J – 1 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall. Operations Scheduling J For Operations Management, 9e by Krajewski/Ritzman/Malhotra

J – 1Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall.

Operations SchedulingOperations SchedulingJ

For For Operations Management, 9eOperations Management, 9e by by Krajewski/Ritzman/Malhotra Krajewski/Ritzman/Malhotra © 2010 Pearson Education© 2010 Pearson Education

PowerPoint Slides PowerPoint Slides by Jeff Heylby Jeff Heyl


The scheduling techniques cut across the various process types found in services and manufacturing Front-office process with high customer

contact, divergent work flows, customization, and a complex scheduling environment

Back-office process has low customer involvement, uses more line work flows, and provides standardized services

Scheduling Service and Scheduling Service and Manufacturing Processes Manufacturing Processes


Performance MeasuresPerformance Measures

Flow time is the amount of time a job spends in the service or manufacturing system

Past due (tardiness) is the amount of time by which a job missed its due date

Makespan is the total amount of time required to complete a group of jobs

Makespan =Time of completion

of last job–

Starting time of first job


Performance MeasuresPerformance Measures

Total inventory is used to measure the effectiveness of schedules for manufacturing processes.

Total Inventory

=Scheduled receipts

for all items+

On-hand inventories of all items

Utilization is the percentage of work time that is productively spent by an employee or a machine


Sequencing JobsSequencing Jobs

Operations schedules are short-term plans designed to implement the sales and operations plan

An operation with divergent flows is often called a job shop Low-to medium-volume production Utilizes job or batch processes The front office would be the equivalent for a

service provider Difficult to schedule because of the variability

in job routings and the continual introduction of new jobs to be processed


Sequencing JobsSequencing Jobs

An operation with line flow is often called a flow shop Medium- to high-volume production Utilizes line or continuous flow processes The back office would be the equivalent for a

service provider Tasks are easier to schedule because the jobs

have a common flow pattern through the system


Sh

ipp

ing

Dep

art

men

t

Raw

Ma

teri

als

Legend:

Batch of parts

Workstation

Job Shop SequencingJob Shop Sequencing

Figure J.1 – Diagram of a Manufacturing Job Shop Process


First-come, first-served (FCFS)

Earliest due date (EDD)

Critical ratio (CR)

Priority Sequencing RulesPriority Sequencing Rules

A ratio less than 1.0 implies that the job is behind schedule

A ratio greater than 1.0 implies the job is ahead of schedule

The job with the lowest CR is scheduled next

CR =(Due date) – (Today’s date)

Total shop time remaining


Shortest processing time (SPT)

Slack per remaining operations (S/RO)

Priority Sequencing RulesPriority Sequencing Rules

The job with the lowest S/RO is scheduled next

S/RO =

Due date

Today’sdate

Total shop time remaining– –

Number of operations remaining


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)

Sequencing One WorkstationSequencing One Workstation


Comparing EDD and SPT RulesComparing EDD and SPT Rules

EXAMPLE J.1

The Taylor Machine Shop rebores engine blocks. Currently, five engine blocks are waiting for processing. At any time, the company has only one engine expert on duty who can do this type of work. The engine problems have been diagnosed, and the processing times for the jobs have been estimated. Expected completion times have been agreed upon with the shop’s customers. The accompanying table shows the current situation. Because the Taylor Machine Shop is open from 8:00 A.M. until 5:00 P.M. each weekday, plus weekend hours as needed, the customer pickup times are measured in business hours from the current time. Determine the schedule for the engine expert by using (a) the EDD rule and (b) the SPT rule. For each rule, calculate the average flow time, average hours early, and average hours past due. If average past due is most important, which rule should be chosen?



