shop floor planning & control

Chapter4 1

Shop Floor Planning Shop Floor Planning & Control& Control

Chapter 4

Production Planning Production Planning & Control& Control

Chapter4 2

Shop Floor Planning Shop Floor Planning & Control & Control

Once the Broadest Strategic decisions concerning manufacturing company viz.,a)What business it is in &b)What territory it will serveAre made the operations managers use the forecasts of expected demand to select most appropriate type of factoryThe choice may be one of following types1.Job Shop2.Flow Shop3.Continuous production4.Project organization for manufacturing or service

Chapter4 3

Shop Floor Planning & ControlShop Floor Planning & Control

In fo rm a tio n E x c h a n g e B e tw e e n L e v e l 3 & 4The Production Environment

Chapter4 4


B u s in e s s F u n c t io n s ( S 9 5 )

R e a l - T im eM o n i t o r i n g

R e a l - T im eE x e c u t io n

R e a l - T im eS P C

R e a l - T im eC o n t r o l

D e m a n dP la n n in g S u p p ly C h a i n P la n n in g

P r o d u c t i o nP la n n in g

C o s t A c c o u n t in g

W a r e h o u s eM a n a g e m e n t

M a in t e n a n c eM a n a g e m e n t

M a te r ia lM a n a g e m e n t

H u m a n R e s o u r c eM a n a g e m e n t

S a le s &D is t r ib u t i o n

E n t e r p r is e P e r f o r m a n c e R e p o r t in g

D e t a i l S c h e d u l in g

P e r f o r m a n c eM a n a g e m e n t

P r o c e s sA n a ly s is

R e c ip eM a n a g e m e n t

P r o c e s sO p t im iz a t io n

P r o d u c t i o nH is t o r y

W IP M a t e r ia lM a n a g e m e n t

R e s o u r c eM a n a g e m e n t

P r o d u c t i o nE x e c u t io n

Q u a l i t yM a n a g e m e n t

L e v e l 4B u s in e s sP la n n in g &L o g is t ic s

L e v e l 3M a n u f a c tu r in gO p e r a t io n s

L e v e l 2P la n t F lo o rC o n t r o l

Business Functions

Chapter4 5


Several generic tasks characterize production, the process through which parts and materials are transformed into final products.

These tasks include, among others, the receipt and acknowledgment of orders, the acquisition of materials, the performance of shop floor operations, and the generation of information needed to support continuous improvement.

Together, these tasks (when properly done) constitute a qualified production process.

Qualifying a production process is a demanding and important task that requires people trained and physically qualified for agiven job, machines and

Chapter4 6


process instruments that can be guaranteed to operate within specifications, production capacity that can match the order demand, and the availability of production capacity in the desired time frames.

The information-processing view of a production facility is in essence the same as that for an individual work cell within the facility. Both factories and work cells process orders and turn out products.

For a factory, the order usually comes from a customer outside the factory; for a work cell, the order comes from inside the factory.

Chapter4 7

Production/shop floor Production/shop floor Activity Control Activity Control

The MRP System specifies what products or components are needed &When they are required.The production activity control(PAC)directs how,when,where the product/components should be made in order to ensure delivery of goods as per schedule.

Priority Control

Production activityControl

CapacityControl

Priority Control ensures that production activities are carried out as per plan

Chapter4 8

Objectives of Production Objectives of Production Activity Control Activity Control

To know The current status of jobTo determine what should be next job to be

processed & which work centerTo ensure correct quantity of materials are in

right placeTo minimize work in process inventoryTo minimize setup costsTo maintain control of operations by monitoring

job statusTo maximize operational efficiency

Chapter4 9

Operations Planning Operations Planning & Scheduling& Scheduling

In this context the scheduling process centers around:1. Time to do the work,2. The department which will perform the work,3. The resources to be applied,4. Statusing work progress versus work scheduled, and5. Monitoring and reporting

Chapter4 10


Scheduling is an important tool for manufacturing and engineering, where it can have a major impact on the productivity of a process.

In manufacturing, the purpose of scheduling is to minimize the production time and costs, by telling a production facility what to make, when, with which staff, and on which equipment. Production scheduling aims to maximize the efficiency of the operation and reduce costs.

Production scheduling tools greatly outperform older manual scheduling methods. This provides the production scheduler with powerful graphical interfaces which can be used to visually optimize real-time work loads in various stages of the production,

http://en.wikipedia.org/wiki/Manufacturing

http://en.wikipedia.org/wiki/Engineering

Chapter4 11


and pattern recognition allows the software to automatically create scheduling opportunities which might not be apparent without this view into the data.

For example, an airline might wish to minimize the number of airport gates required for its aircraft, in order to reduce costs, and scheduling software can allow the planners to see how this can be done, by analyzing time tables, aircraft usage, or the flow of passengers . Companies use backward and forward scheduling to allocate plant and machinery resources, plan human resources, plan production processes and purchase materials.

Chapter4 12


Forward scheduling is planning the tasks from the date resources become available to determine the shipping date or the due date.

Forward scheduling is also done if no product is available on the material availability date calculated by backward scheduling. The system does an availability check to determine the first possible date when product will be available. This new material availability date forms the starting point for scheduling the remaining activities. The loading time, pick/pack time, transit time, and transportation lead time are added to the new material availability date to calculate the confirmed delivery

Chapter4 13


Backward scheduling is planning the tasks from the due date or required-by date to determine the start date and/or any changes in capacity required.Backward scheduling is the calculation of deadline dates: the arrival time at the customer site is calculated as the earliest possible goods receipt time at the customers unloading point on the requested delivery date. All four of the delivery and transportation scheduling lead times are subtracted from the customer’s requested delivery date to determine if this date can be met.

