Customer Service in Pull Production Systems Mark L. SPEARMAN Presented By: Ahu SOYLU

Customer Service in Pull Customer Service in Pull Production SystemsProduction Systems

Mark L. SPEARMANMark L. SPEARMAN

Presented By: Ahu SOYLUPresented By: Ahu SOYLU

OutlineOutline

The Comparison of Pull & Push SystemsThe Comparison of Pull & Push Systems

Overview of Pull SystemsOverview of Pull Systems

Customer Service in Pull SystemsCustomer Service in Pull Systems

Customer Service in CONWIPCustomer Service in CONWIP

Comparison of Pull Systems with Comparison of Pull Systems with CONWIPCONWIP

ConclusionConclusion

The Success of Pull SystemsThe Success of Pull Systems

The success of Japanese manufacturing The success of Japanese manufacturing systems has attracted attentionsystems has attracted attention

The system is a set of techniques known The system is a set of techniques known as Just-In-Time (JIT)as Just-In-Time (JIT)

An integral feature of JIT is the use of pull An integral feature of JIT is the use of pull shop floor control systemsshop floor control systems

There are still a number of issues that There are still a number of issues that require study; such as require study; such as customer servicecustomer service..

Push vs. PullPush vs. Pull

In a push system customer service is In a push system customer service is measured with well known methods like measured with well known methods like the fraction of jobs on-time and the the fraction of jobs on-time and the average tardiness.average tardiness.A job is on-time if the time to complete a A job is on-time if the time to complete a job is less than or equal to its lead time.job is less than or equal to its lead time.TardinessTardiness is the positive difference is the positive difference between the completion time and the due between the completion time and the due date of a job (date of a job (TTjj=max{C=max{Cjj-d-djj,0}).,0}).


In a pull system, each process is both a In a pull system, each process is both a supermarket for downstream processes and a supermarket for downstream processes and a customer to preceding processes.customer to preceding processes.A supermarket is a place where a customer A supermarket is a place where a customer can getcan get

1.1. What’s neededWhat’s needed2.2. At the time neededAt the time needed3.3. In the amount neededIn the amount needed

Service measures are the probability of Service measures are the probability of stockout, the expected time to fill demand, the stockout, the expected time to fill demand, the expected backlog of orders. expected backlog of orders.


MRP and Master MRP and Master Production Schedule Production Schedule are used to control are used to control productionproductionInput/Output control Input/Output control provides capacity provides capacity checkcheckControls throughput Controls throughput and measures WIPand measures WIP

““The day is not done The day is not done until every job has until every job has been completed”been completed”The due date of a The due date of a new job is established new job is established by considering the by considering the current production current production quota and the current quota and the current backlog of jobsbacklog of jobsControls WIP and Controls WIP and measures throughputmeasures throughput


A system employs A system employs pushpush if it schedules the if it schedules the release of work a priori.release of work a priori.

A A pullpull system authorizes the release of system authorizes the release of work based on current plant conditionswork based on current plant conditions

A A hybridhybrid system involves aspects of both. system involves aspects of both.

Two-card Kanban SystemTwo-card Kanban System

Benefits of Pull SystemBenefits of Pull System

All workers can immediately see what work All workers can immediately see what work needs to be doneneeds to be done

Excessive WIP is not pushed to the system Excessive WIP is not pushed to the system whenever the system capacity is overestimatedwhenever the system capacity is overestimated

It is easier to control WIP than outputIt is easier to control WIP than output

When the system works well, there is no need to When the system works well, there is no need to schedule productionschedule production

Adapting the production environment to Adapting the production environment to improvements is easier improvements is easier

Kanban is not for everybodyKanban is not for everybody

The conditions necessary for Kanban to The conditions necessary for Kanban to work well are:work well are: ““Smooth” production involving a stable Smooth” production involving a stable

product mixproduct mix Short setupsShort setups Proper machine layoutProper machine layout Standardization of jobsStandardization of jobs Improvement activitiesImprovement activities Autonomation (autonomous defect control)Autonomation (autonomous defect control)

Modeling a Pull SystemModeling a Pull System

A simplified -one card- version of the A simplified -one card- version of the Kanban system is examinedKanban system is examined

AssumptionsAssumptions The cards move instantly so that when a The cards move instantly so that when a

demand arrives to an idle system, production demand arrives to an idle system, production will start at each station immediatelywill start at each station immediately

Last station has always partsLast station has always parts The standard containers are small and The standard containers are small and

multiples of the container sizemultiples of the container size


The service measure will be the expected The service measure will be the expected time required to fill the demand.time required to fill the demand.The probability of stockout is not sufficient The probability of stockout is not sufficient in terms of being a service measure in terms of being a service measure because in a pull system, the longer the because in a pull system, the longer the stockout occurs, the more likely to result in stockout occurs, the more likely to result in disruption of downstream processes.disruption of downstream processes.N single server stations in series N single server stations in series producing a single product.producing a single product.


