chapter 4 : scheduling

CHAPTER 4 :SCHEDULING

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OUTLINE

4.1 Introduction4.2 Job Shop Scheduling Terminology4.3 Sequencing Rules

4.3.1 FCFS4.3.2 SPT4.3.3 EDD4.3.4 CR

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4.1 INTRODUCTION

What is Scheduling ? Last stage of planning before production occurs Specifies when labor, equipment, facilities are

needed to produce a product or provide a service

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Operations Scheduling

Scheduling is an allocation decision Scheduling decisions allocate resources over relatively short

time periods: a few months, weeks, or hours. The results are time allocations of production resources to

different jobs All the orders can be completed while all production

resources are utilized with their loads being balance

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Production Management

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Objectives of Operations Scheduling

1. Meet customer due dates2. Minimize job lateness3. Minimize completion time4. Minimize idle time5. Minimize WIP inventory6. Minimize the average flow time through the system7. Reduce setup cost

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Typical Scheduling and Control Functions

The following functions must be performed in scheduling and controlling a shop floor:

Allocating orders, equipment, and personnel to work centers or other specified location-short term capacity planning

Determining the sequence of order performance Initiating performance of the scheduled work, commonly termed the

dispatching of jobs Shop-floor control, involving

Reviewing the status and controlling the progress of orders as they are being worked onExpediting the late and critical orders

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Operations Scheduling

Operations schedules are short-term plans designed to implement the master production schedule. Operations scheduling focuses on how best

to use existing capacity. Often, several jobs must be processed at one

or more workstations. Typically, a variety of tasks can be performed at each workstation.

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Cont… Operations Scheduling

1. Scheduling in High-Volume System – To obtain a smooth rate of flow of goods or customers through the system in order to get a high utilization of labor and equipment.

Often referred as flow systems; scheduling refer to flow shop scheduling

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2. Scheduling in Intermediate-Volume System – Typically produce standard outputs. The run sizes are relatively small compared to flow shop.

3. Scheduling in Low Volume System – Job shop scheduling

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Cont… Operations Scheduling

Low-Volume System

Low-volume, job shop (batch) operations, are designed for flexibility.

Products are made to order and orders usually differ considerably in terms of processing requirements, materials needed, processing time and sequence and setup.

Each product or service may have its own routing (scheduling is much more difficult)

Many service operations have similar issues – how to distribute the workload among work centers and what job processing sequence to use

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Job Shop

Turnning CenterDrilling Center

Milling CenterGrinding Center

A job shop is organized by machines which are grouped according to their functions.

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Sequencing 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

No similar pattern of movements of jobs from one machine to the

next

Difficult to schedule because of the variability in job routings and

the continual introduction of new jobs to be processed

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Sh

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Dep

artm

ent

Raw

Mat

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Legend:Batch of partsWorkstation

Diagram of a Manufacturing Job Shop Process

Job Shop Sequencing

Not all jobs are assumed to require exactly the same number of operations, and some jobs may require multiple operations on a single machine.

Each job may have a different required sequencing of operations.

Operations scheduling of shop floor usually means job shop scheduling;

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An operation with line flow is often called a flow shop Medium- to high-volume production Utilizes line or continuous flow processes All jobs follow the same paths from one machine to the

next Tasks are easier to schedule because the jobs have a

common flow pattern through the system

Cont…. Sequencing Jobs

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Flow Shop Sequencing

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Types of Shop Floor Planning and Control for Job Shop

1. Gantt Chart Used for variety of purposes related to loading and

Scheduling The purpose is to organize and visually display the

actual or intended use of resources in a time framework.

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2. Loading Refer to the assignments of jobs to processing (work)

centers. Loading decisions involve assigning specific jobs to work

centers and to various machines in the work centers.

3. Scheduling Forward scheduling and Backward scheduling

Cont……Types of Shop Floor Planning and Control for Job Shop

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1. Gantt Charts Developed in the early 1900’s by Henry Gantt 1.1 Load charts

- Illustrates the workload relative to the capacity of a resource - Shows job schedule by employee

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1.2 Progress charts: - Illustrates the planned schedule compared to actual performance - Brackets show when activity is scheduled to be finished. Note that design and pilot run both finished late and feedback has not started yet.


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2. Loading

2.1 Infinite loading: Ignores capacity constraints,

but helps identify bottlenecks in a proposed schedule to enable proactive management

2.2 Finite loading: Allows only as much work to

be assigned as can be done with available capacity – but doesn’t prepare for inevitable slippage


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3. Scheduling

3.1 Forward Scheduling Scheduling ahead from a point in time If the issue is “How long will it take to complete this job?”

