An Integrated Framework for Responsive Supply Chain Management

Transcription

1 1 An Integrated Framework for Responsve Supply Chan Management 1 Darsht Parmar 1 Teresa Wu 1 John Fowler Tom Callarman 3 Vncent Hargaden 4 Eamonn Ambrose 1 Phlp Wolfe 1 Department of Industral Engneerng Arzona State Unversty, PO Box Tempe, Arzona , USA Chna Europe Internatonal Busness School 699 Hongfeng Road, Pudong Shangha, P. R. Chna UCD School of Busness Unversty College Dubln Belfeld, Dubln 4, Ireland 4 Natonal Insttute of Technology Management Unversty College Dubln Belfeld, Dubln 4 ABSTRACT In today s hghly dynamc, globalzed and compettve envronment, companes are under pressure to mprove ther supply chan strateges n order to be more responsve to customer demands. Indeed the geographcally dstrbuted nature as well as the dfferng objectves across these dspersed enttes of a supply chan can often lead to dffcultes n makng a supply chan responsve. Addtonally, rregulartes and dsruptons occurrng at any pont n the system make responsve supply chan management even more challengng. These dsruptons, often occurrng wthout warnng due to the dynamc nature of a supply chan, can lead to poor performance of the supply chan. A key component n responsve supply chan management s the ablty to effectvely sense and response n order to maxmze responsveness and flexblty and avod system dsruptons. Recent advances n communcaton can facltate the sensng and data collecton. However, the huge amount of data generated can mpede effectve response, partcularly, when some data may be ncomplete or have errors. Inaccurate estmate or sensng of the system state can lead to ncorrect decsons, wth consequent adverse effects on supply chan performance. To address ths ssue, ths research proposes a Kalman flter based approach for excepton detecton. Some prelmnary work, specfcally, wth a focus on the manufacturng porton of the IBM supply chan for server fulfllment s presented n ths paper. The results show system estmaton can be mproved by usng a Kalman flter. 1. INTRODUCTION Supply Chan Management (SCM) emphaszes the ntegraton of actvtes and nformaton flows whle focusng on ncreasng value for the customer. The dversty of partcpants n terms of sze, technologcal capabltes, cultural dfferences, effcences etc. makes SCM a dffcult task. Two addtonal dffcultes are: (1) the presence of uncertanty n such aspects such as customer requrements (demand), capacty, transportaton tme, manufacturng tme, costs, qualty, due dates, prortes, etc. and () the realty of mssng nformaton, ambguous nformaton, and the bullwhp effect [1]. Recent developments n communcaton technologes and standards make mproved data sharng feasble and assst the decsons on managng and controllng the operatons. However, n practce, the data collected may be ncomplete, naccurate and nconsstent. Based on such data, the provson of accurate estmates of the state of a supply chan for decson makng s questonable. Therefore, there s a need to mprove system

2 Flexble Automaton and Intellgent Manufacturng, FAIM006, Lmerck, Ireland estmaton when ncomplete data and errors n the data are present. The ntent of ths paper s to take an ntal step forward n ths drecton. Consderng an IBM server fulflment supply chan, each manufacturng faclty faces a bg challenge to meet the quota at the end of each quarter. The cost of an unfulflled order can run nto mllons and thus t s extremely mportant to sense any potental exceptons that mght occur. Better sensng of the manufacturng states and better estmaton of the processng states can help to manage the supply chan responsvely and effectvely. However, manufacturng data collecton s prone to measurement errors. Ths s largely due to the fact that where automated systems don t exst, the operators wat for a group of jobs to complete, and then scan them nto the system. In addton, such errors are very common durng shft changeovers. Whle the completed jobs wat to be handled, the operators of the frst shft pass on nformaton to the second shft operators. Ths nduces bas n the estmaton of the cycle tme and can throw off any predcton mechansms whch mght be n place to estmate the fnal job completon. Kalman flters have tradtonally been used for stochastc estmaton and control. They have been used to obtan better state estmatons. In ths work, a Kalman flter approach s used to take nto account the measurement errors and to obtan a better state estmaton, namely the estmated start and end processng tmes of the jobs. A better state estmaton ultmately leads to better estmaton of the fnal job completon. In addton to obtanng a better estmaton of the fnal job completon, a new approach s proposed to calbrate the path that a job s expected to take over tme. In other words, as and when more nformaton s obtaned, the expected travel path of the jobs changes over tme and these changes are ncorporated n real tme to obtan a better dea of whether a job s on course for tmely completon or not. Ths approach s used to sense any potental exceptons that mght occur. The format of the paper s as follows. Frst, the background of Kalman flters s revewed followed by the applcatons of Kalman flters. Then, the bass of the proposed approach s descrbed. Fnally, an example s presented followed by conclusons and deas for future research.. BASICS OF KALMAN FILTERS The Kalman flter provdes an effcent computatonal (recursve) means to estmate the state of a process []. Kalman [3, 4] formulates the Wener problem, a flter problem for communcaton and control from the state pont of vew and the resultng Kalman flter s recursve soluton to the dscrete-data lnear flterng problem. A Kalman flter s a set of mathematcal equatons that supports estmatons of past, present, and even future states. The power comes from the fact that t can do these estmatons even when the precse nature of the modeled system s unknown []. Fgure 1 shows the general procedure of Kalman flter. Fgure 1: Typcal Kalman flter Applcaton (Adopted from [5]) Mathematcally, a Kalman flter s a set of recursve equatons used to estmate the state x R n of a dscretetme controlled process such as manufacturng process that s governed by the transton equaton and measurement equaton.