Engine Block

Business Hours Since Order

Arrived

Processing Time, Including Setup

(hours)

Business Hours Until Due Date (customer

pickup time)

Ranger 12 8 10

Explorer 10 6 12

Bronco 1 15 20

Econoline 150 3 3 18

Thunderbird 0 12 22


Engine Block Sequence

Hours Since Order

ArrivedBegin Work

Processing Time, (hr)

Finish Time (hr)

Flow Time (hr)

Scheduled Customer

Pickup Time

Actual Customer

Pickup Time

Hours Early

Hours Past Due

Ranger

Explorer

Econoline 150

Bronco

Thunderbird

12 0 + 8 = 8 20 10 10 2 —

10 8 + 6 = 14 24 12 13 — 2


SOLUTION

a. The EDD rule states that the first engine block in the sequence is the one with the closest due date. Consequently, the Ranger engine block is processed first. The Thunderbird engine block, with its due date furthest in the future, is processed last. The sequence is shown in the following table, along with the flow times, the hours early, and the hours past due.

3 14 + 15 = 17 20 18 18 1 —

1 17 + 3 = 32 33 20 32 — 12

0 32 + 12 = 44 44 22 44 — 22



The flow time for each job is its finish time, plus the time since the job arrived.1 For example, the Explorer engine block’s finish time will be 14 hours from now (8 hours waiting time before the engine expert started to work on it plus 6 hours processing). Adding the 10 hours since the order arrived at this workstation (before the processing of this group of orders began) results in a flow time of 24 hours. You might think of the sum of flow times as the total job hours spent by the engine blocks since their orders arrived at the workstation until they were processed.



The performance measures for the EDD schedule for the five engine blocks are

Average flow time =

Average hours early =

Average hours past due =

20 + 24 + 20 + 33 + 445

= 28.2 hrs

2 + 0 + 1 + 0 + 05

= 0.6 hrs

0 + 2 + 0 + 12 + 225

= 7.2 hrs


Engine Block Sequence

Hours Since Order

ArrivedBegin Work

Processing Time, (hr)

Finish Time (hr)

Flow Time (hr)

Scheduled Customer

Pickup Time

Actual Customer

Pickup Time

Hours Early

Hours Past Due

Econoline 150

Explorer

Ranger

Thunderbird

Bronco

3 0 + 3 = 3 6 19 18 15 —

10 3 + 6 = 9 19 12 12 3 —


b. Under the SPT rule, the sequence starts with the engine block that has the shortest processing time, the Econoline 150, and it ends with the engine block that has the longest processing time, the Bronco. The sequence, along with the flow times, early hours, and past due hours, is contained in the following table:

12 9 + 8 = 17 29 10 17 — 7

0 17 + 12 = 29 29 22 29 — 7

1 29 + 15 = 44 45 20 44 — 24



The performance measures are

Average flow time =

Average hours early =

Average hours past due =

6 + 19 + 29 + 29 + 455

= 25.6 hrs

15 + 3 + 0 + 0 + 05

= 3.6 hrs

0 + 0 + 7 + 7 + 245

= 7.6 hrs


Comparing Sequencing RulesComparing Sequencing Rules

EDD rule Performs well with respect to the percentage of jobs past due

and the variance of hours past due Popular with firms that are sensitive to achieving due dates

SPT rule Tends to minimize the mean flow and maximize shop utilization For single-workstations will always provide the lowest mean

finish time Could increase total inventory Tends to produce a large variance in past due hours

FCFS rule Considered fair It performs poorly with respect to all performance measures


Application J.1Application J.1

Given the following information, devise an SPT schedule for the automatic routing machine.

Order

Standard Time, Including Setup (hr)

Due Date(hrs from now)

AZ135 14 14

DM246 8 20

SX435 10 6

PC088 3 18


Order Sequence

HoursSince Order Arrived

Begin Work

Finish Time (hr)

FlowTime(hr)

Scheduled Customer

Pickup Time

Actual Pickup Time

Hours Early

Hours Past Due

1.

2.

3.

4.

Total

Average

PC088

DM246

SX435

AZ135

2 0 3 5 18 18 15

4 3 11 15 20 20 9

1 11 21 22 6 21 15

5 21 35 40 14 35 25

82 94 24 40

20.5 23.5 6 10



Multiple-Dimension RulesMultiple-Dimension Rules

The priority rules CR and S/RO incorporate information about the remaining workstations

S/RO is better than EDD with respect to the percentage of jobs past due but usually worse than SPT and EDD with respect to average job flow times

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


Sequencing with the CR and Sequencing with the CR and S/RO RulesS/RO Rules

EXAMPLE J.2

The first five columns of the following table contain information about a set of four jobs that just arrived (end of hour 0 or beginning of hour 1) at an engine lathe. They are the only ones now waiting to be processed. Several operations, including the one at the engine lathe, remain to be done on each job. Determine the schedule by using (a) the CR rule and (b) the S/RO rule. Compare these schedules to those generated by FCFS, SPT, and EDD.