SSii~F~Fii: The service times for station i : The service times for station i

{S{Sijij}: set of service times}: set of service times

DDjj: Times that demands in the form of kanbans : Times that demands in the form of kanbans

from an external source are receivedfrom an external source are received

Demands are not iidDemands are not iid

T(i,j): The time the jth container is sent from T(i,j): The time the jth container is sent from station Istation I

mmii: number of kanbans attached to the standard : number of kanbans attached to the standard

containers residing in the stockpoint of station icontainers residing in the stockpoint of station i


These equations represent the relations These equations represent the relations between the completion times, service between the completion times, service times and the demands in the kanban times and the demands in the kanban system.system.

j 0 0j

i-1,j i ij,

T(0, j) = max{D ,T(1, j -m ),T(0, j -1)} +S

j =1,2,...

T(i, j) = max{T(i -1, j) -S ,T(i+1, j -m ),T(i, j -1)} +S

j =1,2,...; i =1,2,...,N

Measures of Customer ServiceMeasures of Customer Service

The time to satisfy the jth demand The time to satisfy the jth demand

The expected time to satisfy demand after The expected time to satisfy demand after the nth demandthe nth demand

Average time to satisfy demandAverage time to satisfy demand

τ +j 0 j= [T(1, j -m ) -D ]

jE[ ]n

nj=1

1U =

n

nn

U lim U

Some ResultsSome Results

T(i,j) is nonincreasing in mT(i,j) is nonincreasing in mii

T(i,j) is increasing convex in ST(i,j) is increasing convex in S ikik, k=1,2,…,j, k=1,2,…,j

ττjj is increasing convex in is increasing convex in SSijij

Stochastic Ordering in Kanban Stochastic Ordering in Kanban SystemsSystems

Consider two kanban systems Consider two kanban systems

k=1,2. Then Sk=1,2. Then Sii(1)(1)≤≤stst SSii

(2)(2) implies implies UU(1)(1)≤ ≤ UU(2)(2)

Consider two systems having processing times Consider two systems having processing times SSijij

(k)(k)==θθii(k) (k) ++ ξξjj, k=1,2; i=1,…,N; j=1,2,…, where, k=1,2; i=1,…,N; j=1,2,…, where θθii

(k)(k)

is a constant and is a constant and ξξjj are iid random variables with are iid random variables with

zero mean. Then zero mean. Then θθ(1)(1) ≤ ≤ θθ(2) (2) implies implies UU(1)(1)≤ ≤ UU(2)(2)

For systems with processing times whose For systems with processing times whose means represent a location parameter, faster means represent a location parameter, faster processing times imply a better service.processing times imply a better service.

�� (k)K(S ,m)

Stochastic Ordering in Kanban Stochastic Ordering in Kanban SystemsSystems

These results deal with variability reduction.These results deal with variability reduction.

Consider two kanban systems Consider two kanban systems

j=1,2. If Sj=1,2. If Sii(1)(1)≥≥icxicx SSii

(2)(2) , i=1,2,…,N implies , i=1,2,…,N implies

TT(1) (1) (0,j)≥(0,j)≥icxicx T T(2)(2)(0,j), j=1,2,… and (0,j), j=1,2,… and UU(1)(1)≥≥icxicx UU(2)(2)

If SIf Sijij(1)(1)~F and S~F and Sijij

(2)(2)~G where F and G have the ~G where F and G have the

same mean and where F crosses G at most same mean and where F crosses G at most once and from below, then Uonce and from below, then U(1)(1)≤ ≤ UU(2)(2)

If SIf Sijij(k) (k) ,k=1,2 ~N(,k=1,2 ~N((k)(k),,(k)(k)) and ) and (1) (1) << (2)(2)

then Uthen U(1)(1)≤ ≤ UU(2)(2)

�� (j)K(S ,m)

The Effect of Increasing Inventory The Effect of Increasing Inventory LevelsLevels

Consider two kanban systems, Consider two kanban systems,

j=1,2. Then mj=1,2. Then mii(1)(1)≥ m≥ mii

(2)(2); i=1,…,N implies ; i=1,…,N implies UU(1)(1)≤ ≤ UU(2)(2)

Tradeoff of inventory vs. serviceTradeoff of inventory vs. serviceAlthough extra inventory improves service, Although extra inventory improves service, it also reduces flexibilityit also reduces flexibilityAlso, inventory hides major sources of Also, inventory hides major sources of variability and allows us to live with variability and allows us to live with problems that could be eliminated.problems that could be eliminated.