3 Transton Equaton: x k = G*x k-1 + ε k-1, x R n Measurement Equaton: z k = H* x k + η k, z R m Where G nxn s the system state matrx that relates the state at the prevous tme step k-1 to the present step k, H mxn relates the system states to the measurements. The random varables ε k and η k represent the process and measurement nose respectvely. They are assumed to be whte nose wth normal dstrbutons: p (ε k ) N (0, Q k ) and p (η k ) N (0, R k ). The equatons for the Kalman flter fall nto two groups: tme based equatons (Equaton 1 and ), appled to obtan the current system state, and measurement based equatons (Equaton 3-5), used to adjust the system state from the measurements. xˆ ˆ k = Gxk 1 (1) T Pk = G Pk 1G + Qk () T T 1 Kk = Pk H ( HPk H + Rk) (3) x ˆ ˆ k = xk + Kk( zk H xk) (4) Pk = ( I KkH) P k (5) where K k s the Kalman gan, P k s the error covarance, xˆ ks the estmaton of x k before the measurement, and xˆ k s the estmaton of x k gven measurement z k. The Kalman flter assembles the two groups of equatons to gve the best estmate of the system state. The system of measurement and transton equatons can be combned nto an teratve process to determne the state of the system x. The Kalman flter has been appled n a varety of applcatons ncludng Inertal Navgaton and Gudance [6], Global Postonng Systems [7], Target Trackng [8], Fnance [9, 10], etc. In the doman of supply chan, Avv [11] proposes an adaptve nventory replenshment polcy that utlzes the Kalman flterng technque. Wu and O Grady [1] develop an ntegrated approach that uses Kalman flterng and Petr Net model to obtan a better state estmaton of the supply chan system. Vensm [ an optmzer tool provded by Ventana Systems, uses Kalman flterng to track the actual nventory and clam that Kalman flterng tracks the nventory much better than ether smple smulaton alone or the measured nventory alone. Ths research ams to explore the applcaton of Kalman flter to an IBM manufacturng process n the context of a sense and response supply chan DESCRIPTION OF THE APPROACH As shown n Fgure, the proposed approach can be dvded nto two phases: the estmaton phase and the sensng phase. In the estmaton phase, an estmate of when the job wll complete the fnal process s obtaned, based on what has been happenng. Predcted fnshng tme s obtaned by runnng a smulaton module. When a job s n a process, an emulaton module provdes real progress. The Kalman flter module wll calbrate the results and provde a more realstc estmate. Gven an mproved estmate, a sensng phase wll determne whether the job wll come out as scheduled. Fgure. Proposed Framework