Job

Processing Time at Engine Lathe

(hours)

Time Remaining Until Due Date

(days)

Number of Operations Remaining

Shop Time Remaining

(days) CR S/RO

1 2.3 15 10 6.1 2.46 0.89

2 10.5 10 2 7.8 1.28 1.10

3 6.2 20 12 14.5 1.38 0.46

4 15.6 8 5 10.2 0.78 –0.44



SOLUTION

a. Using CR to schedule the machine, we divide the time remaining until the due date by the shop time remaining to get the priority index for each job. For job 1,

CR =Time remaining until the due date

Shop time remaining= = 2.46

15

6.1

By arranging the jobs in sequence with the lowest critical ratio first, we determine that the sequence of jobs to be processed by the engine lathe is 4, 2, 3, and finally 1, assuming that no other jobs arrive in the meantime.



b. Using S/RO, we divide the difference between the time remaining until the due date and the shop time remaining by the number of remaining operations. For job 1,

S/RO =

Time remaininguntil the due date

Shop timeremaining–

Number of operations remaining = = 0.89

15 – 6.1

10

Arranging the jobs by starting with the lowest S/RO yields a 4, 3, 1, 2 sequence of jobs.



Priority Rule Summary

FCFS SPT EDD CR S/RO

Average flow time 17.175 16.100 26.175 27.150 24.025

Average early time 3.425 6.050 0 0 0

Average past due 7.350 8.900 12.925 13.900 10.775



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.


Critical Ratio Slack/Remaining Operation

Job Priority IndexSequence on

Drill Press Job Priority IndexSequence on

Drill Press


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

AA

BB

CC

DD

EE

1.25

1.83

1.44

1.50

2.33

First

Fourth

Second

Third

Fifth

AA

BB

CC

DD

EE

0.33

1.25

0.70

2.00

0.80

First

Fourth

Second

Fifth

Third


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

Computer simulation models are effective tools to determine which priority rules work best in a given situation

Multiple WorkstationsMultiple Workstations


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

The group of jobs is completed in minimum time The utilization of the two-station flow shop is maximized

Scheduling a Two-Station Flow ShopScheduling a Two-Station Flow Shop


Johnson’s RuleJohnson’s Rule

Minimizes makespan when scheduling a group of jobs on two workstations

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.

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.

Step 3: Eliminate the last job scheduled from further consideration. Repeat steps 1 and 2 until all jobs have been scheduled.


Scheduling Jobs on Two Workstations

EXAMPLE J.3

The Morris Machine Company just received an order to refurbish five motors for materials handling equipment that were damaged in a fire. The motors have been delivered and are available for processing. The motors will be repaired at two workstations in the following manner.

Workstation 1: Dismantle the motor and clean the parts.

Workstation 2: Replace the parts as necessary, test the motor, and make adjustments.



The customer’s shop will be inoperable until all the motors have been repaired, so the plant manager is interested in developing a schedule that minimizes the makespan and has authorized around-the-clock operations until the motors have been repaired. The estimated time to repair each motor is shown in the following table:

Time (hr)

Motor Workstation 1 Workstation 2

M1 12 22

M2 4 5

M3 6 3

M4 15 16

M5 10 8



SOLUTION

The logic for the optimal sequence is shown in the following table:

Establishing a Job Sequence

Iteration Job Sequence Comments

1 M3 The shortest processing time is 3 hours for M3 at workstation 2. Therefore, M3 is scheduled as late as possible.

2 M2 M3 Eliminate M3 from the table of estimated times. The next shortest processing time is 4 hours for M2 at workstation 1. M2 is therefore scheduled first.