The transit time, loading time, and pick/pack time are subtracted from the customer’s requested delivery date to calculate the required material availability date.

Chapter4 14


The system calculates backward scheduling as follows: Requested delivery date minus transit time = Goods issue

date Goods issue date minus loading time = Loading date Loading date minus transportation lead time = Transportation scheduling date Loading date minus pick/pack time = Material availability date

By default, the system will calculate delivery dates the closest day, taking into consideration the working days of the shipping point and a rounding profile. In this case the system assumes a 24 hour work day and lead times can be entered in days up to 2 decimal points. This is referred to as daily scheduling.

Chapter4 15


Precise scheduling calculated down to the day, hour and minute is supported. This allows the scheduling of a delivery within a single day. It is activated by maintaining the working hours for a particular shipping point.

Backward scheduling is always carried out first. If the material availability date or transportation scheduling date is calculated to be in the past, the system must then use forward scheduling.

Chapter4 16


Forward scheduling is also done if no product is available on the material availability date calculated by backward scheduling.

The system does an availability check to determine the first possible date when product will be available. This new material availability date forms the starting point for scheduling the remaining activities.

The loading time, pick/pack time, transit time, and transportation lead time are added to the new material availability date to calculate the confirmed delivery date.

Chapter4 17


Example of forward scheduling

Dept.X Dept.ZDept.Y

L.T =3WKL.T =5WKL.T =4WKOperation A Operation B Operation C

OrderReleaseDate

CompletionDate

Start Start Start FinishFinishFinish

Total manufacturing lead time

Chapter4 18


Example of backward scheduling

Dept.X Dept.ZDept.Y

L.T =3WKL.T =5WKL.T =4WKOperation A Operation B Operation C

Today’sDate

CompletionDate

Start Start Start FinishFinishFinish

Total manufacturing lead time

Chapter4 19

Stages in SchedulingStages in Scheduling

Scheduling is performed in two stages1.Loading: is the process of determine which work center receives which job.It involves assessing a jog or task,machine/worker, raw material availability 2.Dispatching:is sequencing and selecting the jobs waiting at work center(determining which job to be done next).It lists all jobs waiting at work center & arrange as per priority

Chapter4 20


Finite loading :Start with specific Capacity for each work centers and a list of jobs processed at the work centers(sequencing)

The work center capacity is allocated to job s by simulating job starting times and completion times

Period Weeks

Load in StandardHours

50

100Hr/Week

0 2 4 6 8 10

Chapter4 21


Infinite loading :The process of loading work centers with all jobs without regard to the actual capacity available at he work center

Period Weeks

Load in StandardHours 50

100Hr/Week

0 2 4 6 8 10

Work centerCapacity

100

200

Chapter4 22


The benefits of production scheduling include:Process change-over reduction Inventory reduction, leveling Reduced scheduling effort Increased production efficiency ,Labor load

leveling Accurate delivery date quotes ,Real time

information

Chapter4 23

Gantt ChartGantt ChartPlanning and scheduling complex projectsGantt Charts are useful tools for analyzing and planning complex projects. They:•Help you to plan out the tasks that need to be completed •Give you a basis for scheduling when these tasks will be carried out •Allow you to plan the allocation of resources needed to complete the project, and Help you to work out the critical path for a project where you must complete it by a particular date.

http://en.wikipedia.org/wiki/Image:WbsConstruction.png

Chapter4 24

Gantt ChartGantt ChartWhen a project is under way, Gantt Charts help you to monitor whether the project is on schedule. If it is not, it allows you to pinpoint the remedial action necessary to put it back on schedule.Sequential and parallel activities:An essential concept behind project planning (and Critical Path Analysis) is that some activities are dependent on other activities being completed first. As a shallow example, it is not a good idea to start building a bridge before you have designed it!

These dependent activities need to be completed in a sequence, with each stage being more-or-less completed before the next activity can begin. We can call dependent activities 'sequential' or 'linear'.


Chapter4 25

Gantt ChartGantt ChartOther activities are not dependent on completion of

any other tasks. These may be done at any time before or after a particular stage is reached. These are nondependent or 'parallel' tasks.

Drawing a Gantt ChartTo draw up a Gantt diagram (Gant diagram), follow

these steps:

1. List all activities in the planFor each task, show the earliest start date, estimated length of time it will take and whether it is parallel or sequential. If tasks are sequential, show which stages they depend on.

http://www.mindtools.com/pages/article/newPPM_01.htm


Chapter4 26

Gantt ChartGantt Chart



Chapter4 27




Chapter4 28

What Is Sequencing?•Predictable, consistent ordering and delivery of learning activities, in an instructionally meaningful manner, regardless of delivery environment

•Designers/authors specify sequencing behaviors at design/authoring time.

•Activities are sequenced at time of delivery depending on specified behaviors and the learner’s actions.

•Sequencing behaviors are external from the content to enable greater degree of granularity and reuse


Chapter4 29

Priority SequencingPriority SequencingPriority sequencing in a real world job shop

An engineering industry job shop that manufactures 19 types of products against orders is described, with the objective of evaluating a new sequencing rule based on the monetary value of the job and its processing time, the highest value time ratio rule.

