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In this presentation, we will discuss shop floor planning and operation pipeline, objectives of production activity, operations planning various stages of scheduling, Gantt chart preparation, its importance, Johnson’s rule of algorithm, flow shop, batch scheduling. We will also talk about scheduling and controlling production for delivery schedules – line of balance method. To know more about Welingkar School’s Distance Learning Program and courses offered, visit: http://www.welingkaronline.org/distance-learning/online-mba.html
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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
Shop Floor Planning Shop Floor Planning & Control & Control
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
Shop Floor Planning Shop Floor Planning & Control & Control
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
Shop Floor Planning Shop Floor Planning & Control & Control
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
Operations Planning Operations Planning & Scheduling& Scheduling
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,
Chapter4 11
Operations Planning Operations Planning & Scheduling& Scheduling
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
Operations Planning Operations Planning & Scheduling& Scheduling
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
Operations Planning Operations Planning & Scheduling& Scheduling
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
Operations Planning Operations Planning & Scheduling& Scheduling
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
Operations Planning Operations Planning & Scheduling& Scheduling
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
Operations Planning Operations Planning & Scheduling& Scheduling
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
Operations Planning Operations Planning & Scheduling& Scheduling
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
Operations Planning Operations Planning & Scheduling& Scheduling
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
Stages in SchedulingStages in Scheduling
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
Stages in SchedulingStages in Scheduling
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
Operations Planning Operations Planning & Scheduling& Scheduling
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.
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.
Chapter4 26
Gantt ChartGantt Chart
Gantt ChartGantt Chart
Chapter4 27
Gantt ChartGantt Chart
Gantt ChartGantt Chart
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
Illustration for Sequencing(Rules)Illustration for Sequencing(Rules)
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
Illustration for Sequencing(Rules)Illustration for Sequencing(Rules)
JobJob Processing Processing Time(Days)Time(Days)
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
JobJob Processing Processing Time(Days)Time(Days)
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
Dynamic Sequencing Dynamic Sequencing Rules Illustration Rules Illustration
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
Dynamic Sequencing Dynamic Sequencing Rules Illustration Rules Illustration
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
Batch SchedulingBatch Scheduling
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
Batch SchedulingBatch Scheduling
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
Batch SchedulingBatch SchedulingInstantaneous Supply with no simultaneous consumption
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
Batch SchedulingBatch SchedulingInstantaneous Supply with no simultaneous consumption
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
Batch SchedulingBatch SchedulingInstantaneous Supply with simultaneous consumptionCase 2Case 2
(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
Batch SchedulingBatch SchedulingInstantaneous Supply with simultaneous consumptionCase 2Case 2
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
Line of Balance method SolutionLine of Balance method Solution
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
Line of Balance method SolutionLine of Balance method Solution
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
Line of Balance method SolutionLine of Balance method Solution
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
Line of Balance method SolutionLine of Balance method Solution
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
Line of Balance method SolutionLine of Balance method Solution
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
Line of Balance method SolutionLine of Balance method Solution
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
Chapter4 93
Line of Balancing Methods Line of Balancing Methods
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
Line of Balancing Methods Line of Balancing Methods
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
Work station 2Work station 2
Work station 3Work station 3
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
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