3 M2 M5 M3 Eliminate M2 from the table. The next shortest processing time is 8 hours for M5 at workstation 2. Therefore, M5 is scheduled as late as possible.

4 M2 M1 M5 M3 Eliminate M5 from the table. The next shortest processing time is 12 hours for M1 at workstation 1. M1 is scheduled as early as possible.

5 M2 M1 M4 M5 M3 The last motor to be scheduled is M4. It is placed in the last remaining position, in the middle of the schedule.



M2 (4)

M1 (12)

M4 (15)

M5 (10)

M3 (5)

Idle—available for further work

Idle M2 (5)

M1 (22)

M4 (16)

M5 (8)Idle

Figure J.2 – Gantt Chart for the Morris Machine Company Repair Schedule

(3)M3

Workstation

0 5 10 15 20 25 30Hour

35 40 45 50 55 60 65

1

2



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



Workstation 1 Workstation 2

Start Finish Start Finish

C

B

E

D

A

0 2

2 12

12 26

26 34

34 38

2 17

17 37

37 50

50 57

57 60


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

Labor-Limited EnvironmentLabor-Limited Environment

Some possible labor assignment rules Assign personnel to the workstation with the job that

has been in the system longest Assign personnel to the workstation with the most jobs

waiting for processing Assign personnel to the workstation with the largest

standard work content Assign personnel to the workstation with the job that

has the earliest due date


The Neptune’s Den Machine Shop specializes in overhauling outboard marine engines. Some engines require replacement of broken parts, whereas others need a complete overhaul. Currently, five engines with varying problems are awaiting service. The best estimates for the labor times involved and the promise dates (in number of days from today) are shown in the following table. Customers usually do not pick up their engines early.

Solved Problem 1Solved Problem 1

EngineTime Since Order

Arrived (days)

Processing Time, Including Setup

(days)Promise Date

(days from now)

50-hp Evinrude 4 5 8

7-hp Johnson 6 4 15

100-hp Mercury 8 10 12

50-hp Honda 1 1 20

75-hp Nautique 15 3 10



a. Develop separate schedules by using the SPT and EDD rules

b. Compare the two schedules on the basis of average flow time, percentage of past due jobs, and maximum past due days for any engine



SOLUTION

a. Using the SPT rule, we obtain the following schedule:

Repair Sequence

Days Since Order

ArrivedProcessing

TimeFinish Time

Flow Time

Promise Date

Actual Pickup

DateDays Early

Days Past Due

50-hp Honda 1 1 1 2 20 20 19 —

75-hp Nautique 15 3 4 19 10 10 6 —

7-hp Johnson 6 4 8 14 15 15 7 —

50-hp Evinrude 4 5 13 17 8 13 — 5

100-hp Mercury 8 10 23 31 12 23 — 11

Total 83



Using the EDD rule we obtain this schedule:

Repair Sequence

Days Since Order

ArrivedProcessing

TimeFinish Time

Flow Time

Promise Date

Actual Pickup

DateDays Early

Days Past Due

50-hp Evinrude 4 5 5 9 8 8 3 —

75-hp Nautique 15 3 8 23 10 10 2 —

100-hp Mercury 8 10 18 26 12 18 — 6

7-hp Johnson 6 4 22 28 15 22 — 7

50-hp Honda 1 1 23 24 20 23 — 3

Total 110



b. Performance measures are as follows:

Average flow time is 16.6 (or 83/5) days for SPT and 22.0 (or 110/5) days for EDD. The percentage of past due jobs is 40 percent (2/5) for SPT and 60 percent (3/5) for EDD. For this set of jobs, the EDD schedule minimizes the maximum days past due but has a greater flow time and causes more jobs to be past due.



The following data were reported by the shop floor control system for order processing at the edge grinder. The current date is day 150. The number of remaining operations and the total work remaining include the operation at the edge grinder. All orders are available for processing, and none have been started yet. Assume the jobs were available for processing at the same time.

Current OrderProcessing Time (hr)

Due Date (day)

Remaining Operations

Shop Time Remaining

(days)

A101 10 162 10 9

B272 7 158 9 6

C106 15 152 1 1

D707 4 170 8 18

E555 8 154 5 8



a. Specify the priorities for each job if the shop floor control system uses slack per remaining operations (S/RO) or critical ratio (CR).

b. For each priority rule, calculate the average flow time per job at the edge grinder.



