Intelligent pipeline control - a simulation study in the automotive sector

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1 Intellgent ppelne control - a smulaton study n the automotve sector Phlp G. Brabazon, Andrew Woodcock, Bart L. MacCarthy Mass Customzaton Research Centre, Nottngham Unversty Busness School, Jublee Campus, Nottngham, NG8 BB, UK phlp.brabazon@nottngham.ac.uk; andrew.woodcock@nottngham.ac.uk; bart.maccarthy@nottngham.ac.uk Abstract Automotve producers are amng to make ther order fulflment processes more flexble. Openng the ppelne of planned products for dynamc allocaton to dealers/ customers s a sgnfcant step to be more flexble but the behavour of such Vrtual-Buld-To-Order systems are complex to predct and ther performance vares sgnfcantly as product varety levels change. Ths study nvestgates the potental for ntellgent control of the ppelne feed, takng nto account the current status of nventory (level and mx) and of the volume and mx of unsold products n the plannng ppelne, as well as the demand profle. Fve ntellgent methods for selectng the next product to be planned nto the producton ppelne are analysed usng a dscrete event smulaton model and compared to the unntellgent random feed. The methods are tested under two condtons, frstly when customers must be fulflled wth the exact product they request, and secondly when customers trade-off a shorter watng tme for compromse n specfcaton. The two forms of customer behavour have a substantal mpact on the performance of the methods and there are also sgnfcant dfferences between the methods themselves. When the producer has an accurate model of customer demand, methods that attempt to harmonse the mx n the system to the demand dstrbuton are superor. Keywords: order fulflment, automotve.. Introducton The level of product varety on offer from the large automotve producers, partcularly on passenger vehcle models, can be very consderable. In copng wth a wde product range premum producers are movng to fulfl the majorty of ther customers by buldng to order (BTO) [] but most of the manstream large producers use several fulflment mechansms. Retal customers are served by dealers and n European markets t has become common practce for the dealer to be able to search the stocks of other dealers as well as ther own, and search the vehcles scheduled for producton [2]. If no vehcle s found they have the opton to request a BTO vehcle. A schematc of ths mult mode open ppelne fulflment system s n Fgure. Feed Ppelne (Producton plan) Factory Stock Customer BTO request queue Three fulflment mechansms Fgure. Schematc of the order fulflment model wth three fulflment mechansms From an operatons management perspectve the mult-mode fulflment system s nterestng and potentally attractve to stakeholders n the system ncludng the producer, dealers and customers. The system has a stock of unsold vehcles whch s replenshed from the factory, the producton plan for whch s typcally mapped out for several weeks nto the future. As can be expected, the producer s concerned wth the volume and composton of stock, wantng these fnshed vehcles to be of an approprate mx to satsfy as hgh a proporton of customers as possble. If the ppelne s closed from dsturbance the mx n stock could be predcted usng standard nventory analyss, assumng the customer demand for each product varant s known accurately. However, n mult-mode fulflment the ppelne s open and hence a fracton of vehcles n the plan wll be sold before they reach the

