improving car body production at psa

8/6/2019 Improving Car Body Production at PSA

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Interfaces , 2003 INFORMSVol. 33, No. 1, JanuaryFebruary 2003, pp. 3649

0092-2102/03/3301/0036$05.001526-551X electronic ISSN

Improving Car Body Production at PSAPeugeot Citroen

Alain Patchong Thierry Lemoine Gilles KernPSA Peugeot Citroen, Route de Gisy, 78943 Velizy, France

[email protected] [email protected] [email protected]

In 1998, following a change in top management, the new CEO of PSA Peugeot Citroen decidedto adopt a triple-axis strategy of growth, innovation, and protability and set an ambitioustarget for each. To meet these objectives, PSA decided to focus on the car-body shops, whichwere the bottlenecks of its plants. An R&D team conducted a project to support car-bodyproduction for PSA Peugeot Citroen. PSA manufactures over 75 percent of its cars on linesdesigned and continually improved with the teams new analytic operations research tools.These OR tools, which combine simulation and Markov-chain models of series-parallel sys-tems, have improved throughput with minimal capital investment and no compromise inqualitycontributing US $130 million to the bottom line in 2001 alone. The impact of thisproject went beyond the boundaries of PSA as its suppliers acquired the tools without beingrequested to do so.( Industries: automotive. Production/scheduling: applications.)

The Body Shop, the Paint Shop, andthe Final Assembly ShopPSA Peugeot Citroen, established through a merger ofthe two prominent French carmakers Peugeot and Ci-troen in 1976, is the sixth-largest carmaker in the worldand the second-largest in Europe (PSA stands for Peu-geot Societe Anonyme). PSA is on a strong growth tra- jectory; it is, in fact, the fastest-growing car companyin the world. Production for 2004 is projected to be 3.5million cars, up from 3.1 million in 2001 and 2.3 millionin 1998. PSA will launch 25 new car models between2001 and 2004. The nancials are also very robust, withnet prots of $2.33 billion in 2001 on sales of $45.49 billion. PSAs sustained protability and growth arestrongly supported by its 16,000-person research anddevelopment organization.

A typical PSA car plant contains three shops (Figure1). The body shop has the most complex manufactur-ing ow and is located at the beginningof the assemblyprocess. Welders in the body shop assemble the rawmaterials, which are stamped parts, creating the bodyin white. After leaving the body shop, the body in

white goes to the paint shop. The last step is the nalassembly shop, where the painted body is merged withthe remaining parts to make a marketable product.

These parts range in importance from vital (for ex-ample, the engine system) to decorative (for example,the hubcaps). The car that leaves the nal assemblyshop is shipped to retailers.

PSA Strategy and Business NeedsIn 1998, following a change in top management, thenew CEO of PSA Peugeot Citroen decided to adopt atriple-axis strategy of growth, innovation, and prot-ability. His goals for these axes were (1) to produce 3.5million cars in 2004, (2) to introduce 25 new models between 2001 and 2004, and (3) to increase prots onsales in 2002 to ve percent, up from the target of 4.6percent in 2001.

PSA management decided to pursue these goalsthrough the so-called common-platform policy. Acommon-platform is a base used in several vehicles.Two vehicles based on the same platform share thesame subframe, engines and gearboxes, front and rear


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Figure 1: The body shop is at the upstream end of the work ow in a typical car plant.

suspension, and a number of other parts except styleand personality features. The goal of the common plat-form policy is to reach a 60 percent level of commonparts among all cars assembled on the same platform,regardless of their brandPeugeot or Citroen (Figure2). This policy, which would reduce investment by re-lying on a exible process at low cost, would affect themanufacturing system.

PSA encountered two problems in implementing itscommon-platform policy in car-body shops: (1) Itssingle-ow architecture, meant that every car modelwent through the same sequence of stations, limitingPSAs ability to handle diverse models. (2) Itsproduction-line design was based on intuition and tra-dition, with some ingrained beliefs and practices caus-ing inefciency. So, the process of redesigning the pro-duction line for new car models was lengthy anderratic. As a result, PSA suffered from painfully slowramp-ups and production shortfalls.

We needed a new architecture for the car-body pro-duction line that could handle model diversity andnew car launches easily and quickly and an accuratemethod of sustaining quick innovation withoutoverinvestment.

