Supplement
J Operations Scheduling
1. Performance Measures for Scheduling Processes
• The scheduling techniques discussed in this supplement cut across the various process types
found in services and manufacturing.
o Front-office process with high customer contact, divergent work flows, customization,
and, consequently, a complex scheduling environment
o Back-office process has low customer involvement, uses more line work flows, and
provides standardized services.
TEACHING TIP
Our discussion of the operations scheduling techniques in this supplement has application to job,
batch, and line processes in services as well as manufacturing. Schedules for continuous
processes can be developed with linear programming (see the “Linear Programming”
supplement).
• Performance measures (a “job” is defined as the object receiving service or being
manufactured)
o Flow time is the amount of time a job spends in the service or manufacturing system.
o Past due (tardiness) is the amount of time by which a job missed its due date.
o Makespan
▪ The total amount of time required to complete a group of jobs.
▪ Minimizing makespan supports the competitive priorities of cost (lower inventory)
and time (delivery speed).
Makespan
=
Time of completion
of last job
−
Starting time
of first job
o Total inventory
▪ Used to measure the effectiveness of schedules for manufacturing processes.
Total
inventory
=
Scheduled receipts for
all items
+
On-hand inventories
of all items
▪ Minimizing total inventory supports the competitive priorities of cost (inventory
holding costs).
o Utilization
▪ The percentage of work time that is productively spent by an employee or a machine.
▪ Maximizing the utilization of a process supports the competitive priority of cost
(slack capacity).
o These performances are interrelated
▪ Minimizing the average flow time tends to increase utilization.
▪ Minimizing makespan for a group of jobs tends to increase utilization.
2. Job Shop Scheduling
• Operations schedules are short-term plans designed to implement the sales and operations
plan. In this section, the focus is on scheduling approaches that can be used for environments
that have either: (1) divergent flow processes or (2) line flow processes.
• A manufacturer’s operation with divergent flows is often called a job shop.
o Specializes in low-to medium-volume production and utilizes job or batch processes
o The front office would be the equivalent for a service provider.
o Jobs in divergent flow are difficult to schedule because of the variability in job
routings and the continual introduction of new jobs to be processed.
• A manufacturer’s operation with line flow is often called a flow shop.
o Specializes in medium- to high-volume production and utilizes line of continuous
flow processes.
o The back office would be the equivalent for a service provider.
o Tasks are easier to schedule because the jobs have a common flow pattern through
the system.
1. Priority sequencing rules
TEACHING TIP
Already covered two important sequencing rules in Chapter 10, “Operations Planning and
Scheduling.” The first-come, first-served (FCFS) rule gives the job arriving at the workstation
first and highest priorities. The earliest due date (EDD) rule gives the job with the earliest due
date based on assigned due dates the highest priority.
a. Additional priority sequencing rules.
• Critical ratio (CR)
remaining timeshop Total
date) s(Today’ – date) (Due
=CR
remaining operations ofNumber
The job with the lowest S/RO is scheduled next.
2. Scheduling jobs for one workstation
a. Single-dimension rules
• A job’s priority assignment based only on information waiting for processing at the
individual workstation (e.g., FCFS, EDD, and SPT).
• Example J.1 Comparing the EDD and SPT
The SPT schedule provided a lower average job flow time.
The EDD schedule gave better customer service as measured by the average
hours past due and lower maximum hours past due.
SPT rule, which is often referred to as the world champion, tends to minimize the
mean flow time, and the percentage of jobs past due. It also tends to maximize
shop utilization.
• Tutor J.1 in MyLab Operations Management provides a new example to practice
EDD and SPT rules.
• Scheduling at One Operation Using SPT. Use Application J.1:
Given the following information, devise an SPT schedule for the automatic routing
machine.
(Students complete highlighted sections)
Order
Sequence
Begin
Work
Finish
Time
(hr)
Flow
Time
(hr)
Scheduled
Customer
Pickup Time
Actual
Pickup
Time
Hours
Early
Hours
Past
Due
1.
PC088
0
3
3
18
18
15
2.
DM246
3
11
11
20
20
9
3.