2 factory and so do not replensh stock. Prevous research has shown the volume and mx of stock n an open ppelne system s dfferent from the stock n a conventonal system wth a closed ppelne [3]. That research uncovered nherent and fundamental behavour of the fulflment system but dd not look at how the system could be controlled. Ths s the focus of the current research. A producer may wsh for customers to fnd the exact product varant they are seekng wthout watng,.e. the majorty are fulflled from stock. However, as varety ncreases, a pont s reached where the volume of vehcles n stock and ppelne are fewer than the number of varants on offer. Whatever process or rule the producer uses to feed the ppelne, n ths crcumstance ether some proporton of customers must wat for a BTO product, or they must be wllng to compromse on vehcle specfcaton. In ths study these two behavours are modelled explctly to assess ther mpact on fulflment performance across a wde range of varety levels. The objectve of ths study s to test methods for selectng the product varants to feed nto ppelne. To do so a dscrete event smulaton has been created whch models the ppelne as a sequence of p products. At each tme step of the smulaton the products ncrement one poston along the ppelne wth one beng fed nto the upstream entrance of the ppelne and one leavng the downstream end. The extng product goes nto stock unless t has been sold already n whch case t s removed from the system. Customer arrvals are synchronsed wth the ncrementng ppelne, wth one customer served n each tme perod. Every customer s allocated a product, ether from stock or the ppelne or by requestng a bult-to-order product. As customer arrvals are synchronsed wth producton the number of avalable products n the system remans constant, mplyng that the producer s forecast s accurate n terms of volume. Therefore, f the system s prmed wth a ppelne full of p products and none n stock, the frst customer wll take one and reduce the count to p- (condtonal on there beng a match), but t wll return to p when the next product enters the ppelne. Although the count of avalable products s constant ther locaton n the system depends on the level of varety on offer to the customer. When only a few varants are on offer, many customers are fulflled from stock, but when varety s hgh only a few wll fnd a sutable product n stock and a hgh proporton wll need vehcles bult-to-order. In the former stuaton the level of stock s low and most of the avalable products wll be n the ppelne. In the latter stuaton the avalable products are mostly n stock, and the ppelne s conveyng BTO products. These condtons are llustrated n Fgure 2. Ppelne Stock Intal condton: ppelne s prmed wth products Low varety: most customers fulflled from stock, some from ppelne, few by BTO Hgh varety: many customers fulflled by BTO, few from stock or from the ppelne Avalable BTO Ppelne sale Fgure 2. Indcatve locaton of products n low and hgh varety condtons Fve Methods for selectng the next product to feed nto the ppelne have been developed and are compared to a random feed. Four of the methods are based on comparng the mx of avalable products n the ppelne and n stock to a target dstrbuton. The ffth method s a smple but pragmatc rule, whch s to feed n the varant the last customer wanted. In realty the producer has the challenge of estmatng the relatve demand for each varant but n ths study we make the producer s target dstrbuton dentcal to the demand dstrbuton. Each product varant has a unque number to represent ts specfcaton. The dfference n specfcaton between two varants s the dfference n ther numbers. To llustrate, the varant #7 s one step dfferent from #8, 2

3 and 5 steps dfferent from #98. Ths property s used when customers are modelled as beng wllng to compromse. The relatve demand for each varant follows an 8/2 dstrbuton,.e. 2% of the varants account for 8% of demand as llustrated n the rght plot n Fgure 3. Ths s modelled n the smulaton usng a Beta dstrbuton wth the shape parameters set to and Percentage Percentage Varant Ranked Varant Fgure 3. Demand for each varant n number order (left plot) and ranked by demand proporton to show the shape of the 8/2 dstrbuton (product range 2) In the study a range of varety levels are smulated from 2 to,38 (.e. from 2 to 2 ) and n all cases a skew equvalent to 8/2 s appled. Fgure 3 shows the relatve demand for varants when there are 2 varants and t s mportant to note that demand per varant s randomsed to avod a correlaton between varant specfcaton and varant demand. Ths s to emulate the real world stuaton n whch the most commonly requested varants from a product range dffer greatly. 2. Descrpton of the ppelne control methods Ths secton descrbes the control methods and how they are mplemented. All the methods functon n the same way, n that they select one product to feed nto the ppelne. Common symbols are gven n Table. Symbol Descrpton Symbol Descrpton Varant dentfer l Number of products held n the ppelne s Probablty of stock out on varant p m Number of varants a Probablty of a customer seekng a varant Volume of varant n ppelne and stock c Number of customers A Volume of products n ppelne and stock, A = d Volume of demand for varant, d p A Table. Symbols 2. Method : Random feed. The next varant to be fed nto the ppelne s chosen at random from the target dstrbuton, whch s modelled as a Beta dstrbuton. 2.2 : Reduce stockout probablty. The next varant to be fed nto the ppelne wll be the one that has the hghest probablty of stockng out. Probablty s of a varant stockng-out s calculated as the probablty that demand for varant wll exceed ts current avalablty a after c customers are processed (where c s equal to the sum of all products currently n stock and ppelne). The number of customers demandng varant are estmated usng a bnomal approxmaton,.e. d B( c, p ), so the value of () s calculated usng the cumulatve densty functon of the bnomal ~ = m = a 3