The Car-Body AssemblyThe term car body designates the naked steel shell ofthe car, including the openings (doors, hood, and trunkdoor). It does not include the engine system or deco-rative items. The assembly process begins in the off-ow area where workers preassemble raw materials(mainly stamped steel parts) using simple machinesand put them in containers. Carriers move these con-tainers to the assembly area and place them along theassembly lines. Robots load and weld the parts storedin containers on assembly lines. At the start, robotsweld preassembled parts on specic lines to form sep-arately the front and the rear parts of the understruc-ture, respectively called the front unit and the rear unit.

Then, robots weld the two parts together with an up-per part (called the upper front) to form the cars un-derstructure, which is welded to the bodys sides andthe roof to produce the car body less the openings. Thecar body less the openings goes to the nal assemblyline, where workers perform nal nishing operationsand add the opening parts, such as the exhaust, hood,and doors. The resulting car body then goes to thepaint shop.

The Original Car-Body ShopBefore we implemented the new assembly process, themain disadvantage of the car-body manufacturing sys-tem was that it consisted of only one ow (Figure 3).Because all products manufactured in the system hadthe same route, the shop operated under rigidconstraints:

To handle the diverse car models made at a plant,PSA needed a complex and rigorous control policy. Itresequenced models whenever the parts schedulechanged. When the control system was down, the shopceased operations, reducing its efciency. These prob-lems damaged PSAs growth and protability, two ofthe three axes of PSAs strategy.

PSA had to redesign and reconstruct all the pro-duction lines in a shop when it launched a new prod-uct because all its car models shared manufacturingsystems. This problem hindered innovation, the thirdaxis of PSAs strategy.

To improve the shops efciency, we decided to sim-plify and minimize the extent of PSAs plant controlpolicy. We redesigned the shops structure to makethem more agile in handling new products.

A New Standard for Shop StructureTo implement PSAs triple-axis strategy we needed totransform the manufacturing facilities to produce asmany different models as possible using common


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Figure 2: PSAs new strategy emphasizes using a common understructure for multiple car-body models,producedin the shop regardless of brand. The objective is to merge parts wherever possible without altering the identityor personality of the brands. For all the models, namely sedans, coupes, convertibles, estates, and peoplecarriers, each brand brings a distinctive personality.

parts. PSA decided to reorganize all 12 original Peu-geot and Citroen production sites by platform, regard-less of brand. It dedicated each plant to a single plat-formsmall, medium, or large. Together the plantscover all PSAs offerings.

To launch 25 new models in four years, PSA needed

plants that could be recongured quickly and easily(Figure 4). We developed a new standard shop archi-tecture to achieve this exibility by treating the twokinds of welding stations on the line differentlytheframe-welding stations and the nish-welding sta-tions. Frame welding is directly related to the geome-try of a car and, in a way, denes the cars shape. Theframing tools used for this type of welding are difcultto modify for a new model. Finish weldingstrengthensthe cars structure and, unlike frame welding, is easyto move or modify simply by reprogramming robottrajectories. Our rationale was to put as many framingstations as possible on specic lines and to put the n-ishing stations only on common lines (Figure 4). Bydoing so, we achieved two key objectives: (1) quickchange because we needed to build only specic ad-ditional lines, and we were able to do so without dis-rupting the production, and (2) greater model diver-sity, because the common lines robots just needed to

load the corresponding programs to work on differenttypes of parts.

After redesigning the production line, we alsoneeded tools the staff could use to accurately andquickly design the manufacturing systems for newcars.

Designing Manufacturing ShopsA well-designed shop produces cars the marketing de-partment requests. The costs include the money to build the shop and the money to run it. Designers ofmanufacturing systems must determinate (1) the pa-rameters that affect shop efciency: buffer sizes andlocations, assembly lines efciency, and cycle time;and (2) a control policy that allows the shop to deliverthe right products at the right time without degradingits efciency.

Solution ApproachTo realize its ambitious forecasts, PSA needed toolsR and D personnel could use to design shops accu-rately and quickly. The main tools we knew about forevaluating performance were simulation and analyticmethods (Dallery and Gershwin 1992) (Table 1).