Analysis of this rule has not appeared in literature on job shop scheduling. For purposes of comparison, based on the performances in paststudies, the following four sequencing rules are included:


Chapter4 30

Priority SequencingPriority Sequencing

(These rules were evaluated on the following criteria: work-in- process inventory in monetary terms, and delivery performance, and a combination of the two measures.

Results of the study show that the highest value time ratio rule results in minimum work-in-process inventory. The shortest processing time rule results in maximum delivery performance; the same rule is superior on combined measure of performance.


Chapter4 31

Priority Sequencing(Rules)Priority Sequencing(Rules)1) Shortest processing time (SPT) :

The jobs are having the shortest processing time is given the highest priority.

2) Least Slack per operation (LS): the highest priority given to job which has least slack

3) First-Cone, first-Served (FCFS):Jobs are selected in the same sequence as they come

4) Earliest Due date (EDD):Jobs are processed according to due dates


Chapter4 32

Priority Sequencing(Rules)Priority Sequencing(Rules)5) Longest Processing Time(LPT):the highest priority given to job which has longest processing time

6) Shortest Processing Time(LPT) :Jobs are selected as per Shortest Processing Time .

7) Random Selection: Jobs are selected randomly

8) Cost over time(COVERT):Uses the ratio of expected delay cost over the processing cost

9) Preferred Customer order(PCO):As per customer order

10 Least Change Over cost ((LCOC):The sequencing of jobs is done by analyzing the total cost of making all the machine changeover between jobs


Chapter4 33

Illustration for Sequencing(Rules)Illustration for Sequencing(Rules)

XYZ company has received the following jobs at a work center to be processed.

The processing time (in days),arrival date and due date are given Determine the sequence in which jobs should be processed according to priority rules FCFS,SPT,LPT,EDD,TSPT,LS & COVERT

Assume today is is day 100 & jobs can not be delayed more than 60 days

Assume expected cost of delay is Rs 10/day


Chapter4 34


JobJob Processing Processing Time(Days)Time(Days)

Arrival Arrival DateDate

Due DateDue Date

9595 185185200200175175235235180180

220220

110110112112125125125125

130130

15152020101030302525

1818

AABBCCDDEE

FF


Chapter4 35

Illustration for Sequencing(Rules)Illustration for Sequencing(Rules)Priority Rules: FCFS Sequence A B C D E FPriority Rules: SPT Sequence C A FB E DPriority Rules: LPT Sequence D E B F C APriority Rules: EDD Sequence C E A B F DFor TSTP rule ,it is specified that the jobs can not be delayed by more than 60 days if we apply SPT Rule .If none of the jobs violets the constraints ,the sequence will be identical for SPT and TSPT rule.To examine this ,we should know the wait time for the jobs as per SPT rule ,which is determined as per next slide


Chapter4 36



Arrival Arrival Date DaysDate Days

Start Date Start Date DaysDays

Wait Time Wait Time daysdays

112112 NilNil

27277745455050

7575

122122135135155155175175

200200

112112

9595130130110110125125

125125

1010

1515181820202525

3030

CC

AAFFBBEE

DD

SPT Rule


Chapter4 37

Illustration for Sequencing(Rules)Illustration for Sequencing(Rules)Least Slack Rule


Available Available time Daystime Days

Slack DaysSlack Days Sequence(Rank)

7575 5533226611

44

7070535380803030

7272

90(18590(185--95)95)909063631101105555

9090

15152020101030302525

1818

AABBCCDDEE

FF

JOB sequence E C B F A D


Chapter4 38

Dynamic Sequencing Dynamic Sequencing RulesRules

Dynamic slack(DS) rule:When the least slack rule is used repeatedly at each machine/work center for sequencing the jobs ,it is known as dynamic slack rule.

Dynamic slack per remaining operation(DS/RO) rule: In this rule ,the ratio of total slack time available for the job to the number of operations remaining including the current operation is obtained.

Total Slack time

Total number of operations remaining (including the current operation is obtained.)

DS/RO ratio =

Job with Smallest DS/RO ratio is scheduled first


Chapter4 39

Dynamic Sequencing Dynamic Sequencing RulesRules

Critical Ratio rule:The critical ratio rule is designed to give priority to

jobs that have most urgently needed work to meet the shipping schedule.

Due date-Date now

Days required to complete the

= D.D-D.NL.T.R

C/R ratio =


Chapter4 40

Dynamic Sequencing Dynamic Sequencing Rules Illustration Rules Illustration ABC Company has 6 jobs arriving at random at several work stations & passing through them,requiring different processing time.For particular work station the data is given below.