4 dstrbuton. The varant to be fed nto the ppelne satsfes max{ } probablty of stockng out. arg.e. the varant wth the hghest s s = P( d a ) () 2.3 : Reduce weghted error from target dstrbuton. Ths approach consders the error between the actual number of a partcular varant n both stock and ppelne a and the expected demand for that varant d. The error s weghted accordng to the demand for the varant n (2). The arg mn. varant to be fed nto the ppelne satsfes { } e e = p a d (2) 2. Method : Reduce dstance (to reduce compromse). Ths method apples the concept of compromse dstance to select a varant. Consder the stuaton n whch a producer can stock only one varant k. All customers wll receve varant k regardless of whch varant they request. To mnmse the compromse of the customer populaton, the producer selects the varant whch mnmses the average expected dstance defned n (3). m dst = cp spec spec c k (3) = The procedure for mplementng the method s as follows: The current holdng of each varant n stock and ppelne s a. Sum to fnd total, A Add to the holdng and estmate the expected number of customers per varant, d = p ( A +) Select the frst varant and add to the volume of ths varant,.e. a = a. + Then nspect each varant, attemptng to fulfl the expected customer demand d, frstly from a. The fulflled volume s f,. If f, s less than d, then try to fulfl the remander from a whch wll be f,, and f some remans stll then fulfl from a +, and so on, followng the general max{, m }, + j= sequence of fllng from a j then a + j untl f j = d The dstance calculaton sums the product of volume fulflled and dfference between varants,.e. dst = m j= f, j j notng that when j = the dstance s zero, hence f the volume of stock and ppe s dstrbuted over the varants n an deal way, the dstance calculaton would return. arg mn dst. Repeat for all varants and select the varant that gves { } The number of calculatons s proportonal to m 2 so to obtan results at hgher varety levels a stoppng rule s mplemented but even wth ths ncluded results have not been obtaned for the two hghest varety levels of 892 and 38.

5 2.5 : Increase forward sales coverage. The expected forward sales cover fsc of a varant s calculated usng the bnomal approxmaton,.e. d ~ B( c, p ) and the property that the expected successes for an outcome s the product of the number of trals and the probablty of success per tral. To calculate the forward sales coverage for each varant, s added to the number of that varant currently n stock and ppelne. The varant selected to wholesale s the one whch gves arg mn{ fsc } where fsc s calculated usng (). ( a +) fsc = () p 2. Method : Follow the prevous customer s request. In ths method the sequence of wholesaled products repeats the sequence of customer orders. 3. Prmng of the ppelne Four of the methods (2, 3, & 5) can be compared by how they prme the ppelne. The prmng process starts wth an empty ppelne and the method selects the frst product varant. Ths s fed nto the ppelne and s taken nto account when the method selects the next varant, and so on untl the ppelne s full. The plots n Fgure analyse the characterstcs of the ppelne dstrbuton once prmed by each of the methods. The ppelne holds 2 products and the target dstrbuton s from Fgure 2 above. The plots rank the varants by ther demand fracton n descendng order and measure the dfference n frequency from the target dstrbuton. Three of the methods exhbt a smlar form of saw tooth pattern. Ths s the consequence of the actual number of a varant n the ppelne beng an nteger, whereas the target frequences are n fractons. In Methods 2 and 3 the teeth alternate between over- and under- representaton of varants n the ppelne (wth a value above zero ndcatng over representaton). In the teeth to the left are all for over-represented varants, but then begn to alternate. In all three methods the lower demanded varants to the rght of the plots are under-represented. The overall pattern of Method s also a saw-tooth but the over- and under- represented varants are nterleaved. A second notable dfference from the other methods s that many of the lower demanded varants are over-represented. Statstcs about these dfferently prmed ppelnes are gven n Table 2. feeds fewer than 3% of varants (29) whle Method feeds n just under 5% (5). Furthermore, the varants fed n by Methods 2, 3 and 5 are the hghest ranked varants whereas Method spreads ts selectons from across the product range. In terms of evaluatng the shape of the dstrbutons aganst the target dstrbuton, usng the measure of mean squared dfference the methods are ranked from best to worst as 2, 3,, and 5. Method Number of varants represented n the ppelne Lowest ranked varant represented n the ppelne (ranked by demand) Mean Square Dfference from the target dstrbuton E E E E-3 Table 2. Analyss of how methods prme the ppelne, for varety 52 5