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Figure 3: The car body is only the naked steel shell of the car, including openings. It does not include the enginesystem or decorative items. In the typical workow in the original PSA body shop, workers preassembled rawmaterials in the off-ow assembly area using simple machinesand routed the resulting part in containers (dashedline arrow) to the assembly area. There, robots assembled the rear unit, the front unit, and the upper front ofthe car separately on specic lines and sent them by conveyors (solid line arrow) to the understructure line,where other robots assembled them and sent the resulting part to the framing line, also by conveyors. On theframing line, robots assembled the understructure, the bodys sides, and the roof to produce the car body lessopenings, which went to the nal assembly line. Workers added openings. Then, the resulting car body went tothe paint shop.

Simulation is too time consuming to be completelysatisfactory. Analytic methods alone, however, couldnot be used to model some complex details or observedynamic effects accurately. Therefore, we opted for anapproach encompassing both simulation and analyticmethods. We developed an iterative three-step designmethod that takes advantage of the speed of analyticmethods and the accuracy of simulation. To insuresome exibility, we expressly chose not to automatethe implementation and the transition between thesteps. The design engineers manage those activities.

In step 1, initialization, we calculate the initialtarget values for the cycle time and efciency of allthe production lines based on the most recent valuesfor similar existing lines. We use analytic methods forthis step.

In step 2, macrosimulation, using analytic meth-

ods or simulation software (for complex lines), we es-timate the efciency of the production lines. We adjustthe cycle times and the efciency of production linesand modify their processes accordingly until we obtainestimates that are as close as possible to targets set instep 1.

In step 3, validation, we estimate production-lineperformance using simulation software. We plug theresult of step 2 into a detailed simulation model forvalidation. We can make slight modications, if nec-essary, to make the shops estimated production ratemeet the objective forecast.

SimulationAt PSA, we perform discrete-ow simulation using off-the-shelf commercial software called Arena. Depending


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Figure 4: In the new PSA body shop, we put as many framing stations as possible on specic lines (ModeledPlatform and Framing), while we put the nishing stations only on common lines (Understructure and Body). Bydoing so, we achieved two key objectives: (1) quick change, because we needed to build only additional speciclines and we were able to do so without disrupting the production, and (2) greater model diversity, becausecommon lines robots just needed to load the corresponding programs to work on different types of parts.

Advantage Weakness

Simulation Accurate modelingDynamic aspects

Time consumingSpecialist needed

Analytic methods Easy to useInstant results

No dynamic aspectLimited in modeling

Table 1: Simulation is time consuming and requires specialists, whileanalytic methods are quick and easy to use (not to develop) but cannothandle complex modeling.

on the complexity of the process, the simulation lastsfrom 400,000 to 800,000 time units. During the rst50,000 time units, we do not collect statistics. We usethis warm-up period to reduce the inuence of the ini-tial transient phase on the nal results.

To speed up the modeling process, we developedspecic modules for modeling the most common ele-ments or sets of elements encountered in our shops.

We constantly enriched this library of most-commonelements and keep it up to date. We also developedgeneric framework models for the most common ar-chitectures of assembly lines. Experienced engineersvalidated the simulation model. They studied thesimulations animations and numerical results in a va-riety of situations: purely random failures, no failures,failures on specic machines at specic times, andmul-tiple simultaneous failures, and they determined thatthe simulated systems response was realistic in everycase. After this work, people did not have to redevelopthe most common components every time they wereneeded, nor did they have to start from zero whenmodeling, whatever the assembly line. We thus re-duced the time spent in developing models and min-imized the risk of error. We calculate that modelingthat used to take three weeks now takes a single day,almost a 95 percent reduction in development time.

Uptimes and downtimes of the stations on the line


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are the random variables of our simulations. We usedexponential distributions after conducting researchthat showed they were very accurate. We found out

that adding another moment to the downtime distributions in our plants (as in, for example, the hyper-exponential distribution) would bring more complex-ity without really improving the accuracy of ourresults.

The results we provide in our simulation report arehourly production, average level of buffers, and shop ef-ciency. We also provide curves depicting the evolutionof the buffer level and production rate versus time.

The Analytic MethodsIn developing our general approach, we were guided by the principle that the end product had to be easyfor our technicians to learn and use. We took asystems-analysis approach of isolating each problem,nding a solution, and then choosing carefully be-tween developing a separate tool for the problem orintegrating the solution into a larger set of tools. When-ever possible, we sought to adapt existing technologyto meet our needs.