JobJob ArrivalTime

ProcessiProcessingngTime Time HrsHrs

Due Time

No of No of subsequentsubsequentoperationsoperations

Time forsubsequentsubsequentoperationsoperationsHrsHrs

Due Due time time HrsHrs

12Nil30102025

201250254538

22NilNil44332244

4,00PM4,00PM5PM5PM8PM8PM7PM7PM12PM12PM8Am8AmNext dayNext day

222244336644

12122 PM2 PM3,30PM3,30PM3,30PM3,30PM4,30PM4,30PM6PM6PM

12233445566


Chapter4 41

Dynamic Sequencing Dynamic Sequencing Rules Illustration Rules Illustration

JobJob ArrivalTimeHrs

ProcessingProcessingTime HrsTime Hrs

Due Time Dynamic SlackDynamic SlackAvailable timeAvailable time--Total Total operation time (Hrs)operation time (Hrs)

201250254538

2020--14=614=61212--2=102=10

5050--35=1635=162525--13=1213=124545--261926193838--29=929=9

2+122+122+nil2+nil4+304+303=103=106+206+204+254+25

12121414

15.515.515.515.516.516.51818

123456

Ds /Ro RuleDs /Ro Rule


Chapter4 42


JobJob Dynamic Dynamic Slack(DS)Slack(DS)

Remaining Operations(RO) DS/RO RatioDS/RO Ratio

2+1=3Nil+1=14+1=53+1=42+1=34+1=5

6/3=26/3=210/1=1010/1=10

16/5=3.3316/5=3.3312/4=312/4=3

19/3=6.3319/3=6.339/5=1.89/5=1.8

66101016161212191999

123456

Calculation of Ds /Ro Ratio Calculation of Ds /Ro Ratio

Sequence As per Ds/Ro rule: 6,1,4,3,5,2


Chapter4 43


JobJob Processing Time Processing Time HrsHrs

Available time(Hrs.)

Critical ratioCritical ratio

43

4.53.57.514

4/2=24/2=23/2=1.53/2=1.5

4.5/4=1.1254.5/4=1.1253.5/3=1.1663.5/3=1.1667.5/6=1.257.5/6=1.2514/4=3.514/4=3.5

222244336644

123456

Critical Ratio RuleCritical Ratio Rule

Sequence As per CR rule: 3,4,5,2,1,6


Chapter4 44

FLOW SHOP SCHEDULINGFLOW SHOP SCHEDULING(n JOBS, m MACHINES)(n JOBS, m MACHINES)n JOBS BANK OF m MACHINES (SERIES)

12

3

4 n

M1 M2 Mm

JohnsonJohnson’’s Rule or algorithms Rule or algorithm

Chapter4 45

FLOW SHOPSFLOW SHOPS

PRODUCTION SYSTEMS FOR WHICH:A NUMBER OF OPERATIONS HAVE TO BE DONE ON

EVERY JOB.THESE OPERATIONS HAVE TO BE DONE ON ALL JOBS IN

THE SAME ORDER, i.e., THE JOBS HAVE TO FOLLOW THESAME ROUTE.

THE MACHINES ARE ASSUMED TO BE SET UP IN SERIES.

COMMON ASSUMPTIONS:UNLIMITED STORAGE OR BUFFER CAPACITIES IN

BETWEEN SUCCESIVE MACHINES (NO BLOCKING).A JOB HAS TO BE PROCCESSED AT EACH STAGE ON

ONLY ONE OF THE MACHINES (NO PARALLEL MACHINES).

Chapter4 46

PERMUTATION FLOW SHOPSPERMUTATION FLOW SHOPS

FLOW SHOPS IN WHICH THE SAME SEQUENCE OR PERMUTATION OF JOBS IS MAINTAINED THROUGHOUT: THEY DO NOT ALLOW SEQUENCE CHANGES BETWEEN

MACHINES.PRINCIPLE FOR Fm||Cmax:

THERE ALWAYS EXISTS AN OPTIMAL SCHEDULE WITHOUT SEQUENCE CHANGES BETWEEN THE FIRST

TWO MACHINES AND BETWEEN THE LAST TWO MACHINES.

THERE ARE OPTIMAL SCHEDULES FOR F2||Cmax AND F3||Cmax THAT DO NOT REQUIRE SEQUENCE CHANGES

BETWEEN MACHINES.

Chapter4 47

JOHNSONJOHNSON’’S F2S F2||Cmax PROBLEM||Cmax PROBLEM

FLOW SHOP WITH TWO MACHINES IN SERIES WITH UNLIMITED STORAGE IN BETWEEN THE TWO

MACHINES.

THERE ARE n JOBS AND THE PROCESSING TIME OF JOB jON MACHINE 1 IS p1j AND THE PROCESSING TIME ON

MACHINE 2 IS p2j.

THE RULE THAT MINIMIZES THE MAKESPAN IS COMMONLY REFERRED TO AS JOHNSON’S RULE.

Chapter4 48

JOHNSONJOHNSON’’S PRINCIPLES PRINCIPLE

ANY SPT(1)-LPT(2) SCHEDULE IS OPTIMAL FOR Fm||Cmax.

(THE SPT(1)-LPT(2) SCHEDULES ARE NOT THE ONLY SCHEDULES THAT ARE OPTIMAL. THE CLASS OF OPTIMAL SCHEDULES APPEARS TO BE HARD TO

CHARACTERIZE AND DATA DEPENDENT).

Chapter4 49

DESCRIPTION OF JOHNSONDESCRIPTION OF JOHNSON’’S ALGORITHMS ALGORITHM

1. IDENTIFY THE JOB WITH THE SMALLEST PROCESSING TIME (ON EITHER MACHINE).

2. IF THE SMALLEST PROCESSING TIME INVOLVES:

• MACHINE 1, SCHEDULE THE JOB AT THE BEGINNING OF THE SCHEDULE.

• MACHINE 2, SCHEDULE THE JOB TOWARD THE END OF THE SCHEDULE.