6 Percentage Percentage Varant. Varant Percentage Percentage Varant Fgure. Dfferences n proportons of varants n a prmed ppelne from the target percentage. Clockwse from upper left:,,, Method -. Varant. Analyss approach The methods are tested under two customer behavours. In one the customer must receve the varant requested, referred to as the Exact match search (and the oldest matchng vehcle fulfls the customer). In the second the customer wll trade-off watng tme and specfcaton dfference. Ths s denoted as the Compromse search and a customer s fulflled by the oldest product gvng the mnmum value for (5). score = spec spec + leadtme (5) requested Results are collected usng the batch means method wth the ntal transent dscarded and data from 2 batches used to calculate metrcs and confdence ntervals (whch are shown on many plots) as explaned n []. Many of the results are plotted aganst the rato of varety to ppelne length, denoted as the v/p rato, whch has been observed to allow fulflment systems of dfferent magntudes to be compared [3]. 5. Results 5. Zero ntal stock. In ths condton the ppelne s prmed wth products but there s no stock. The pattern of fulflment when customers are fulflled wth the exact product they are requestng s gven n Fgures 5 to 8. Fgures 5, and 7 show the proporton of customers fulflled from stock, ppelne and BTO, and Fgure 8 plots ther average watng tme. Evdent from these four plots are: Methods 2, 3 and 5, whch all try to match the target dstrbuton, have smlar performance and they are superor to the other methods. In the v/p range from. to the contrbuton of each fulflment mechansm s near constant. From ratos above, BTO fulflment rses and other mechansms reduce but are stll sgnfcant. Each of Methods, and has a dstnct pattern. Methods and have smlar performance to 2, 3, and 5 at the lowest v/p ratos, but then dverge as v/p rses wth lower stock fulflment, hgher BTO and longer watng tme. Method dverges less compared to the substantal dfference of Method.

7 The random feed (Method ) has the poorest performance n terms of stock fulflment whch s less than half of the superor methods 2, 3 and 5. Average customer watng tme s an order of magntude longer at low v/p ratos. Fulflment proporton 8% 7% % 5% % 3% Method Method Method 2% % %... v/p rato Fgure 5: Fulflment from Stock (Exact Match search) Fulflment proporton % 9% 8% 7% % 5% % 3% 2% Method Method Method % %... v/p rato Fgure : Fulflment from Ppelne (Exact Match search) Fulflment proporton % 9% 8% 7% % 5% % 3% 2% Method Method Method % %... v/p rato Fgure 7: Fulflment from Buld-to-Order (Exact Match search) 7