Because no commercial software was available foranalytic methods, we had to develop our own soft-ware. To do so, we needed to collect reliability data onthe most common machines (or elements), develop aneasy-to-use interface, and adapt or develop analyticequations for the body shop.

Series-Parallel Production LinesFigure 5 depicts a small body shops production linewith three stages. Because this line contains two sta-tions in parallel (stations 21 and 22), we called it aseries-parallel ow line. A series-parallel system issimilar to a classical ow line, the only difference beingthat a given stage (the second in our example) mayconsist of parallel machines. As we did not nd a sat-isfactory solution for a series-parallel line in theliterature, we had to develop a new technique(Patchong and Willaeys 2001).

A line can exhibit the following problematic featuresthat we had to deal with in our project:

Unlike the classical system generally described in

the literature, buffers can fail. We developed a methodto handle such failures.

In PSAs lines, human operators perform such

tasks as loading, welding, and drilling. The impact ofhuman operators was not addressed in the literature,so we developed a method to take it into account inour analytic models.

Functional stops for changing tools require opti-mal organization and human resources managementto reduce their effect on the lines efciency. We de-veloped a solution for this issue.

Various processes have different working times.We used the law of conservation of ow to solve thisissue.

Modeling and Analyzing Series-Parallel Production LinesWe developed a method for modeling and analyzingseries-parallel ow lines that amounts to replacingeach parallel-machine stage by a single equivalent ma-chine to obtain a classically-structured ow line withmachines in series. We dened the parameters of theequivalent machine to make its behavior in the linematch that of the actual set of parallel machines. Wedeveloped our model based on the Markov chain ofthe states of a machine in a production line (Appen-dix). After this transformation, we were able to useclassical analytic methods for long lines to solve theresulting production line. We used a variant of analyticmethods for long lines based on the work of Le Bihan(1998). Patchong and Willaeys (2001) give the details.

Unreliable BuffersStanley Gershwin (1987) developed an analyticmethod for long production lines. He used a decom-position technique to transform a problem with manymachines into a two-machine problem whose exact so-lution can be used as a close approximation to the

original lines solution. In our new technique for ac-commodating buffer unreliability, we replace the un-reliable buffer with a new machine coupled with a re-liable buffer. The new machines reliability matchesthat of the unreliable buffer it represents. With thisstructure, we can then combine Gershwins (1994) two-machine solution method with Buzacotts (1967) zero- buffer model to obtain an analytic solution (Figure 6).


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Figure 5: The series-parallel line comprises three stages separated by intermediate buffers. The rst and thesecond stages have one station each (station 10 and station 30), while the second stage has two stations inparallel (stations 21 and 22). The part arrives in the system on the station 10. When its operation is nished arobot moves the part to the downstream buffer where it has two possible ways to go. Depending on theiravailability, the part can go to station 21 or station 22, which perform the same operation. The part that leavesstation 21 or station 22 goes to the downstream buffer. A robot moves this part from the buffer to the station30. After the completion of the operation on station 30, the part goes out of the system.

Processes with Different Working

TimeIf shops, which operate in three shifts, are to producethe maximum number of parts, we must design theproduction lines of all the shops to work as long aspossible in a 24-hour day, while taking into accounttwo major constraints: (1) idle time for preventivemaintenance (three hours per day for areas with com-plex processes and two hours for the rest of the shop),and (2) worker breaks imposed by labor legislation(lines that need human operators to produce cease dur-ing breaks, but highly automated lines, because theyneed very few people to work, operate during breaks).As a consequence, a typical ow shop has three typesof ow sectors (Figure 7): (1) The upstream ow in-cludes complex processes (need for three-hour main-tenance) and human operators (one-hour break (three20 minutes breaks) for the three shifts) and produces20 hours a day. The upstream ow receives preassembled parts only. This sector comprises the lines for the

front unit, rear unit, front upper, and body sides (Fig-ure 4). (2) The main ow includes complex processes(need for three-hour maintenance) and is highly au-tomated (no need for human operators) and produces21 hours a day. The main ow receives the parts com-ing from the upstream ow. This sector comprises theplatform, modeled platform, understructure, framing,and body lines (Figure 4). (3) The other ow sectorincludes simple operations, namely preassembly ma-chines and the nal assembly line (need for two-hourmaintenance). This sector, which also uses many hu-man operators (one-hour break for the three shifts),produces 21 hours a day and comprises the nal as-sembly lines and off-ow preassembly (Figure 4).