3. IF THERE IS SOME UNSCHEDULED JOB, GO TO 1. OTHERWISE STOP.

Chapter4 50

EXAMPLEEXAMPLE

CONSIDER THE FOLLOWING INSTANCE OF THE JOHNSON’S (Fm||Cmax) PROBLEM:

JOB 1 2 3 4 5 p1j 4 4 10 6 2 p2j 5 1 4 10 3

SEQUENCE:

Chapter4 51

EXAMPLE: SCHEDULEEXAMPLE: SCHEDULE SEQUENCE:5 1 4 3 2

JOB 1 2 3 4 5 p1j 4 4 10 6 2 p2j 5 1 4 10 3

t

M1

M2

Chapter4 52

A BOUND ON THE MAKESPANA BOUND ON THE MAKESPAN

FOR JOHNSON’S PROBLEM:

⎪⎭

⎪⎬⎫

⎪⎩

⎪⎨⎧

⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛+

⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛+≥ ∑∑

====

n

1jj2j1

n,..,1j

n

1jj1j2

n,..,1jmax ppmin,ppminmax)OPT(C

Chapter4 53

JOHNSONJOHNSON’’S ALGORITHMS ALGORITHM

LET U = {1, 2,..., n} BE THE SET OF UNSCHEDULED JOBS.k =1,l = n,Ji = 0, i = 1, 2, ..., n.STEP 1: IDENTIFICATION OF SMALLEST PROCESSING TIME

IF U = ∅, GO TO STEP 4.

LET

⎭⎬⎫

⎩⎨⎧

===

j2n,..,1j

,j1n,..,1j

*j*i pminpminminp

IF i* = 1 GO TO STEP 2; OTHERWISE GO TO STEP 3.

Chapter4 54

JOHNSONJOHNSON’’S ALGORITHMS ALGORITHM(CONTINUED)(CONTINUED)

STEP 2: SCHEDULING A JOB ON EARLIEST POSITION

• SCHEDULE JOB j* IN THE EARLIEST AVAILABLE POSITION: Jk = j*.

• UPDATE k: k = k + 1.• REMOVE THE JOB FROM THE SCHEDULABLE SET, U = U – {j*}.• GO TO STEP 1.

STEP 3: SCHEDULING A JOB ON LATEST POSITION

• SCHEDULE JOB j* IN THE EARLIEST AVAILABLE POSITION: Jl = j*.

• UPDATE l: l = l - 1.• REMOVE THE JOB FROM THE SCHEDULABLE SET, U = U – {j*}.• GO TO STEP 1.

Chapter4 55

JOHNSONJOHNSON’’S ALGORITHMS ALGORITHM(CONTINUED)(CONTINUED)

STEP 4: SEQUENCE OF JOBS

THE SEQUENCE OF JOBS IS GIVEN BY Ji, WITH J1 THE FIRST JOB, AND SO FORTH.

Chapter4 56

FFm||Cmaxm||Cmax

Fm||Cmax IS A STRONGLY NP-HARD PROBLEM.

AN EXTENSION OF JOHNSON’S ALGORITHM YIELDS AN OPTIMAL SOLUTION FOR THE F3||Cmax PROBLEM WHEN THE MIDDLE

MACHINE IS DOMINATED BY EITHER THE FIRST OR THIRD MACHINE.

Chapter4 57

MACHINE DOMINANCE: F3MACHINE DOMINANCE: F3||Cmax||Cmax

A MACHINE IS DOMINATED WHEN ITS LARGEST PROCESSING TIME IS NO LARGER THAN THE SMALLEST

PROCESSING TIME ON ANOTHER MACHINE.

FOR F3||Cmax PROBLEM:

⎭⎬⎫

⎩⎨⎧

≤ j3j1j

j2 pmin,pminmaxp

WHICH IMPLIES THAT MACHINE 2 (DOMINATED MACHINE) CAN NEVER CAUSE A DELAY IN THE SCHEDULE.

Chapter4 58

JOHNSONJOHNSON’’S ALGORITHM FOR 3 MACHINESS ALGORITHM FOR 3 MACHINES

FOR F3||Cmax, WHENEVER MACHINE 2 IS DOMINATED, i.e.,

OR }p{max}p{min j2j

j1j

≥

SOLVING AN EQUIVALENT TWO-MACHINE PROBLEM WITH PROCESSING TIMES:

p’1j = p1j + p2j AND p’2j = p2j + p3j

GIVES THE OPTIMAL MAKESPAN SEQUENCE TO THE DOMINATED THREE-MACHINE PROBLEM.

}p{max}p{min j2j

j3j

≥

Chapter4 59

EXAMPLE: F3EXAMPLE: F3||Cmax||Cmax

CONSIDER F3||ΣCmax WITH THE FOLLOWING JOBS:

JOB 1 2 3 4 5 p1j 4 9 8 6 5 p2j 5 6 2 3 4 p3j 8 10 6 7 11

=}p{min j1j

=}p{max j2j

=}p{min j3j

Chapter4 60

EXAMPLE: PROCESSING TIMES, DUMMY EXAMPLE: PROCESSING TIMES, DUMMY MACHINESMACHINES

JOB 1 2 3 4 5 p1j 4 9 8 6 5 p2j 5 6 2 3 4 p3j 8 10 6 7 11 p'1j p'2j

SEQUENCE:

Chapter4 61

EXAMPLE: SCHEDULEEXAMPLE: SCHEDULESEQUENCE:

1 4 5 2 3

JOB 1 2 3 4 5 p1j 4 9 8 6 5 p2j 5 6 2 3 4 p3j 8 10 6 7 11

t

M1

M2

M3

Chapter4 62

Illustration for Johnson's ruleIllustration for Johnson's ruleEstimated processing time (Hours)

JobJob Work Center WC1

Work CenterWC2

22 112.252.252.52.53344

3.53.5

440.751.51.522

22

AABBCCDDEE

FF


Chapter4 63

Illustration for Johnson's ruleIllustration for Johnson's ruleApplying Johnson's rule Job C has the shortest

processing time in either work center (I.e.75hour), assign job C as as the first job in the sequence.