SX435
11
21
21
6
21
15
4.
AZ135
21
35
35
14
35
21
Total
70
94
24
36
Average
17.5
23.5
6
9
• Active Model J.1 in MyLab Operations Management provides additional insight on
the use of a single-dimension rule.
b. Multiple-dimension rules
• The priority rules CR and S/RO incorporate information about the remaining
workstations.
Order
Standard time,
Including
Setup (hr)
Due Date
(hrs from now)
AZ135
14
14
DM246
8
20
SX435
10
6
PC088
3
18
• CR results in longer job flow times than SPT, but CR also results in less variance in
the distribution of past due hours.
• No choice is clearly best; each rule should be tested in the environment for which it is
intended.
• Scheduling at One Operation Using CR and S/RO. Use Application J.2:
The following four jobs have just arrived at an idle drill process and must be
scheduled.
Job
Processing Time
at Drill Press
(wk)
Time Remaining
to Due Date
(wks)
Number of
Operations
Remaining*
Shop Time
Remaining*
(wks)
AA
4
5
3
4
BB
8
11
4
6
CC
13
16
10
9
DD
6
18
3
12
EE
2
7
5
3
* Including drill press
Create the sequences for two schedules, one using the Critical Ratio rule and one using the
S/RO rule. (Students complete highlighted sections)
Critical Ratio
Slack/Remaining Operation
Job
Priority Index
Sequence on
Drill Press
Job
Priority Index
Sequence on
Drill Press
AA
1.25
First
AA
0.33
First
BB
1.83
Fourth
BB
1.25
Fourth
CC
1.77
Third
CC
0.70
Second
DD
1.50
Second
DD
2.00
Fifth
EE
2.33
Fifth
EE
0.80
Third
c. Tutor J.2 in MyLab Operations Management provides a new example to practice the CR
and S/RO rules.
3. Scheduling jobs for multiple workstations
a. Identifying the best priority rule to use at a particular operation in a process is a complex
problem because the output from one operation becomes the input to another.
b. Computer simulation models are effective tools to determine which priority rules work
best in a given situation.
3. Flow Shop Scheduling
• In single-workstation scheduling, the makespan is the same regardless of the priority rule
chosen.
• In the scheduling of two or more workstations in a flow shop, the makespan varies according
to the sequence chosen.
• Determining a production sequence for a group of jobs to minimize the makespan has two
advantages.
o The group of jobs is completed in minimum time.
o The utilization of the two-station flow shop is maximized.
• Johnson’s rule is a procedure that minimizes makespan when scheduling a group of jobs on
two workstations.
o Step 1: Scan the processing time at each workstation and find the shortest processing
time among the jobs not yet scheduled. If two or more jobs are tied, choose one job
arbitrarily.
o Step 2: If the shortest processing time is on workstation 1, schedule the
corresponding job as early as possible. If the shortest processing time is on
workstation 2, schedule the corresponding job as late as possible.
o Step 3: Eliminate the last job scheduled from further consideration. Repeat steps 1
and 2 until all jobs have been scheduled.
o Sequencing Jobs at a Two-Station Flow Shop. Use Application J.3:
Use the following data to schedule two workstations arranged as a flow shop.
Time (hr)
Job
Workstation 1
Workstation 2
A
4
3
B
10
20
C
2
15
D
8
7
E
14
13
Sequence:
C
B
E
D
A
(Students complete highlighted section)
Workstation 1
Workstation 2
Start
Finish
Start
Finish
C
0
2
2
17
B
2
12
17
37
E
12
26
37
50
D
26
34
50
57
A
34
38
57
60
o Tutor J.3 in MyLab Operations Management provides a new example to practice
Johnson’s rule.
4. Labor-Limited Environments
• The resource constraint is the amount of labor available, not the number of machines or
workstations.
• The scheduler must also assign workers to their next workstations.
• Advanced planning and scheduling (APS) systems attempt to link the scheduling process to
demand data and forecasts, supply chain facility and inventory decisions, and the capability
of suppliers so that the entire chain can operate as efficiently as possible.