The following examples illustrate the ideas used indesign and analysis when contiguous areas, say A1and A2, have different working times.

The cycle times of A1 and A2 and their areasshould be roughly proportional to their planned work-ing times.

If A1 respects worker breaks while A2 observes no


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Figure 6: The solution technique for unreliable buffers consists of replacing the unreliable buffer with an unre-liable machine coupled with a reliable buffer.

Figure 7: The upstream ow, which includes complex processes (three-hour maintenance needed) and humanoperators (3 shifts x 20-minute breaks), produces 20 hours a day. The upstream ow receives preassembledparts only. The main ow, which includes complex processes (three-hour maintenance needed) and is highlyautomated (no need for human operators), produces 21 hours a day. The main ow receives parts coming fromthe upstream ow. The other ow sector includes preassembly machines and the nal assembly line (two-hourmaintenance needed). This area, which also uses many human operators (3 shifts x 20-minute breaks), produces21 hours a day.

breaks, the intermediate buffer should have added toits capacity the amount that would be produced duringthe break, if the two areas worked synchronously.

Human FactorsExperience has shown that the more complex a ma-chine is, the less reliable it tends to be. It thereforeseems preferable to use a human operator instead ofan automated and complex machine to perform intri-cate tasks; hence, PSA uses manufacturing systemscomprising both automated and manual stations in its

plants. Patchong et al. (1997) proposed a cost-basedapproach that conrms use of such mixed systems. Al-though the literature abounds with papers on methodsfor analyzing manufacturing systems, few concernmixed manufacturing systems. We performed researchin this area on site at a manufacturing plant within PSAPeugeot-Citroen. Based on this work, we dened amachinelike reliability (determination of a mean timeto repair and a mean time to fail) for a human operator(documented in internal, unpublished reports).

Unlike the processing time of an automated station,which varies very slightly from part to part (Figure 8),


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Figure 8: A record of the processing time of an automated station, whichis represented on the x-axis here, shows that it varies very slightly frompart to part.

Figure 9: The xaxis represents the record of the processing time of amanual station. It shows that, unlike the processing time of an automatedstation, which varies very slightly from part to part (Figure 8), the pro-cessing time of a manual station is highly dispersed.

Figure 10: We denedovertime

for a manual station as the occurrenceduring a cycle of processing time greater than the expected processingtime. Using a variant of Figure 13 in the appendix, we dene for a humanoperator the same parameters as for machines based on an analogy,which consists of considering overtime as failure and, symmetrically, re-sumption as repairing. The operational state becomes a macro statemadeof two states: the overtime state and the normal working state , whichcorresponds to work without overtime. The probability rates of transitionbetween these two states are d and r .

the processing time of a manual station is highly dis-persed (Figure 9). We dened overtime for a manualstation as the occurrence during a cycle of processingtime greater than the expected processing time(Patchong 1997). We took overtime into account usinga variant of Figure 13 in the Appendix. We tried todene for a human operator the same parameters asfor machines so that we could use the human operatoras a machine in existing models or in models we weredeveloping. We did this by using an analogy, whichconsists of considering overtime as failure and, sym-metrically, resumption as repairing. The operationalstate becomes a macro state made of two states: theovertime stateand the normal working state, which cor-responds to work without overtime (Figure 10). Theprobability rates of transition between these two statesare d (average overtime rate)and r (average resumptionrateor average rate of return to the normal working state).In the normal working state, machines process withoutovertime or are idle (waiting for a part to process orevacuating a nished part). Given that we now consid-ered overtimes to be failures, we derived the threemain parameters for the human machine (averagefailure rate, average repair rate, and processing rate)and used them in the analytic methods we developed.The curve depicted in Figure 11 proved very valuable.

It predicts an operators efciency as a function of theextra time he has to perform a task.

We collected data to verify the model results empir-ically. It showed that the production rate of the modelyielded by our method was very close to the actualproduction rate (for example, a 0.7 percent error for amanufacturing system with no intermediate buffers).