Next Job A has Shortest time (I.e 1 Hr) assign Job A as last job in sequence and cross out time for Job

The Next smallest time is 1.5 hours for job D on WC1

The next smallest time is 2 hr for job E and F on WC1,Since there is tie in between jobs E,F choose the job with smaller subscript I.e job E


Chapter4 64

Illustration for Johnson's ruleIllustration for Johnson's rule

Assign the job E as the next job after job D from beginning of the sequence.

The next Job after job E is job F The last job B has to be accommodated in the gap between job F and the last job in the sequence i.e Job A

Hence the sequence is C,D,E,F,B,A


Chapter4 65

Batch SchedulingBatch SchedulingBatch production falls between job shop

production and continuous.

In batch production system, the output is can be stored as inventory for further processing or as finished products and can be produced in substantial volume, even-though the volume may not justify continuous production.

In these situations, it is necessary to determine the lot-size for a batch to be produced at one time in addition to scheduling the batch on the facilities.


Chapter4 66

Batch SchedulingBatch SchedulingExamples of such production are production of

pharmaceutical products, paints etc., Decision to be taken by Operations manager are

(i)the lot size; and (ii)The scheduling decision regarding when to begin the processing of the batch.

A key-off in the determination of the lot size for an item is between set-up costs and inventory carrying costs.

Another important consideration is the requirement to produce a feasible schedule that meets the demand for all items.


Chapter4 67

Batch SchedulingBatch SchedulingFor example, if set-up costs are low as

compared to inventory carrying costs, it may be advantageous to go for small lot sizes

But it may not be possible to produce the required quantities of all items within the specified time period if these small lot sizes are employed. This will happen if much of the time is consumed for machine set-ups thereby reducing the available production time. To overcome this problem, larger lot sizes may have to be employed which will result in higher inventory carrying costs.


Chapter4 68

Batch SchedulingBatch Scheduling

Hence, it is necessary to compute economic lot sizes while maintaining feasibility in scheduling batches of such lot sizes for the items to be produced.

Two types of costs associated with lot manufacture are:

(a)Set up costs i.e. costs/unit which decrease with batch size.(b)Inventory carrying cost which increases with batch size.


Chapter4 69


Set up cost includes:

(i)Cost of releasing work orders, shop orders, stores requisitions, tool requisitions etc.

(ii)Cost of first off inspection, cost of rejections till machine set up is ready for production run.

(iii)Machine set-up cost for mounting accessories, tools, jigs and fixtures on the machine.


Chapter4 70


Inventory carrying costs include:

(i)Cost of working capital tied up in average inventory.

(ii)Cost of handling and storing materials (i.e. parts produced)

(iii)Insurance charges and taxes.

(iv)Cost of spoilage and obsolescence etc.


Chapter4 71

Batch SchedulingBatch SchedulingInstantaneous Supply with no simultaneous consumption

Let A= Annual demand for an ItemS= Set up cost per setupI =Inventory Carrying costC=Cost per unit of item producedQ=Economical batch Quantity

The Solution:No of batches per year =A/QSetup cost per year =A/Q* SAverage inventory held=Q/2

Case1


Chapter4 72


Inventory carrying cost per year=Q/2*C*ITotal Cost per year =Set up cost per year + inventory carrying cost per year.

T.C=A/Q*S+Q/2CIFor minimizing the total cost

d T.C = -(AS/Q*Q)+(CI/2)dQ

For T.C to be minimum d T.C =0dQ

Or –AS/Q8Q+CI/2=0Or CI/2=AS/Q*Q, Hence Q=

٧2AS2ASCICI


Chapter4 73


Maximum Inventory

Average Inventory

TimeTime

Qua

ntity

ER

Q

Q


Chapter4 74

Batch SchedulingBatch SchedulingInstantaneous Supply with simultaneous consumption

Let A= Annual demand for an ItemS= Set up cost per setupI =Inventory Carrying costC=Cost per unit of item producedQ1=Economical batch Quantityd=demand or consumption ratep=Production rate

The Solution:No of Set ups per year =A/Q1Setup cost per year =A/Q1* SAverage inventory held = Maximum inventory/2

Case 2Case 2


Chapter4 75

Batch SchedulingBatch SchedulingInstantaneous Supply with simultaneous consumptionCase 2Case 2

To calculate the inventory built up let us assume that production period is t1( weeks )and consumption only period is t2 (say weeks)

Quantity produced in time t1=Q1(at the rate of “p”per week)

Q1=p*t or t1=Q1/p

Consumption during period t1=dt1

(at the rate of “d”per week)=d*Q1/p or =Q1*d/p


Chapter4 76


(Maximum inventory built up =Qty produced-Qty Consumed

During period t1)

