Chapter 12 – Scheduling Operations
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Chapter 12
Scheduling Operations
Teaching Notes
This chapter presents classic material on scheduling operations. The chapter
discusses the scheduling of batch operations, including such topics as Gantt charting,
finite capacity scheduling, loading, theory of constraints and dispatching rules. The
chapter concludes with descriptions of planning and control systems used to schedule
various types of batch operations.
In teaching this chapter, we usually begin by contrasting the different types of
scheduling problems in operations: line, batch, and project. We also discuss the
relationship among facility planning, aggregate planning, and scheduling problems.
Methods for batch scheduling can be taught by means of a series of example problems.
Depending on how much time is available, topics and examples can be used to teach
Gantt charting, finite capacity scheduling, loading, and dispatching rules. In the process
of working these problems, various scheduling principles can be illustrated, such as the
relationship between scheduling and aggregate planning, the presence of multiple
objectives, and ways to deal with uncertainty. Theory of constraints, as it applies to batch
processes, is also included here.
Answers to Questions
1. a. Hospital – Nurses assigned to shifts in each department, use of operating
rooms, use of special equipment such as X-ray, EEG, EKG, and labs.
2. a. Hospital – Efficient (cost-effective) yet appropriate availability (adequate
capacity) of special equipment and services.
Chapter 12 – Scheduling Operations
3. It is important to view a batch process operation as a network of interconnected
queues because each machine or work center is linked to other machines and
4. Scheduling of patients in a doctor’s clinic is similar to scheduling jobs in a factory
in that patients are comparable to jobs, and waiting rooms, examining rooms and
5. Gantt charting and FCS schedule jobs one at a time according to priorities on the
resources available. FCS differs from Gantt charting in that each work center
6. The m x n scheduling algorithms utilize a highly restrictive set of assumptions:
constant processing time, no passing of jobs, no lot splitting, etc. Real sequencing
7. The purpose of planning and control systems is to implement the schedule (plan)
and then correct (control) it if necessary to meet the plan.
8. The main goal of theory of constraints is to make as much money as possible
Chapter 12 – Scheduling Operations
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9. A bottleneck is any resource whose capacity is less than the demand placed on it,
10. All non-bottleneck resources should be scheduled to ensure that the bottleneck is
not starved for materials and can keep busy processing orders needed for sale. A
11. Measures that can be taken to provide more capacity at the bottleneck work center
Answers to Problems
1. a. Registration (R) and Pay Fees (F):
Sequence D, E, B, C, A requires a total time of 36 minutes.
0 3 7 14 19 31
R | D___|___E___|___B____|___C___ |__________A__________|
Chapter 12 – Scheduling Operations
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2. a. Sequence: 1, 2, 3, 4, 5, 6; requires a total time of 56 minutes.
0 10 16 23 31 34 40
A |_____1____|___2__|___3___|____4___|_5_|___6__|
3.
0 3 7 8 13 14 18
A | [1]___|____[2]____|[4]|____________|[3]|___________|
B | ________|_[1]_|_______[3]________ |_[4]_|___________|
3 6
4 5
11 hours total
e. Sequence: 3, 2, 4, 1 has a makespan of 14 hours.
Chapter 12 – Scheduling Operations
0 3 7 8 9 10 12 14
A ¦____[1]___¦____[2]_______¦_[3] ¦ [4] ¦_ _¦____ __¦_______¦
B ¦_______[3]__________¦__[1]____¦________¦__[4]___¦_______¦
4. a. Finite capacity schedule by means of a Gantt Chart
0 2 3 4 5 6 7 8 9
A1 |___[1]______| |_[4]_|
A2 |______[2]________|_[3]_|
B1 |___[1]___| |__[4]___|
5. a. Jobs are sequenced in order 1, 2, 3, 4, 5, 6
0 6 10 13 16 18 22 23 27 35
A1|___[1]__|___[4]______|
A2|_[2]|___[3]___|[5] |___[6]_____|
Chapter 12 – Scheduling Operations
7. a. Gantt Chart: Priority Order for Samples is Earliest Due Date (1, 3, 2, 5, 4)
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
A | 1 | | 3 | 5 | 4 | | 2 |
b. Finite Capacity Schedule: Earliest due date first 1, 3, 2, 5, 4
0 2 4 6 8 10
A1 | 1 | | 3 | 2 |
A2 | 4 | | 5 |
B1 | 2 | | 5 |
B2 | | 1 | | 4 |
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9. a. Job 1 (1 hour processing time for Job 1 versus 2 hours for Job 4)
10. a. For problem 2, machine B is the bottleneck since jobs 3, 4, 5 and 6 all must
wait for machine B to become available. Another machine of type B (or more
hours of capacity) would reduce the makespan and thus increase shop throughput.
11. a. For problem 2, the theory of constraints could be used in two ways. First, we
could find a better sequence of jobs than 1, 2, 3, 4, 5 and thus reduce job