�� (j)K(S ,m)

The Effect of Increasing Inventory The Effect of Increasing Inventory LevelsLevels

In a make-to-order push system with fixed In a make-to-order push system with fixed lead time and constant throughput rate lead time and constant throughput rate increasing WIP levels will degrade increasing WIP levels will degrade customer service.customer service.

Little’s Law:Little’s Law:Average WIP

Average Flow Time =Throughput

CONWIPCONWIP

Controlling WIP is more robust than controlling Controlling WIP is more robust than controlling throughputthroughputThe fact that WIP is bounded is more important The fact that WIP is bounded is more important than the practice of “pulling” everywherethan the practice of “pulling” everywhereCONWIP maintains a constant amount of WIP CONWIP maintains a constant amount of WIP on each production line and does not pull at on each production line and does not pull at every station.every station.Line production quantities are measured in Line production quantities are measured in terms of standard parts. terms of standard parts. CONWIP can be used when significant setup CONWIP can be used when significant setup times existtimes exist

CONWIPCONWIP

While the pull in kanban occurs between stations While the pull in kanban occurs between stations and is to replenish and is to replenish the particular part that has the particular part that has just been usedjust been used, the pull in CONWIP is over the , the pull in CONWIP is over the entire line and for entire line and for the parts having the same the parts having the same routingrouting..CONWIP is similar to a CONWIP is similar to a closed queueing closed queueing networknetwork. The flow time and throughput rate tend . The flow time and throughput rate tend to be less variable than an equivalent open to be less variable than an equivalent open network with the same output.network with the same output.

Push-Pull-CONWIPPush-Pull-CONWIP

Modeling CONWIPModeling CONWIP

These equations represent the relations These equations represent the relations between the completion times, service between the completion times, service times and the demands in the kanban times and the demands in the kanban system.system.

j 0 0 j

i ij,

T(0, j) max{D ,T(1, j- m ),T(0, j -1)} S

j 1,2,...

T(i, j) max{T(i 1, j - m ),T(i, j 1)} S

j 1,2,...; i 1, 2,..., N

ResultsResults

T(i,j)- ST(i,j)- Sijij≥T(i-1,j) – S≥T(i-1,j) – Si-ji-j, for i=1,2,…,N; , for i=1,2,…,N; j=1,2,…j=1,2,…

��

��Consider a kanban system K(S,m) and a CONWIP

system C(S,m) such that the service times are on the

same probability space. Then T(i, j) T(i, j) , i = 0,1,2,...,N

j =1,2,...

Both systems having the same

service time distributions

at each station implies U U

DiscussionDiscussion

CONWIP behaves like a closed queueing CONWIP behaves like a closed queueing network, kanban looks like a closed queueing network, kanban looks like a closed queueing network with blocking.network with blocking.With the same card counts, CONWIP tends to With the same card counts, CONWIP tends to have higher WIPhave higher WIPCONWIP can dominate kanban in terms of both CONWIP can dominate kanban in terms of both service and average WIPservice and average WIPA simulation study is performed and it is seen A simulation study is performed and it is seen that CONWIP exhibited customer service that that CONWIP exhibited customer service that was statistically superior.was statistically superior.

DiscussionDiscussion

Both CONWIP and kanban limit WIP Both CONWIP and kanban limit WIP growth.growth.Implementation of CONWIP is simpler Implementation of CONWIP is simpler than kanban.than kanban.CONWIP lines can split into many CONWIP lines can split into many segments, then kanban is a subset of segments, then kanban is a subset of CONWIP.CONWIP.So, kanban cannot be superior to So, kanban cannot be superior to CONWIP.CONWIP.

ConclusionConclusion

Customer service in both kanban and Customer service in both kanban and CONWIP production systems is improved CONWIP production systems is improved by:by: Faster machinesFaster machines Extra WIPExtra WIP Less variable processing timesLess variable processing times

CONWIP systems have better customer CONWIP systems have better customer service than do pure kanban systems.service than do pure kanban systems.

Documents

Customer Service in Pull Production Systems Mark L. SPEARMAN Presented By: Ahu SOYLU