=Q1-Q1*d/P =Q1(1-d/P)

Average inventory = Q1/2(1-d/P)

Inventory carrying cost per year= Q1/2(1-d/P)*CI

Total cost per year = Set cost per year+Inventory carrying cost per year

Tc=A/q1*s+Q1/2(1-d/P)*CI


Chapter4 77


For the total cost Tc to be minimum dTc

dQ1

I.e –A.S/Q1*Q1+ (1-d/P)*CI

Q1=

= 0

2222= 0= 0

Solving for Q1Solving for Q1

2As2As

CI(1CI(1--d/p)d/p)


Chapter4 78

Batch SchedulingBatch SchedulingInstantaneous Supply with simultaneous consumption

Maximum Inventory

Average Inventory

TimeTime

Qua

ntity

ER

Q

Q

Production period (t1)Production period (t1) Consumption only Consumption only period (t2)period (t2)


Chapter4 79

Run out or Run out time methodRun out or Run out time methodThis method attempts to use the total production

capacity available in each time period to produce just enough of each product variety so that if production is stopped ,the finished goods inventory for each product would be depleted or would run out at the same point of time.

The run out time is expressed as the ratio of the current inventory to demand forecast for the period.

Run out Time = Current inventory of Item XDemand per period for item X


Chapter4 80

AggregateAggregate Run out or Run out time methodRun out or Run out time method

In case of above , run out time method,it is observed that ,there is shortage of required capacity .If it is necessary to produce all items required for a product ,shortage of any single item should not occur In such case s the aggregate run out method is used.

(Machine hours inventory +(Total Available for all items) Machine hours)

AROT =Machine Hours requirements forecasted for all the itemsMachine Hours requirements forecasted for all the items


Chapter4 81

Scheduling & Controlling Production For Scheduling & Controlling Production For Delivery Schedules Delivery Schedules -- Line of Balance methodLine of Balance method

Line of balance technique has been used in Line of balance technique has been used in production scheduling and control to determine ,at a production scheduling and control to determine ,at a view date,not only how many( quantity )of item view date,not only how many( quantity )of item should have been completed by that date,but also how should have been completed by that date,but also how many should have passed through previous operation many should have passed through previous operation stages by that time so as to ensure the completion of stages by that time so as to ensure the completion of the required delivery schedule.the required delivery schedule.

LOB is a charting and computational technique for LOB is a charting and computational technique for monitoring and controlling products and services that monitoring and controlling products and services that are made to meet specific delivery scheduleare made to meet specific delivery schedule


Chapter4 82

Line of Balance method Line of Balance method --ExampleExample

XYZ company has received orders to deliver a a XYZ company has received orders to deliver a a product for which the operations program and product for which the operations program and delivery schedule s are given belowdelivery schedule s are given below

Week NoWeek No Qty of end product to be deliveredQty of end product to be delivered

1122334455

551010101010101515


Chapter4 83

Line of Balance method Line of Balance method --ExampleExample

Purchased part Fabrication

Assembly Delivery of End product

Develop a LOB chart & determine the Quantities that Develop a LOB chart & determine the Quantities that should have passed through the upstream processing steps should have passed through the upstream processing steps during the review point at the end of 2during the review point at the end of 2ndnd week week

1010 8899 77 66 22 1155 44 33

1 22 33

4455Item AItem A

Item BItem B


Chapter4 84

Line of Balance method SolutionLine of Balance method Solution

Method: the five steps required to be followed in LOB Method: the five steps required to be followed in LOB techniques:techniques:

Preparation of operation program or assembly chartPreparation of operation program or assembly chartPreparation of Cumulative completion/delivery Preparation of Cumulative completion/delivery

schedulescheduleConstruction of LOB chartConstruction of LOB chartConstruction of program progressConstruction of program progress

Analysis of progress and corrective actionAnalysis of progress and corrective action


Chapter4 85

Line of Balance method Line of Balance method --SolutionSolution

Purchased part Fabrication

Assembly Delivery of End product

1010 8899 77 66 22 1155 44 33

1 22 33

4455Item AItem A

Item BItem B

Preparation of operation program or assembly chartPreparation of operation program or assembly chartThe operation program shows the The operation program shows the ““lead timelead time””for each for each

operation.The lead time is shown as length of time prior to operation.The lead time is shown as length of time prior to completion of final Completion operation.completion of final Completion operation.

Time DaysTime Days


Chapter4 86


Preparation of operation program or assembly chartPreparation of operation program or assembly chartThe delivery date for the finished product (end The delivery date for the finished product (end

item) is zero & the time scale indicating item) is zero & the time scale indicating ““lead lead timetime””runs from left to right.runs from left to right.

The operation program indicates that Purchased part The operation program indicates that Purchased part A must be combined with B in operation stage 4 three A must be combined with B in operation stage 4 three days before completion of end item.days before completion of end item.

Item B ,prior to combination has undergone a Item B ,prior to combination has undergone a conversion operation which has to be completed five conversion operation which has to be completed five days before the completion of end item,The purchased days before the completion of end item,The purchased part for item B must be available ten days prior to part for item B must be available ten days prior to delivery date for end item which means longest lead delivery date for end item which means longest lead time is ten daystime is ten days


Chapter4 87


Stage 2 : Preparation of Cumulative completion Stage 2 : Preparation of Cumulative completion /delivery schedule/delivery scheduleThe quantities of end item to be completed week by The quantities of end item to be completed week by week and cumulatively indicated in table as shown week and cumulatively indicated in table as shown belowbelow

Week NoWeek No Qty of end item to be completed Nos.