4 4 Flexble Automaton and Intellgent Manufacturng, FAIM006, Lmerck, Ireland 3.1. NOMENCLURE L E TB(E L 1 ) TB(L L +1 ) Tme when entty starts or completes a process. For example, L 1 refers to the start of the frst process, L refers to the end of the frst process, L 3 refers to the start of the second process, and so on. Entty arrval tme Estmate of tme between entty arrval and start tme of the frst process Estmate of tme between the nstant when entty s at the startng of process and the end of the process. Ths accounts for the queue tme between the end and begnnng of a process and the processng tme at a process. TB( L L 1 ) Estmate of tme between the start of one process to the end of the overall process Est ( L ) Estmated tme for entty to be at the start or the end of the process Msd ( L ) Measured tme for entty to be at the start or the end of the process Cor ( L ) Corrected tme for entty to be at the start or the end of the process K ( L ) Kalman correcton ˆ σ ( Est L ) Estmate of varance n estmated tme of L ˆ σ ( Msd L ) Estmate of varance n measured of L (assumed to be 36) ˆ σ ( Cor L ) Estmate of varance n corrected tme of L ˆ σ ( TB( E L1 Estmate of varance n estmated tme between entty arrval tme and the start tme of the frst process ˆ σ ( TB( L L + 1) ) Estmate of varance n estmated tme between the nstance when entty s at the start and the end of the process ˆ σ ( TB( L L1 Estmate of varance n estmated tme between the start of one process and the end of the overall process 3.. PROBLEM SPECIFICION Ths research studes the IBM server manufacturng process, a sx step seral process that s dentfed as shown n Fgure 3. The processng tme dstrbuton for all sx processes s trangular wth the parameters shown n Table 1. Fgure 3: Sx step seral process Table 1: Assumed parameters of trangular dstrbuton for processng tme at each process Process Low (n hours) Mode (n hours) Hgh (n hours) A B C D E F The tme between arrvals of enttes (or jobs) s assumed to be exponentally dstrbuted wth a mean of ten hours. It s also assumed that there s a provson to take measurements (or collect nformaton) on the start and the

5 end tmes at every process for every entty, and there are errors n these measurements and that these errors are normally dstrbuted ESTIMION PHASE Frst, an estmate of when an entty wll pass through every process s obtaned. Ths estmate s obtaned usng smulaton. The entre process s smulated for 30 replcatons. For each replcaton, the arrval tme of the entty to the system, s kept the same. An estmate of the queue tmes for all enttes and an estmate of the processng tmes for all enttes at every process are calculated by takng the average from the 30 replcatons. The standard devaton n these estmates s also calculated. Table gves an example of what these numbers mght look lke for one partcular entty. Table : Estmated queue tmes and processng tmes for a sample entty Descrpton Average from 30 replcatons (n hours) Standard devaton from 30 replcatons (n hours) Queue tme before A Processng tme at A Queue tme before B Processng tme at B Queue tme before C Processng tme at C Queue tme before D Processng tme at D Queue tme before E Processng tme at E Queue tme before F Processng tme at F To emulate the real world, an addtonal smulaton s run, usng the same dstrbuton and usng the same parameters for the processng tmes as used n the smulaton wth 30 replcatons. We call ths emulaton. In other words, measurements obtaned from emulaton are assumed to represent measurements obtaned from the real world. At ths pont, nformaton from two dfferent sources s avalable and both these sources have varablty smulaton has varance n estmaton and emulaton has varance n measurement. These two peces of nformaton are now combned usng equatons (6) (14) to obtan a better estmate of the job completon. Equaton (6) estmates the start tme of the process at process A. Equaton (7) estmates the varaton n the estmate of the start tme. Equaton (8) calculates the Kalman correcton requred to account for the measurement error n the state. Equaton (9) apples the Kalman correcton and obtans the corrected estmates of the state. Equaton (10) estmates the varance n the corrected estmate of the state. Equaton (11) uses the corrected estmate for ntermedate states to estmate when an entty wll complete the last process (process F). Equaton (1) estmates the corrected varance n the estmate of the state when an entty wll complete the last process (process F). Equaton (13) estmates the next entty state from the corrected current state. Equaton (14) estmates the varance n the estmate of the next entty state. ( L1 ) E + TB ( E L 1 ) ( Est L1 ) = ˆ σ ( E + TB( E L1 = σ ( TB( E L1 ( L ) ˆ ( )/ ( ˆ ( ) ˆ σ Est L σ Est L + σ ( Msd L ( L ) Est ( L ) + K( L ) ( Msd ( L ) Est( L ( Cor ( L ˆ σ ( Est L ) K( L )* σ ( Est L ) ( L1 ) Cor( L ) + TB( L L 1 ) ( Est ( L1 = ˆ σ ( Cor( L + σ ( TB( L L1 ( L+ 1 ) = Cor( L ) + TB( L L+1 ) ( Est ( L ˆ σ ( Cor( L + ˆ σ ( TB( L L Est = (6) ˆ σ ˆ (7) K = (8) Cor = * (9) ˆ σ = ˆ (10) Est = (11) ˆ σ ˆ (1) Est (13) ˆ σ + 1 = + 1 (14) Note that the numbers used to show the start and the completon tmes of an entty at a process are n terms of the smulaton clock tme. Also, the estmates of tme are n hours. Thus, varance s n terms of squared hours.