8 Average customer watng tme Method Method Method... v/p rato Fgure 8: Customer watng tme (Exact Match search) Performance of the methods s greatly altered when customers are wllng to trade-off specfcaton and watng tme, as shown n Fgures 9 to. In the varety range analysed there s no BTO fulflment except for Method at the hghest varety studed (,38 varants). In respect of the fulflment mechansms and watng tme all methods have smlar performance, wth Method beng the only one to trend away at hgher v/p ratos. At the lowest v/p ratos only a small fracton are fulflled from stock (Fgure 9), but ths s a lttle msleadng snce the majorty of customers are beng fulflled from products just about to leave the ppelne whch s evdent from the plot of watng tme (Fgure ) whch shows the average to be close to tme perod at the lowest rato (whch s the watng tme for a stock vehcle). The pattern of specfcaton compromse depends on how t s measured. In terms of the dfference n varant number, the amount of compromse rses as the v/p rato rses (Fgure, left plot) but when measured as a percentage of the product range, the compromse s greatest at a low v/p rato and drops toward zero (Fgure, rght plot). 5% % Fulflment proporton 35% 3% 25% 2% Method 5% % Method 5% Method %... v/p rato Fgure 9: Fulflment from Stock (Compromse search) 8

9 Method Average customer watng tme Method Method... v/p rato Fgure : Customer watng tme (Compromse search) 8 2% Method Average Compromse on Specfcaton Method Method Average Compromse on Specfcaton % 8% % % 2% Method Method Method... v/p rato %... v/p rato Fgure : Customer compromse n specfcaton, left: varant steps, rght: percentage of product range 5.2 Increasng stock levels. In ths secton the system s nvestgated further at the v/p rato of whch corresponds to varety of 2. The ssue consdered s how the methods control stock mx, and ths s nvestgated by prmng the system wth greater volumes of stock. Once steady-state condtons are reached the methods are compared n respect of fulflment from stock and customer watng tme. Fgures 2 and 3 plot the stock fulflment proportons, the former for the exact match search and the latter for the compromse search. Fgure 3 confrms the pattern observed above n that Methods 2, 3 and 5 are smlar and they are superor to the other methods. Method s farly close to them, dfferng by ~ percentage ponts and converges to them at stock levels above 2. Method also converges at ths stock volume. The random feed of Method stands out as beng a poor approach. It does not acheve 9% stock fulflment n the condtons analysed, but from extrapolaton ths method wll requre an order of magntude more stock than Methods 2, 3 or 5. Fgure 3 also confrms the pattern observed earler, wth all but Method havng smlar performance, though Method has slghtly less stock fulflment when stock s below ~3. In the exact match condton, the random method s poor, but t converges to the other methods at stock levels above. The data on customer watng tmes n Fgure show smlar dfferences between methods. Comparsons of the fulflment curves n Fgures 2 and 3 and the watng tme plots n Fgure hghlght how substantal the mpact on performance s of customer behavour. At the v/p rato of, over products are requred n stock for 9% of customers to be fulflled from stock n the exact match search, but when customers compromse the same proporton s acheved wth a stock of less than 2. In ths condton the average compromse n specfcaton s small at ~.5% (Fgure 5, left plot) and the maxmum that any customer compromses s n the regon of 5% to % (Fgure 5, rght plot). 9

10 % 9% Method 8% Fulflment proporton 7% % 5% % 3% 2% Method Method % % % 9% 8% Steady state Stock Volume Fgure 2: Fulflment from Stock (Exact Match search) Fulflment proporton 7% % 5% % 3% Method 2% % Method Method % Steady state Stock Volume Fgure 3: Fulflment from Stock (Compromse search) Method 5 Method Average Customer Watng Tme Method Method Average Customer Watng Tme Method Method 5 Steady state Stock Volume Steady state Stock Volume Fgure : Customer watng tme, left: Exact Match search, rght: Compromse search