Cumulative Qty to be completed Nos.

551010101010101515

551515252535355050

1122334455


Chapter4 88


Stage 3 : Construction of line of balance chartStage 3 : Construction of line of balance chartThe line of balance shows the quantity of item The line of balance shows the quantity of item

that should have completed at each operation that should have completed at each operation stage in a particular week at which progress will stage in a particular week at which progress will be reviewed.be reviewed.So as to meet the delivery scheduleSo as to meet the delivery schedule

The line of balance chart can be constructed as The line of balance chart can be constructed as shown in next slideshown in next slide


Chapter4 89


11 3322 44 55

55

1010

1515

2020

2525

303035354040

45455050

11 22 33 44 55

Line of BalanceLine of Balance

35 Nos. 35 Nos.

25 Nos. 25 Nos.

21 Nos. 21 Nos. 5 Nos. 5 Nos.


Chapter4 90


Stage 4 : Construction of progress chartStage 4 : Construction of progress chartThe progress chart for review week is shown The progress chart for review week is shown

below.below.

11 3322 44 55

55

1010

1515

2020

2525

303035354040

45455050

35 Nos. 35 Nos.

15 Nos. 15 Nos. 21 Nos. 21 Nos.

Excess productionExcess production

Shortage productionShortage production

Exact productionExact production



Chapter4 91


Stage 5 : Analysis of progress & corrective action Stage 5 : Analysis of progress & corrective action delivery scheduledelivery schedule

By referring to programme process chart which is By referring to programme process chart which is prepared every week the difference between the prepared every week the difference between the desired production (as indicated by line of desired production (as indicated by line of balance)for the review week can be compared with balance)for the review week can be compared with the actual production achieved at the end of the the actual production achieved at the end of the review week.review week.

The excess production or shortage production can The excess production or shortage production can be found out & appropriate actions taken to bring be found out & appropriate actions taken to bring production in lineproduction in line


Chapter4 92

Line of Balancing Methods Line of Balancing Methods

The various Line balancing methods are:The various Line balancing methods are:Heuristic methodHeuristic methodLinear programmingLinear programmingDynamic programmingDynamic programmingComputer based sampling techniqueComputer based sampling technique

A heuristic is a method for helping in solving of a problem, commonly informal. It is particularly used for a method that often rapidly leads to a solution that is usually reasonably close to the best possible answer. Heuristics are "rules of thumb, educated guesses, intuitive judgments or simply common sense. In more precise terms, heuristics stand for strategies using readily accessible though loosely applicable information to control problem-solving in human beings and machine

http://en.wikipedia.org/wiki/Rules_of_thumb




Chapter4 93


Heuristic method (Illustration)Heuristic method (Illustration)The table below shows the number of work stations (N),Cycle time( C) & daily production for a product

No of Workstations N

Cycle TimeCycle TimeC SecC Sec

Daily production(8 Hrs shift)

1206040302420

24048072096012001440

112233445566


Chapter4 94

Line of Balancing Methods Line of Balancing Methods Heuristic method (Illustration)Heuristic method (Illustration)

It is desired to have two assembly lines each producing 720 units per day,the cycle time will be 40 seconds & there will be 3 work stations in each assembly line

The precedence diagram is shown in next slide.The activity time in seconds are given in bracket

for each of twenty operations involvedAssuming that activities may be combined within

given zone ,without violating the precedence relationship ,assign the activities into three workstations.This can be done by trial & error basis by adding activity time


Chapter4 95


1

7

6

5

4

3

2

10

18

12

11

19

9

813 16 20

14 17

15

55 3388

55

22

12121010

2233 1313

77

1414 4444

6677

55

66

55

99


Chapter4 96

Line of Balancing Methods Line of Balancing Methods Heuristic method (Illustration)Heuristic method (Illustration)

Activities Total time Sec

1,7,2,8,9,111,7,2,8,9,11

4,5,10,12,13,34,5,10,12,13,3

14,15,16,17,18,14,15,16,17,18,19,2019,20

5+5+2+14+5+7+2=40

3+8+12+7+4+6=40

6+3+4+9+10+3+5=40

Work station 1Work station 1



A perfect balance is obtained since all work stations have A perfect balance is obtained since all work stations have exact the same workload of 40 sec.exact the same workload of 40 sec.


Chapter4 97

Scheduling ServicesScheduling ServicesServices are those economic activities in which the primary product is nether a product nor a construction.Some of the examples of services are

TransportationUtilitiesCommunicationWholesale tradeRetail tradeReal estateHotel & restaurantHospital services


Chapter4 98

Scheduling ServicesScheduling Services

Four approaches that are usually used areFour approaches that are usually used areUse of waiting linesUse of waiting linesUse of appointment schedulesUse of appointment schedulesPersonal schedulesPersonal schedulesEmergency servicesEmergency services


Chapter4 99

Shop Floor Planning Shop Floor Planning & Control& Control

End Of

Chapter 4

“Like” us on Facebook: http://www.facebook.com/welearnindia p // /

“Follow” us on Twitter:http://twitter com/WeLearnIndiahttp://twitter.com/WeLearnIndia

Watch informative videos on Youtube: http://www.youtube.com/WelingkarDLP

shop floor planning & control

Education