6 6 Flexble Automaton and Intellgent Manufacturng, FAIM006, Lmerck, Ireland [Example] Table 3 gves an example of how equatons (6) (14) can be appled to estmate the states of the entty as t moves through the process. Table 3: Example showng state estmaton for one sample entty Parameter Descrpton Smulaton clock Source tme Entty arrval tme Smulaton Estmate of tme between entty arrval and start tme of the frst process 0 Smulaton Estmate of varance n estmated tme between entty arrval tme and the start tme of the frst process 0 Smulaton Estmated tme for the entty to be at the start of process Derved usng Eq (6) Estmate of varance n estmated tme for the entty to be at the start 0 Derved usng Eq (7) of process 1 Measured tme for entty to be at the start of process Emulaton Estmate of varance n measured tme when entty s at the start of 36 Assumed process 1 Kalman correcton 0 Derved usng Eq (8) Corrected tme for entty to be at the start of process Derved usng Eq (9) Estmate of varance n corrected tme for entty to be at the start of 0 Derved usng Eq (10) process 1 Estmate of tme between the start of the frst process and the end of 0.14 Smulaton the overall process Estmate of varance n estmated tme between the start of the frst Smulaton process and the end of the overall process Estmate of tme for entty to be at the end of the overall process Derved usng Eq (11) Estmate of varance n estmated tme for entty to be at the end of Derved usng Eq (1) the overall process Estmate of tme between the start of the frst process and the end of 9.5 Smulaton the frst process Estmate of varance n estmated tme between the start of the frst 6.37 Smulaton process and the end of the frst process Estmate of tme for entty to be at the end of process Derved usng Eq (13) Estmate of varance n estmated tme for entty to be at the end of process Derved usng Eq (14) The above example s only for estmatng one state. Ths process of estmaton s contnued as the entty moved through the process. Fgure 4 shows how ths process mproves the state estmaton. In other words, usng ths process, we get a better estmate of when an entty s lkely to start or complete a partcular process as the varance of the corrected estmate s less than the varance of the measurement as well as the varance of the estmate (Fgure 4b). (a) (b) Fgure 4. Smulaton Results

7 SENSING PHASE It s assumed that there s a method n place for quotng the delvery date to the customer. For our purposes, t s assumed that the delvery date s determned based on the results from 30 replcatons of the smulaton. Also, the delvery date s n terms of the smulaton clock tme. The steps for sensng exceptons are explaned below wth an example. Suppose that we are nterested n determnng how entty number 516 s dong. The estmated completon tme from 30 replcatons of smulaton for ths entty s (n terms of smulaton clock tme). In other words, ths entty s expected to complete process F at Suppose that ths s the tme quoted to the customer. Now, when the entty s actually gong through each of the sx processes, we apply the Kalman flter correctons and re-estmate ts completon tme. These estmates, whch are changed n real tme, can be used to compare wth the completon tme quoted to the customer. And dependng on the amount of tolerable rsk, a control chart can be plotted. For example, suppose that we want to know whether the entty s lkely to take more than days than the quoted tme to the customer. Table 4 below summarzes the results showng the dfference between the delvery tme quoted to the customer and the estmated process F completon from dfferent estmate ponts, for one entty. Table 4: Example showng the calculaton of dfference between the delvery tme quoted to the customer and the estmated process F completon from dfferent estmate ponts for one entty Estmate pont Estmate for Process F completon (n smulaton clock tme) Delvery tme quoted to the customer (n smulaton clock tme) Absolute dfference between quoted delvery tme and estmated completon of process F (n hours) Start of process A End of process A Start of process B End of process B Start of process C End of process C Start of process D End of process D Start of process E End of process E Start of process F Fgure 5: Control chart based on table wth 48 hours and 7 hours control lmts To determne whether ths method sensed accurately or not, we used the fnal corrected completon tme for end of process F. A dfference between the quoted delvery tme to the customer and the corrected completon tme for end of process F was computed. The threshold s set as 48 hours, that s, f the control chart sgnaled when the dfference exceeded 48 hours, t was consdered as correct classfcaton. On the other hand, f ths dfference was less than 48 hours, and f the control chart sgnaled, t was consdered as an naccurate classfcaton. In ths prelmnary research, we set the threshold based on experence. More experments need to be done to tune ths parameter to account for the tolerable rsk. Same calculatons were performed for all enttes and the results are summarzed n Table 5.