SOLUTION

a. We specify the priorities for each job using the two sequencing rules. The sequence for S/RO is shown in the brackets.

remaining operations of Number

remaining time Shopdate sToday'date DueS/RO

18005

8150154S/RO:E555 .

22209

6150158S/RO:B272 .

32508

18150170S/RO:D707 .

430010

9150162S/RO:A101 .

50011

1150152S/RO:C105 .



The sequence of production for CR is shown in the brackets.

remaining time Shopdate sToday'date Due

CR

15008

150154CR:E555 .

33316

150158CR:B272 .

211118

150170CR:D707 .

43319

150162CR:A101 .

50021

150152CR:C105 .



b. We are sequencing a set of jobs at a single machine, so each job’s finish time equals the finish time of the job just prior to it in sequence plus its own processing time. Further, all jobs were available for processing at the same time, so each job’s finish time equals its flow time. Consequently, the average flow times at this single machine are

hours 23.305

442919158S/RO

:

hours 22.45

442919128:CR

In this example, the average flow time per job is lower for the CR rule, which is not always the case. For example, the critical ratios for B272 and A101 are tied at 1.33. If we arbitrarily assigned A101 before B272, the average flow time would increase to (8 + 12 + 22 + 29 + 44)/5 = 23.0 hours.



The Rocky Mountain Arsenal, formerly a chemical warfare manufacturing site, is said to be one of the most polluted locations in the United States. Cleanup of chemical waste storage basins will involve two operations.

Operation 1: Drain and dredge basin.

Operation 2: Incinerate materials.

Management estimates that each operation will require the following amounts of time (in days):

Storage Basin

A B C D E F G H I J

Dredge 3 4 3 6 1 3 2 1 8 4

Incinerate 1 4 2 1 2 6 4 1 2 8



Management’s objective is to minimize the makespan of the cleanup operations. All storage basins are available for processing right now. First, find a schedule that minimizes the makespan. Then calculate the average flow time of a storage basin through the two operations. What is the total elapsed time for cleaning all 10 basins? Display the schedule in a Gantt machine chart.

SOLUTION

We can use Johnson’s rule to find the schedule that minimizes the total makespan. Four jobs are tied for the shortest process time: A, D, E, and H. E and H are tied for first place, while A and D are tied for last place. We arbitrarily choose to start with basin E, the first on the list for the drain and dredge operation. The 10 steps used to arrive at a sequence are as follows:



2. Select basin H next; put it toward the front.

E H — — — — — — — —

3. Select basin A next (tied with basin D); put it at the end.

E H — — — — — — — A

4. Put basin D toward the end. E H — — — — — — D A

5. Put basin G toward the front. E H G — — — — — D A

7. Put basin I toward the end. E H G — — — I C D A

8. Put basin F toward the front. E H G F — — I C D A

9. Put basin B toward the front. E H G F B — I C D A

10. Put basin J in the remaining space.

E H G F B J I C D A

1. Select basin E first (tied with basin H); put it at the front.

E — — — — — — — — —

6. Put basin C toward the end. E H G — — — — C D A



Several optimal solutions are available to this problem because of the ties at the start of the scheduling procedure. However, all have the same makespan. The schedule would be as follows:

Operation 1 Operation 2

Basin Start Finish Start Finish

E 0 1 1 3

H 1 2 3 4

G 2 4 4 8

F 4 7 8 14

B 7 11 14 18

J 11 15 18 26

I 15 23 26 28

C 23 26 28 32

D 26 32 32 35

A 32 35 35 36

Total 200


E H G F B J I C D A

E H G F B J I C D A


The makespan is 36 days. The average flow time is the sum of incineration finish times divided by 10, or 200/10 = 20 days. The Gantt machine chart for this schedule is given in Figure J.3.

Figure J.3

Storage Basin

Dredge

Incinerate


Documents

J – 1 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall. Operations Scheduling J For Operations Management, 9e by Krajewski/Ritzman/Malhotra