Learning Objectives

After completing today’s lecture, the students should be able to develop a comprehensive understanding of scheduling and sequencing operations with the help of Hungarian Methods and Johnson Rules. The students would be able to understand the priority rules along with the need of effective scheduling and sequencing. The students would be able to develop an Operations Strategy with respect to both Scheduling and Sequencing.

Sequencing: Determine the order in which jobs at a work center will be processed. Requires order for sequencing at all work centers as well as sequencing at individual work centers.

Workstation: An area where one person works, usually with special equipment, on a specialized job. Sequencing

Job time: Time needed for setup and processing of a job.

Priority rules: Simple heuristics (Commonsense rules) used to select the order in which jobs will be processed.

1.  Local Rules ( pertaining to single workstation)

2.  Global Rules( pertaining to multiple workstation)

3.  Job processing times and due dates are important pieces of information.

4.  Job time consists of processing time and setup times

Priority Rules

1.  FCFS – First Come, First Served: Jobs are processed in the order in which they arrive at a machine or work center.

2.  SPT- Shortest Processing Time: Jobs are processed according to processing time at a machine or work center, shortest job first.

3.  DD – Due Date: Jobs are processed according to due date, earliest due date first.

4.  CR – critical ratio: Jobs are processed according to smallest ratio of time remaining until due date to processing time remaining.

5.  S/O – slack per operation: Jobs are processed according to average slack time (time until due date minus remaining time to process). Compute by dividing slack time by dividing slack time by number of remaining operations including the current one.

6.  Rush – emergency: Emergency or Preferred Customers first.
Assumptions to Priority Rules

1.  The set of jobs is known, no new jobs arrive after processing begins and no jobs are canceled.

2.  Setup time is deterministic

3.  Processing times are deterministic rather than variables.

4.  There will be no interruptions in processing such as machine breakdowns , accidents or worker illnesses.


Job Flow Time: The length of time a job is in the shop at a particular workstation or work center.

Job Lateness: This is the length of time the job completion date is expected to exceed the date the job was due or promised to a customer.

Makespan: This is the total time needed to complete a group of jobs. It is the length of time between the start of the first job in the group and the completion of the last job in the group.

Average Number of Jobs: Jobs that are considered in a shop are considered to be work in process inventory. Mathematically Average Number of Jobs= Total Flow Time / Makespan.

Determine the sequence of jobs, average time flow, average days late and average number of jobs at the work center, for each of these rules FCFS SPT DD CR Example Data

JOB Processing Time Due Date
A 2 7
B 8 16
C 4 4
D 10 17
E 5 15
F 12 18

Part A. FCFS

Assume Jobs arrived in the following order 1. A-B-C-D-E-F

JOB Sequences Processing Time (1) Flow Time ( cumulative processing time) (2) Due Date (3) (2)-(3)
A 2 2 7 0
B 8 10 16 0
C 4 14 4 10
D 10 24 17 7
E 5 29 15 14
F 12 41 18 22
41 120 54

Part A. FCFS Average Flow time= Total Flow Time/Number of Jobs=120/6=20 days Average Tardiness=54/6=9 The makespan =41 days Average Number of Jobs at workstation=

120/41=2.93 jobs per workstation SPT, the sequence is A-C-E-B-D-F Average Flow time= Total Flow Time/Number of Jobs=108/6=18 days Average Tardiness=40/6=6.67days The makespan =41 days Average Number of Jobs at workstation=

JOB Sequences Processing Time (1) Flow Time ( cumulative processing time) (2) Due Date (3) (2)-(3)
A 2 2 7 0
C 4 6 4 2
E 5 11 15 0
B 8 19 16 3
D 10 29 17 12
F 12 41 18 23
41 108 40

108/41=2.63 jobs per workstation Summary Part A,B,C and D

JOB Sequences Rule Average Flow Time (Days) Average Lateness (Days) Average Number of Jobs of the Work Center
FCFS 20.00 9.00 2.93
SPT 18.00 6.67 2.63
DD 18.33 6.33 2.68
CR 26.67 14.17 3.9

Summary Part A,B,C and D

1.  Generally Speaking FCFS and CR rule seems to be the least effective.

2.  CR is the worst in each aspect of measurement.

3.  The primary limitation of FCFS is that long jobs will tend to delay other jobs.

4.  However in scheduling of service systems, the FCFS has the advantage of simplicity, inherent fairness (first come first served) but also due to non availability of realistic estimates of processing times for individual jobs.

Johnson’s Rule (Two Work Center Sequencing)

Johnson’s Rule: technique for minimizing completion time for a group of jobs to be processed on two machines or at two work centers.

1.  Minimizes total idle time

2.  Several conditions must be satisfied

Johnson’s Rule Conditions

1.  Job time must be known and constant

2.  Job times must be independent of sequence

3.  Jobs must follow same two-step sequence

4.  Job priorities cannot be used

5.  All units must be completed at the first work center before moving to second

Johnson’s Rule Optimum Sequence

1.  List the jobs and their times at each work center

2.  Select the job with the shortest time

1.  Eliminate the job from further consideration

2.  Repeat steps 2 and 3 until all jobs have been scheduled

Johnson’s Rule Example

JOB Work Center 1 Work Center2
A 5 5
B 4 3
C 8 9
D 2 7
E 6 8
F 12 15

1.  Select the job with shortest processing time. In our case it is Job D

2.  Eliminate the row of JOB D & proceed further to select the next job with shortest processing time which is B in our case and that too at work center2

3.  Similarly sequencing other jobs at work centers, we follow that if there is tie of no of hours, we can sequence it at the beginning or the end.