8 8 Flexble Automaton and Intellgent Manufacturng, FAIM006, Lmerck, Ireland Table 5: Results for all enttes Descrpton Number Total number of enttes 1000 Total sgnals 33 Correct sgnals 15 False sgnals 14 Mssed sgnals 4 As shown n Table 5, there were 1000 total enttes to whch the above descrbed approach was appled. There were sgnals for 9 enttes. No sgnal was later than the end of process E. There were 15 correct sgnals and 14 ncorrect sgnals. Out of the 14 ncorrect sgnals, there were 6 enttes whch dffered from the quoted delvery date to the customer by more than 40 hours. They were ncorrect because the control chart sgnaled that these enttes would take more than 48 hours than the quoted delvery date. We call these 6 sgnals as close false sgnals. In addton, there were 8 other false sgnals meanng that the control chart ndcated that these enttes would take more than 48 hours, whereas n realty, these enttes dd not exceed 48 hours. Also, there were 4 mssed sgnals. These were the enttes whch took more than 48 hours, but the control chart dd not sgnal. The overall accuracy usng ths approach to sense exceptons s ( ) / 1000 = 98.%. 5. SUMMARY One management strategy for a responsve supply chan s sense and response whch requres contnuously montorng busness process, detectng exstng or antcpated busness ssues, resolvng these ssues as early as possble. Ths paper proposes an ntegrated framework for sensng, utlzng smulaton technques and a Kalman flter. In partcular, an IBM server fulfllment supply chan s studed. To valdate the proposed framework, we concentrate on the server manufacturng process. The results ndcate that usng a Kalman flter can help n gettng a more realstc estmate of when an entty s lkely to come out of the factory. The mproved estmates are then used to sense whether an entty s on course to meet customer delvery expectatons. In the future, t s ntended to repeat the estmaton and sensng phases at other IBM server manufacturng stes. We wll then explore the applcaton of the proposed framework to a fully fledged supply network. In addton, more scenaros such as dfferent types of exceptons n the sensng phase need to be explored. Fnally, we wll develop a response model when exceptons are sensed. REFERENCES [1] J., Blackhurst, J., T., Wu and P., O Grady, Network-based approach to modelng uncertanty n a supply chan, Internatonal Journal of Producton Research, 15, 4, 8, 004, pp [] G. Welch and G. Bshop: An ntroducton to the Kalman flter, Techncal Report No. TR , Department of Computer Scence, Unversty of North Carolna, [3] R.E. Kalman, and R.S. Bucy., "New Results n Lnear Flterng and Predcton Theory", Transactons of the ASME seres D: Journal of Basc Engneerng, 83 (3): , [4] R.E. Kalman, "A New Approach to Lnear Flterng and Predcton Problems", Transactons of the ASME seres D: Journal of Basc Engneerng, 8 (1): 35-45, [5] P. S. Maybeck: Stochastc Models, Estmaton, and Control, Vol 1, Academc Press, Inc., New York, [6] P. Zarrchan., "Tactcal and Strategc Mssle Gudance", AIAA, Inc., Washngton, DC, [7] R.P. Denaro and P.V.W. Looms., "GPS Navgaton Processng and Kalman flterng", AGARD, NO. 161, pp , [8] C. K. Chu and G. Chen, Kalman flterng wth Real-Tme Applcatons, Sprnger-Verlag, New York, [9] C. Wells, "The Kalman flter n Fnance", Kluwer Academc Publshers, Dordrecht, [10]P.J. Bolland and J.T. Connor, "A Constraned Neural Network Kalman flter for Prce Estmaton n Hgh Frequency Fnancal Data", Internatonal Journal of Neural Systems, Vol. 8., No. 4, August, [11] Y. Avv: A Tme Seres Framework for Supply Chan Inventory Management, Operatons Research, Vol. 51, No., pp. 10-7, 003. [1] T. Wu and P. O Grady: A Methodology for Improvng the Desgn of a Supply Chan, Internatonal Journal of Computer Integrated Manufacturng, Vol. 17, No. 4, pp , 004.