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Figure 11: Based on the data collected in our manufacturing plants, wemodeled human efciency as dependant on the extra time the operatorhad to perform a task. This curve shows that the more extra time anoperator had the greater his efciency. For example, an operator with twopercent of extra time would have a 96 percent efciency, whereas with10 percent of extra time, he would have had an efciency of 99 percent.

Other IssuesWe also analyzed the design of kanban buffers andoperating policies for the manufacturing systems in theupstream ow sector. Our goal was to guarantee in-dependence between the diversities to reduce the dis-order in the production schedule. We took functionalstops (for example, stops for grinding welding-gun

tips, changing welding-gun tips or welding guns, andcleaning tools) into account. (We discuss the work onkanban and functional stops in internal, unpublisheddocuments.)

After developing the design method, we had to col-lect reliability data. We developed a unied process forcollecting accurate reliability data and conducted acampaign in the plants to explain why it was so im-portant to maintain the process. Before collecting data,we rst determined the most common elements (ma-chines) in the manufacturing process. We decided tofocus on the 20 percent of elements that constituted 80percent of the manufacturing systems in the bodyshop. This approach helped us save money whileguar-anteeing a good level of accuracy for our results. Then,we collected data within PSAs major factories to ndthe MTTR (mean time to repair) and the MTTF (meantime to failure) of these most common elements.

After implementing the new method, we conducted

training sessions in PSAs plants and research and de-velopment divisions on use of the method and soft-ware and new shop standards. During these sessions,

we taught employees how to design manufacturingsystems.

TrainingWe believe that the best operations research projectsgo beyond tool building and analysis. They shouldhave lasting value beyond the solution of the currentproblem. To educate and help R and D staff membersdesign better lines, we created new teaching materials.Armed with lessons learned from this project, they arecreating efcient lines and responding quickly to car-

model changes.

An Example of LessonIn The Goal,Eli Goldratt and Jeff Cox (1986) stressedthat eliminating (or protecting, if not) bottlenecks is thekey to improving manufacturing systems. PSA did agreat job over the years of eliminating bottlenecks, sowe often faced the question, How do we improve aline that has no bottlenecks? The answer is to worknext on improving the performance in the neighbor-hood of the buffer closest to half full.

For example, to determine which machine to im-prove rst in a line with 11 identical machines in seriesand no bottleneck, we consider improving each of the11 machines one at a time. We have three ways to im-prove a machines performance (Figure 12): (1) by re-ducing the mean time to repair (MTTR), (2) by increas-ing the mean time to failure (MTTF), or (3) by reducingthe cycle time. Regardless of which type of improve-ment we made, our model showed that the lines pro-ductivity would be greatest when the improved ma-chine was at the middle of the line where the buffersare half full. So the answer to our question appeared

to be, in practice, the application of a rule we set, whichimproved rst the performance of the station whose buffer is closest to half full.

ImpactUsing OR methods we created

User-friendly software called DispO,


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Figure 12: To improve a line with 11 identical machines in series and nobottleneck, on which of the 11 machines must we focus rst? We havethree ways to improve a machines performance: (1) reducing the meantime to repair (MTTR), (2) increasing the mean time to failure (MTTF), or(3) reducing the cycle time. This graph depicts system performance aspredicted by our analytic models for each type of improvement applied toeach of the 11 machines. The position of the machine improved is rep-resented by the x-axis. The graph shows that, regardless of which type ofimprovement we made, the lines productivity would be greatest when theimproved machine was at the middle of the line where the buffers are halffull. This is consistent with our teaching with respect to improving rstthe performance of the station whose buffer is closest to half full.

Methods people could use to deal with specicissues, and

Training documents to help staff members design

production lines quickly.Our work has helped PSA and its suppliers, and

other companies using the new tools. The methodswe developed have gained the attention of someacademics.

Impact on PSAWe wanted to create software that production-line de-signers could use on their own without supervision.Those people, who are at the lowest level on a projectteam, perform many tasks. We spent a lot of time on

the human-machine interface to make the softwareuser-friendly and easy to learn, a necessity to insure itsviability. In addition, we assert that our software toolconsistently enables users to produce fundamentally better results that they would have otherwise. Theygain greater mastery of their assembly line and there-fore develop better designs quickly while drawing onfewer human resources.

