contend with random arrivals and variations in service times and
8. Forward scheduling means scheduling ahead from a point in time. Backward scheduling means
9. To the extent that scheduling efforts can achieve a balance in facility or equipment loading, the
10. The factors to take into account when deciding to split a job include: Will throughput time
11. Makespan is the total time needed to complete a group of jobs from the start of the first job to the
completion of the last job.
Taking Stock
1. In sequencing jobs, we have to consider the trade-off between customer service and operational
efficiency. For example, sequencing job A before job B may result in higher customer service
because we could meet the due dates of both jobs, but this sequence may be inefficient due to the
2. In large facilities, the production planning and control manager, or planners and schedulers are
3. Technology, more specifically information technology, has had a profound impact on scheduling.
When the schedule is determined, it can be released automatically from production planning and
control to the shop floor, and the workers on the shop floor can get the machines and materials
ready for production without wasting valuable time. In addition, schedulers can check
Chapter 16 – Scheduling
16-4
Education.
Critical Thinking Exercises
1. a. A production bottleneck limits the production of the entire system due to insufficient
capacity and/or excessive demand at a given work station. The throughput of the entire
production system will depend on the output of the bottleneck work station.
b. Small lot sizes (transfer batches) can be moved from the bottleneck operation to downstream
2. Unless each customer or job is expected to have identical processing time requirements,
scheduling at regular intervals will tend to create waiting lines if the intervals are too short.
However, the scheduler may prefer to use short intervals to maximize the use of the doctor’s time
3. Student answers will vary. Some possible answers follow (any three are sufficient):
a. If a scheduler intentionally underloaded a department to help out the manager of the
department, a close friend, this action would violate the Utilitarian Principle, the Fairness
Principle, and the Virtue Principle.
b. If a scheduler intentionally overloaded a department and this resulted in excess pollution, this
action would violate the Utilitarian Principle and the Common Good Principle.
c. If a scheduler at a doctor’s office knowingly set the interval between appointments too short
and this caused excessive wait times, this action would violate the Utilitarian Principle.
d. If a scheduler at a doctor’s office booked a friend at the same appointment time as another
patient, this action would violate the Virtue Principle.
Chapter 16 – Scheduling
Solutions:
1. Given:
Cost information for assigning workers to jobs:
1
5
8
6
Step 1:
Row reduction: Subtract the smallest number in each row from every number in the row.
Column Min.
Step 2:
Column reduction: Subtract the smallest number in each column of the previous table from every
number in the column.
Job
A
B
C
Job
A
B
C
1
0
3
1
Job
A
B
C
1
0
2
1
Education.
Chapter 16 – Scheduling
2. Given:
Profit information for assigning workers to jobs:
3
4
5
3
Relative Profits
3
5
4
6
4
Step 2:
Column reduction: Subtract the smallest number in each column of the previous table from every
number in the column.
Worker
2
2
2
0
Job
A
B
C
1
5
8
6
Worker
2
6
7
9
Job
A
B
C
1
4
1
3
Worker
2
3
2
0
Job
A
B
C
1
3
0
2
Worker
2
3
2
0
3
1
0
2
Column Min.
1
0
0
Job
A
B
C
1
2
0
2
Chapter 16 – Scheduling
A
B
C
1
0
2
Worker
2
2
2
Step 3:
Test whether an optimum assignment can be made. Determine the minimum number of lines
(horizontal and/or vertical) needed to cover all zeros. If the number of lines equals the number of
rows, an optimum assignment is possible.
Worker
2
2
2
0
3
0
0
2
Step 4:
Make the assignments. Begin with rows or columns with only one zero. Match items that have
zeros, using only one match for each row and column. Eliminate both the row and the column
after the match.
Start with Row 1, Row 2, Column A, & Column C because each has one zero.
Step 5:
Compute the profits.
Assignment
Profit
1-B
$8
2-C
$9
3-A
$4
Total =
$21
Job
A
B
C
1
2
0
2
Job
3
0
0
2
Chapter 16 – Scheduling
3. Given:
Cost information for assigning trucks to delivery routes:
Route
Row
A
B
C
D
E
Min.
1
4
5
9
8
7
4
2
6
4
8
3
5
3
Truck
3
7
3
10
4
6
3
4
5
2
5
5
8
2
5
6
5
3
4
9
3
Step 1:
Row reduction: Subtract the smallest number in each row from every number in the row.
Route
A
B
C
D
E
1
0
1
5
4
3
2
3
1
5
0
2
Truck
3
4
0
7
1
3
4
3
0
3
3
6
5
3
2
0
1
6
Column
Min.
0
0
0
0
2
Step 2:
Column reduction: Subtract the smallest number in each column of the previous table from every
number in the column.
Route
A
B
C
D
E
1
0
1
5
4
1
2
3
1
5
0
0
Truck
3
4
0
7
1
1
4
3
0
3
3
4
5
3
2
0
1
4
Chapter 16 – Scheduling
Step 3:
Test whether an optimum assignment can be made. Determine the minimum number of lines
(horizontal and/or vertical) needed to cover all zeros. If the number of lines equals the number of
rows, an optimum assignment is possible.
Route
A
B
C
D
E
1
0
1
5
4
1
2
3
1
5
0
0
Truck
3
4
0
7
1
1
4
3
0
3
3
4
5
3
2
0
1
4
Note: A minimum of four lines is needed, which is less than the number of rows (five).
Step 4:
Because the number of lines is less than the number of rows, we must modify the table.
a. Subtract the smallest uncovered number (1) from every uncovered number in the table.
Route
A
B
C
D
E
1
0
2
6
4
1
2
3
2
6
0
0
Truck
3
3
0
7
0
0
4
2
0
3
2
3
5
2
2
0
0
3
Route
A
B
C
D
E
1
0
2
6
4
1
2
3
2
6
0
0
Truck
3
3
0
7
0
0
4
2
0
3
2
3
5
2
2
0
0
3