4.  Construct a chart to determine the throughput time and idle times at the work centers. We have

5.  1st D,2nd E,3rd C,4th F,5th A and 6th B

Scheduling Difficulties

1. Variability in

a.Setup times

b.Processing times


d.Changes in the set of jobs

1.  No method for identifying optimal schedule

2.  Scheduling is not an exact science

3.  Ongoing task for a manager

Minimizing Scheduling Difficulties

1.  Set realistic due dates

2.  Focus on bottleneck operations

3.  Consider lot splitting of large jobs

Scheduling Service Operations

1. Appointment systems

a. Controls customer arrivals for service

2. Reservation systems

a. Estimates demand for service

3. Scheduling the workforce

a. Manages capacity for service

4. Scheduling multiple resources

a. Coordinates use of more than one resource

Cyclical Scheduling

1.  Hospitals, police/fire departments, restaurants, supermarkets

2.  Rotating schedules

3.  Set a scheduling horizon

4.  Identify the work pattern

5.  Develop a basic employee schedule

6.  Assign employees to the schedule

Service Operation Problems

1.  Cannot store or inventory services

2.  Customer service requests are random

1.  Scheduling service involves

1.  Customers

2.  Workforce

3.  Equipment


Maintenance: All activities that maintain facilities and equipment in good working order so that a system can perform as intended Breakdown maintenance: Reactive approach; dealing with breakdowns or problems when they occur Preventive maintenance: Proactive approach; reducing breakdowns through a program of lubrication, adjustment, cleaning, inspection, and replacement of worn parts

Maintenance Reasons

Reasons for keeping equipment running

1.  Avoid production disruptions

2.  Not add to production costs

3.  Maintain high quality

4.  Avoid missed delivery dates

Breakdown Consequences

Some of the important consequences are:

1.  Production capacity is reduced : Orders are delayed

2.  No production: Overhead continues

3.  Cost per unit increases: Quality issues

4.  Product may be damaged

1.  Safety issues

1.  Injury to employees

2.  Injury to customers

Total Maintenance Cost

production and operations management  SEQUENCING

Preventive Maintenance

Preventive maintenance: goal is to reduce the incidence of breakdowns or failures in the plant or equipment to avoid the associated costs

1.  Preventive maintenance is periodic

2.  Result of planned inspections

3.  According to calendar

4.  After predetermined number of hours

Example 1 Frequency of breakdown

Number of breakdowns 0 1 2


Frequency of occurrence .20 .30 .40 .10

If the average cost of a breakdown is Rs.10,000, and the cost of preventative maintenance is Rs.12,500 per month, should we use preventive maintenance? Example 1 Solution

Number of Breakdowns Frequency of Occurrence Expected number of Breakdowns
0 1 2 3 .20 .30 .40 .10 1.00 0 .30 .80 .30 1.40

Expected cost to repair = 1.4 breakdowns per month X Rs.10,000

= Rs.14,000 Preventive maintenance = Rs.12,500. PM results in savings of Rs.1500 per month

Predictive Maintenance

Predictive maintenance: An attempt to determine when best to perform preventive maintenance activities Total productive maintenance: JIT approach where workers perform preventive maintenance on the machines they operate

Breakdown Programs

1.  Standby or backup equipment that can be quickly pressed into service

2.  Inventories of spare parts that can be installed as needed

3.  Operators who are able to perform minor repairs

4.  Repair people who are well trained and readily available to diagnose and correct problems with equipment


1.  Trade-off decisions

2.  Cost of replacement vs. cost of continued maintenance

3.  New equipment with new features vs. maintenance

4.  Installation of new equipment may cause disruptions

5.  Training costs of employees on new equipment

6.  Forecasts for demand on equipment may require new equipment capacity

7.  When is it time for replacement?

Operations Strategy

1.  Scheduling can hinder or help the Operations Strategy.

2.  An on time delivery of a product or service is only possible if the Operations Managers is able to do effective scheduling.

3.  An ineffective scheduling would result in inefficient use of resources and possible dissatisfied customers.

4.  Scheduling as an Operations Strategy can provide an organization a competitive advantage over its competitors.

5.  Time based competition depends on good scheduling.

6.  Good design, superior quality and other elements of a well run organization are meaningless if effective scheduling is absent from Operations Management Strategy.

7.  Scheduling is that bank balance which may seem great in numbers but if not used effectively would not make any sense.


Scheduling involves timing and coordination of operations. Scheduling is different for high volume, intermediate volume and low volume. Scheduling for job shops is very complex, because of variety jobs that need to be processed. The two major problems in Scheduling is the assigning of jobs to the machines (work centers) and sequence of operations at a machine.

Gantt Load charts are used to help managers visualize the work load situation. Scheduling of service systems require appointment or reservation systems, although all systems are not amenable to this. When multiple resources are involved, the balancing can be difficult. Maintenance Activities ensure that sequence activities are completed on time and as per schedule. Maintenance adds to revenue and not to costs.

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