The new methods and software put to rest someincorrect but deeply ingrained beliefs and practices.For instance, manufacturing engineers used to ask us

to build shops in which each machine had a lowercycle time than that of the downstream machine(s).They called this philosophy pushed ow. We provedthat, in a balanced shop, the machines to improve rstare those in the middle of the shop (Figure 12). Sothere was no reason to add potential to upstreammachines.

The following are some lessons people learned fromthe tools we developed:

People used to think that the capacity of buffersthat are always full must be increased so that therewould be enough place to store more material for thegood of the production. We proved that one must fo-cus on half-full buffers and then, whenever possible,reduce the capacity of buffers that are full all of thetime to increase the capacity of half-full buffers.

People used to believe that buffer allocation didnot really matter. We showed that given equal total buffer space, several smaller buffers are better than afew bigger buffers.

People used to think that the action that paid backthe most was decreasing cycle time. We demonstratedthat for equivalent impact, the most protable actions

were, in order: (1) decreasing MTTR, (2) increasingMTTF, and (3) decreasing cycle time (Figure 12).Some manufacturing people used to calculate the

equivalent cycle time of a set of parallel machines asequal to the mean of their cycle times. We showed thatthe inverse of the equivalent cycle time of a set of par-allel machines is the mean of the inverse of their cycletime.

It was commonly believed that the resulting ef-ciency of a set of machines in a series without an in-termediate buffer is the product of their efciency. Thisis inaccurate, and for the kinds of systems we dealtwith, the difference with the accurate formula is overfour percent. Buzacott (1967) gives the accurateformula.

The new methods and software demonstrated thatsustained improvement was possible for all the manu-facturing systems in PSAs body shops. PSA raised itsstandards accordingly.


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Credibility for Operations ResearchPSA personnel, initially skeptical about operations re-search (OR), had the opportunity to compare the re-sults the analytical methods predicted with the actual

Modeling that used to take threeweeks now takes a single day.

outcomes. Persuaded by the accuracy of the forecasts,they have come to respect OR. Consequently, otherPSA divisions have adopted the tools we developedand have initiated further OR projects. The success ofthe project helped management to understand thevalue of OR in our daily mission. PSA managementdecided to create a new section dedicated to shop de-sign and performance improvement.

Prot IncreaseBecause we could improve production-line designsrapidly, the plants could ramp up quickly and satisfystrong demand in the market without pressuring theworkforce to work overtime. These improvements ledto a better social climate and fewer human errors,which implied better-quality products. We took care-

ful measurements of productivity before and after thechanges. In 2001, the average increase in productivitywas four percent and 75 percent of the cars PSA man-ufactured worldwide were directly affected by this ORwork. This percentage will be over 90 percent beforelong.

Knowing that the car shop is the bottleneck ofPSAs plants, we based our calculation of the beneton the belief that improving the plants efciency im-plies increased volume which implies additionalprot. We assume that PSA sells all the cars pro-duced, and that is precisely the case. PSAs lines arerunning at their full capacity, and its waiting listdoes not decrease. We conservatively estimate that,in 2001, our work brought PSA US $130 million ofadditional prot! US $130 million dollars is about 6.5percent of PSAs total prot from selling cars in 2001.This is money that the company would not havemade without OR.

Impact on Other CompaniesBy using the new tools and the accompanying trainingdocuments, PSAs suppliers gained knowledge aboutmanufacturing system engineering. As a result, theydesigned accurate systems quickly. Furthermore, us-ing the same tools led PSA and its suppliers to use thesame standards, reducing the time they spent negoti-ating production schedules. Almost all of PSAs sup-pliers now use the new tools, even though PSA does

In 2001, our work brought PSA US$130 million of additional prot.

not require them to do so. We expect the impact of our

work to go beyond PSA and its suppliers as other com-panies acquire the software. PSA management is eval-uating an outside companys proposal to market thesoftware.

Impact on AcademiaAs the lead analyst on this project, Alain Patchong wasinvited to present this work at Massachusetts Instituteof Technology, and at some top grandes ecoles (Frenchengineering schools) before audiences consistingmainly of tomorrows decision makers. His presenta-tions, which have become annual events at someschools, illustrate how applied OR can bring great benets to organizations.

AcknowledgmentsWe thank Stanley B. Gershwin, senior research scientist at MIT, forhis helpful suggestions. We also thank Richard Rosenthal for hisvaluable advice.