3.2 Backward Scheduling Scheduling backward from a due date If the issue is “When the latest the job can be started and still be

completed by the due date?”


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Start processing when order is received regardless of due date

Schedule the job’s last activity so it is finished right before the due date

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4.2 Job Shop Scheduling Terminology

1. Parallel processing versus sequential processing Sequencing Processing: the m machines are distinguishable, and

different operations are performed by different machines. Parallel processing: The machines are identical, and any job can be

processed on any machine.

M1 M2

M3 M4

Job A

Job B

M1, M2, M3, and M4 are different; Job A has 2 operations which should be

processed on different Machines: M1and M2;

Job B has 3 operations which should be processed on different Machines: M3, M2 and M4;

M1 M2

M3 M4

Job A

Job B

M1, M2, M3, and M4 are identical;

Jobs A and B can be processed on any one of the 4 machines

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2 Flow time The flow time of job i is the time that elapses from the initiation of

that job on the first machine to the completion of job i. The mean flow time, which is a common measure of system

performance, is the arithmetic average of the flow times for all n jobs

Job 1 Job 2

Job 1

Job 3

Job 2 Job 3

Machines

M1

M2

TimeF1: FT of Job 1

F2: FT of Job 2

F3: FT of Job 3

Mean Flow Time=(F1+F2+F3)/3

Cont… Job Shop Scheduling Terminology

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3. Make-span The make-span is the time required to complete a group of jobs (all n

jobs). Minimizing the make-span is a common objective in multiple-machine

sequencing problems.

Job 1 Job 2

Job 1

Job 3

Job 2 Job 3

Machines

M1

M2

TimeF1: FT of Job 1

F2: FT of Job 2

F3: FT of Job 3

Make-span of the 3 jobs


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4. Tardiness and lateness Tardiness is the positive difference between the completion time and the

due date of a job. Lateness refers to the difference between the job completion time and its

due date and differs from tardiness in that lateness can be either positive or negative.

If lateness is positive, it is tardiness; when it is negative, it is earliness

Due date of Job i

Completion time of Job i

Tardiness of Job iDue date

of Job i

Completion time of Job i

When the completion of Job is earlier than due date, the tardiness is 0

Lateness>0---Tardiness

Lateness<0---Earliness


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4.3 Sequencing Rules

1. FCFS (first come-first served) Jobs are processed in the sequence in which they entered the shop; The simplest and nature way of sequencing as in queuing of a bank

2. SPT (shortest processing time) Jobs are sequenced in increasing order of their processing time; The job with shortest processing time is first, the one with the next

shortest processing time is second, and so on;

3. EDD (earliest due date)

Jobs are sequenced in increasing order of their due dates;

The job with earliest due date is first, the one with the next earliest due date is second, and so on;

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4. CR (Critical ratio) Critical ratio is the remaining time until due date divided by processing

time; Scheduling the job with the smallest CR next;

Processing time of Job i

Due date of Job iCurrent time Remaining time of Job i

CRi=Remaining time of Job i/Processing time of Job i

=(Due date of Job i-current time)/Processing time of Job i

For a job, if the numerator of its CR is negative ( the job has been already later), it is naturally scheduled next;

If more than one jobs are later, higher priority is given to one that has shorter processing time (SPT).

Cont… Sequencing Rules

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Example 4.3 A machine center in a job shop for a local fabrication company has five

unprocessed jobs remaining at a particular point in time. The jobs are labeled 1, 2, 3, 4, and 5 in the order that they entered the shop. The respective processing times and due dates are given in the table below.

Sequence the 5 jobs by above 4 rules and compare results based on mean flow time, average tardiness, and number of tardy jobs

Job number Processing Time Due Date

12345

11293112

6145313332

Cont… Sequencing Rules

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1. First Come First Serve (FCFS)


12345

11293112

6145313332

Job Completion Time Due Date Tardiness

1 11 61 0

2 40 45 0

3 71 31 40

4 72 33 39

5 74 32 42

Totals 268 121

Mean Flow time=268/5=53.6Average tardiness=121/5=24.2

No. of tardy jobs=3.