11 .8% %.% Method 2% Method Compromse n Specfcaton.%.2%.%.8%.%.%.2% Method Method Maxmum Compromse n Specfcaton % 8% % % 2% Method Method.% Steady state Stock Volume % Steady state Stock Volume Fgure 5: Average (left) and maxmum (rght) customer compromse n percentage specfcaton (Compromse search). Dscusson The results show n most condtons studed that ntellgent methods are superor to the baselne random feed. In the more demandng stuaton of customers requrng an exact match some of these methods far exceed the random feed n terms of fulfllng from stock and customer watng tme. As can be seen n Fgures 5 to 8, the benefts from these methods s seen across the full v/p range studed. Although the expermentaton here extended to a v/p rato of, the plots suggest that all methods may converge at a v/p rato of or hgher. In contrast, when customers compromse, all of the methods, ncludng the random feed, have near dentcal performance at v/p ratos below. and the dvergence above ths rato s small. The comparson of the two customer behavours shows how mportant ther decsons are to system performance. It s antcpated a real customer populaton wll have a mx of customer types and the mplcatons of the relatve proportons s an ssue for further study. Three of the methods 2, 3 & 5 attempt to harmonse the mx wth the target dstrbuton and they have smlar performance. The results show these methods mprove the stock mx compared to the random method and the greater proporton fulflled from stock shortens customer watng tmes. A further contrbutor to the reduced watng s an mproved mx n the ppelne, evdenced by hstograms of where along the ppelne products are allocated to customers (Fgure ). The left plot s wth the random feed and the bas s toward the upstream start of the ppelne whle the plot for s a near mrror mage, wth the bulk of allocatons n the downstream half of the ppelne. Allocaton frequency Allocaton frequency Ppe poston Ppe poston Fgure : Ppelne slot at whch products are allocated to customers, left: Method, rght: (Exact Match search, varety 2,, customers) Method, whch looks to create a mx n the system to cover the full range of products, performs poorly at hgher varety levels when customers must have the exact specfcaton they are seekng. It s a method conceved for the compromse stuaton but t does not stand out as a superor method n those condtons.

12 Method s notable n that although t underperforms the best methods when customers demand exact matches, ts performance s consderably better than the random method and t would seem to be straghtforward to mplement. It s concevable Methods 2, 3 and 5 wll lose ther superorty f the producer has an naccurate forecast of the customer demand dstrbuton. Method s robust to ths as t does not requre a forecast. It wll lag behnd any change n customer tastes but ths s a challenge to all forecastng technques. A queston worth dwellng on s why Method s superor to the random feed (Method ). In Method the sequence of varants requested by customers s random and the sequence of varants fed nto the ppelne s also random. In Method the ppelne feed follows the customer sequence, hence t can be consdered to be random also. However, because the feed follows the customer sequence t avods a phenomenon observed n earler research on open ppelne systems [3] n whch the mx n stock becomes unrepresentatve of the mx fed n to the ppelne. Consder a stuaton n whch two dce are thrown several tme and one has a sequence of four or more 5s whle n the other s sequence there s no 5. When the equvalent occurs n the open ppelne system, the result s that stock and the ppelne are strpped of 5s and from then on any 5 enterng the ppelne s lkely to be sold to a customer before t can replensh stock. By followng the customer Method duplcates the run of 5 and prevents the strppng effect. 7. Concluson A smplfed verson of an open ppelne system used n the automotve sector has been studed usng a dscrete event smulaton model. A set of methods for selectng products for manufacture have been developed and mplemented. Usng a number of performance metrcs clear dfferences have been observed n the methods. When the producer has an accurate forecast of customer demand the performance attaned by some methods s very much better than a random feed. The approach of producng the products requested by recent customers does not acheve the best results but may be a more robust method. Further research can study the mplcatons of forecast error on the performance of the methods. 8. Acknowledgements Ths research has been funded by the Nottngham Innovatve Manufacturng Research Centre and the Ford Motor Company. Partcular thanks to Gnt Puskorous of Ford for hs comments and suggestons on the work. 9. References. Meyr, H., 2. Supply chan plannng n the German automotve ndustry. OR Spectrum, 2 (), Holweg, M., Pl, F.K., 2. The second century: reconnectng customer and value chan through Buld-to- Order. MIT Press, Cambrdge, Mass. 3. Brabazon, P.G., MacCarthy, B.L., 2. Fundamental behavour of Vrtual-Buld-to-Order systems. Internatonal Journal of Producton Economcs, (2), Law, A.M., Kelton, W.D., 2. Smulaton modelng and analyss. McGraw-Hll, Sngapore. 2