Appendix: States of a Machine in aProduction LineWe graphed a Markov chain for an unreliable machine(Figure 13). The model is based on the continuous-timeassumption. A machine can be in two states: opera-tional (up) or under repair (down). When the machineis working, it can go down (fail) with the probabilityrate k (average failure rate of the machine). Whenthe machine is down, it can go up (be repaired) with


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Figure 13: The Markov chain of an isolated unreliable machine has twostates. When the machine is up, it can go down with the probability ratek . When the machine is down, it can go up with the probability rate l .

Figure 14: Machine behavior in a production line is made up of threestates: up and down states, and an idle state. A machine that is up canbecome idle when it is starved or blocked.

the probability rate l (average repair rate of themachine).A manufacturing-ow line (or a production line) is

made up of material, work areas, and nite storageareas. The material ows from a work area to the fol-lowing storage area. Work areas may consist of ma-chines or of operators who perform a value-addingoperation on the material. The time the materialspends in a work area should generally be consideredstochastic. The variability from part to part arisesfrom random processing times, random failures, anduncertain repair events. In such an environment, if we

assume operation-dependent failures(that is, that fail-ures occur only while the machine is processingparts), machine behavior can be characterized as athree-state Markov chain (Figure 14) made up of upand down states, and an idle state. In fact, we considera machine operational if it is not down; it can theneither be working if it is processing a part or idle oth-erwise. An idle machine is starved or blocked. A ma-

chine is said to be blockedif, after it nishes a part, thedownstream buffer becomes full and the machine hasno place to put additional parts until room becomes

available in the downstream buffer. A machine isstarved if, after nishing a part, the upstream buffer isempty. The starved machine is prevented from pro-cessing additional parts until some arrive in the up-stream buffer.

ReferencesBuzacott, J. A. 1967. Automatic transfer lines with buffer stocks. In-

ternat. J. Production Res.5(3) 163200.Dallery, Y., S. B. Gershwin. 1992. Manufacturing ow lines systems:

A review of models and analytic results. Queueing Systems: The-ory Appl.12(12) 394.

Gershwin, S. B. 1987. An efcient decomposition method for the ap-

proximate evaluation of tandem queues with nite storagespace and blocking. Oper. Res. 35(2) 291305.

. 1994. Manufacturing Systems Engineering. Prentice Hall, Engle-wood Cliffs, NJ.

Goldratt, E. M., J. Cox. 1986. The Goal. North River Press, Croton-onHudson, NY.

Le Bihan, H. 1998. De nouvelles methodes analytiques pourlevaluation des performances de lignes de production. PhDdissertation, Universite Paris 6, Paris, France.

Patchong, A. 1997. Methodes de modelisation, danalyse et de di-agnostic pour lamelioration de lefcacite dun atelier de pro-duction. PhD dissertation, Universite de Valenciennes, France.

, D. Willaeys. 2001. Modeling and analysis of an unreliable owline composed of parallel-machine stages. IIE Trans. 33(7) 559

568., , J. Defrenne. 1997. Cost-based optimization of manufac-

turing systems automation. Proc. 15th IMACS World Conf.Ber-lin, Germany.

Christophe de Baynast, Director, Car Structure En-tity, PSA Peugeot Citroen, Route de Gisy, 78140 Ve-lizy-Villacoublay, France, writes: As Director of theCar Structure Entity of PSA Peugeot Citroen group, Iam well aware of the work described in the submis-sion Improving Car Body Production at PSA Peu-

geot Citroen. This work has had a tremendous im-pact on our recent projects: from the very rst stepwhen we start our forecast to the design phase of ourmanufacturing systems. The success of the softwaredeveloped has largely crossed the boundaries of myentity and is currently used by staff from other PSAdivisions and our suppliers. The implementation of


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the work submitted has dramatically improved ourrecently designed shops efciency. We expect $130 Mrevenue gain just from this improvement. Other bene-

ts due to this work include aid in decision makingand forecasting, more accurate and faster shops de-

sign, and better knowledge of manufacturing systemsin our staff and our suppliers. In summary, I considerthe work performed to be denitely a successful case

of research work vulgarization in industry, and Istrongly give my endorsement to the authors.

improving car body production at psa

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