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2. Shortest Processing Time (SPT)


12345

11293112

6145313332

Job Processing Time Completion Time Due Date Tardiness

4 1 1 33 0

5 2 3 32 0

1 11 14 61 0

2 29 43 45 0

3 31 74 31 43

Totals 135 43



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3. Earliest Due Date (EDD)


12345

11293112

6145313332

Job Processing Time Completion Time Due Date Tardiness

3 31 31 31 0

5 2 33 32 1

4 1 34 33 1

2 29 63 45 18

1 11 74 61 13

Totals 235 33



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4. Critical Ratio (CR)

Current time: t=0

Job number Processing Time Due Date Critical Ratio

12345

11293112

6145313332

61/11(5.545)45/29(1.552)31/31(1.000)33/1 (33.00)32/2 (16.00)

Current time: t=31

Job number Processing Time Due Date-Current Time Critical Ratio

1245

112912

30 14 2 1

30/11(2.727)14/29(0.483) 2/1 (2.000)1/2 (0.500)

Current time should be reset after scheduling one job

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Cont … 4. Critical Ratio (CR)

Current time=60

Job number Processing Time Due Date-Current Time

Critical Ratio

145

1112

1-27-28

1/11(0.0909)-27/1<0-28/2<0

Job number Processing Time Completion Time Tardiness

32451

31291211

3160616374

015283113

Totals 289 87



Both Jobs 4 and 5 are later, however Job 4 has shorter processing time and thus is scheduled first; Finally, job 1 is scheduled last.

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Sequencing Rules——Summary

Rule Mean Flow Time Average Tardiness

Number of Tardy Jobs

FCFSSPTEDDCR

53.627.047.057.8

24.28.66.6

17.4

3144

Discussions SPT results in smallest mean flow time EDD have the minimum tardiness (42, 43, 18, and 31 for the 4 different

rules)

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Exercise

There are five sheet metal jobs are waiting to be assigned at a company work centre. Their work (processing) time and due dates are given below. Then, determine the sequence of processing according to ( FCFS, SPT, EDD and CR)

Figure 1: Jobs are assigned as below:

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Job Processing Time Due Date

A 6 8

B 2 6

C 8 18

D 3 15

E 9 23

1. First Come First Serve (FCFS)


ABCDE

62839

86181523


No. of tardy jobs=3

JOB NUMBER COMPLETION TIME DUE DATE TARDINESS

A 6 8 0

B 8 6 2

C 16 18 0

D 19 15 4

E 28 23 5

Totals 77 11

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2. Shortest Processing Time (SPT)


ABCDE

62839

86181523

Mean Flow time=65/5=13Average tardiness=9/5=1.8

No. of tardy jobs=3

JOB NUMBER

PROCESSING TIME

COMPLETION TIME

DUE DATE TARDINESS

B 2 2 6 0

D 3 5 15 0

A 6 11 8 3

C 8 19 18 1

E 9 28 23 5

Totals 65 9

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3. Earliest Due Date (EDD)


ABCDE

62839

86181523


No. of tardy jobs=2

JOB NUMBER

PROCESSING TIME

COMPLETION TIME

DUE DATE TARDINESS

B 2 2 6 0

A 6 8 8 0

D 3 11 15 0

C 8 19 18 1

E 9 28 23 5

Totals 68 6

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4. Critical Ratio (CR)

Current time: t=0

Job number Processing Time Due Date Critical Ratio

ABCDE

62839

86

181523

8/6 (1.33)6/2 (3.00)18/8(2.25)15/3 (5.00)23/9 (2.56)

Current time: t=6

Job number Processing Time Due Date-Current Time Critical Ratio

BCDE

2839

0 12 9 17

0/2 (0.00)12/8(1.50) 9/3 (3.00)17/9 (1.89)

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Jobs are processed according to smallest ratio



Current time = 8


Critical Ratio

CDE

839

107

15

10/8 (1.25) 7/3 (2.33)15/9 (1.67)

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Current time = 16


Critical Ratio

DE

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-17

-1/3 (-0.33)7/9 (0.77)

Finally, job E is scheduled last.


Job No Processing Time Completion Time Due Date Tardiness

ABCDE

62839

68

161928

8 06 218 015 423 5

Totals 77 11



No. of tardy jobs=3

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Sequencing Rules——Summary

Rule Mean Flow Time Average Tardiness

Number of Tardy Jobs

FCFSSPTEDDCR

15.413.013.615.4

2.21.81.22.2

3323

Discussions SPT results in smallest mean flow time EDD have the minimum tardiness FCFS and CR rule turn out to be the least effective of the rules

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chapter 4 : scheduling

Documents

flow shop scheduling

typical scheduling

operations scheduling

routing scheduling

job shop batch operations

job shoplow

job processing sequence

job lateness3