Dynamic Order Promising: Real-time ATP

Transcription

1 Dnamc Order Promsng: Real-tme ATP Anne G. Robnson and Robert C. Carlson Department of Management Scence and Engneerng, Stanford Unverst, Stanford, Calforna, USA Emal: Fax: Abstract In order to satsf customer demands despte unque specfcatons or schedule constrants, manufacturers have realsed the crtcal need for real-tme avalable-to-promse (ATP). In ths paper, we present a model for real-tme order promsng n a mxed make-to-order, maketo-stock manufacturng envronment. Each fulfllment source s consdered as a separate module. Consstent wth the real-tme nature of the problem, ths model consders a snapshot vew of the enterprse at the moment the customer order enters the sstem. Relevant values from potental fulfllment sources are passed to the ATP optmzaton engne. Followng an nstantaneous decson to accept or reject the order, the newl pegged resources are updated n the sstem. The flexblt n ths modular structure allows the model to adapt to the most fragmented IT sstem or leverage the benefts of a hghl ntegrated ERP sstem. We found that order acceptance levels and costs are most senstve to capact utlzaton. Other factors that showed sgnfcant effects n our real-tme ATP envronment were demand varablt, number or orders per da and the magntude of these orders. Kewords: Real-tme ATP, Dnamc Resource Allocaton, Order Promsng 1

2 1. INTRODUCTION In ths paper, we focus on the problem of determnng an order promsng polc for a real-tme Avalable-to-Promse (ATP) sstem. If orders are assumed to be batched as the arrve before an decsons are made, there are currentl several models and algorthms for determnng optmal sourcng or fulfllment strateges. However, when a decson on order acceptance and fulfllment needs to be made n real-tme, exstng lterature provdes no vald methods. Real-tme ATP sstems are sstems whch allow a customer request to be accepted and sourced based on current avalablt n the suppl chan at the tme the order s placed. Consder, for example, an onlne computer retaler. When a customer request s placed, nformaton avalablt wll determne whch parts and products are avalable and when the order can be completed. However, these dates are often based on standard leads tmes, or at best, rough rules-based estmates of fnshed goods avalablt and scheduled recepts wth lttle or no valdaton. Ths often results n unrelable promse dates. The prolferaton of open IT archtectures has allowed for ncreased compatble data ntegraton. For example, ERP sstems from vendors such as SAP AG or PeopleSoft, Inc. promse nformaton compatblt and consoldaton across the enterprse. Thus, when order acceptance decsons are beng made, there s the potental to consder a greater amount of nformaton allowng for better decson makng. These nformaton archtectures drectl ntegrate the customer nto the fulfllment process, and allow front end and back-end applcatons to share a common vew across the suppl chan. In ths paper, we present a model for real-tme order promsng. We develop an event-drven model that s adaptve and modular, based on nformaton avalablt. Next, a 2

3 smulaton model of the producton sstem s used to analse the success of the real-tme ATP sstem under dfferent parameters. 2. RELEVANT LITERATURE Recentl, the ssues of order promsng and customer servce have receved consderable attenton n popular press (see, for example, Best Practces (2003), Schultz (2002), Hem (2001) and Greene (2001)). Man ndustr segments have dentfed a dspart between ther nformaton avalablt and order promsng capabltes. New addtons to the academc lterature present the foundatons of ATP modellng. Ths lterature can be separated based on three characterstcs: 1. Order Acceptance Strateg 2. Due Date Generaton 3. Model Scope Order acceptance strateg refers to whether orders are accepted n batches or on an order-per-order bass. There are several papers that address batchng orders before makng acceptance and fulfllment decsons (Kern and Guerrero (1990), Chen et al. (2002)). However, gven current customer expectatons wth respect to response tmes, ths s not consstent wth current busness practces. In ths research, we address order acceptance from a real-tme perspectve, and as such consder orders on an ndvdual bass. Another sgnfcant factor for ATP models s whether order due dates are generated exogenousl or endogenousl to the model. There s a wealth of lterature on due-date assgnment and leadtme quotng (Baker and Bertrand (1981), Hopp and Sturgs (2001)) where the customer s presented wth a delver date. However, ths supposes that the busness manager has complete control over determnng order due date. Common practces suggest that ths assumpton does not reflect realt. 3

4 Fnall, the model scope descrbes the perspectve of the ATP model, from ether a machne shop level or enterprse/suppl chan level. Talor and Plenert (1999) consder a job-shop model where ATP s consdered from an avalable capact perspectve. In contrast, a number of papers have dealt wth the enterprse perspectve where nventor and capact avalablt are consdered across the suppl chan (Ervolna and Detrch (2001), Xong et al.(2003)). Jeong et al. (2002) develop an ATP model that consders nventores across the suppl chan, as well as shop floor capact avalablt. However, unlke those papers, ths paper consders a modular vew of the enterprse. The model s constructed usng modules such that t mmcs true nformaton avalable from an ERP or smlar sstem. In ths paper, we consder an ATP model wth real-tme, order-for-order acceptance and fulfllment from an enterprse perspectve. Customer due dates are assumed to be exogenousl generated. The model presented here s a combnaton of optmzaton and smulaton. Our ntent s to determne the long-term effects of dnamc real-tme optmzaton n an order-promsng envronment. 3. PROBLEM DESCRIPTION In practce, real-tme ATP suggests that when a customer request s ntated, ATP determnes avalablt based on the customer requested due date. Thus, real-tme resource allocaton and schedulng decsons must be made on an order-per-order bass. When a customer order enters the sstem, the ATP process s executed based on the requrements of that order. The essence of an ATP sstem s to explot the relatonshps among the varous busness unts n an organzaton to meet demand n order to mantan hgh levels of customer servce. Thus, fnshed goods nventores, work-n-process, raw materals, producton schedulng, as well as other consderatons such as cost, are smultaneousl consdered across the suppl chan as possble sources for order fulfllment. 4

5 Throughout ths research, we consder a mxed push-pull manufacturng envronment. Ths mples the producton sstem s partall make-to-stock (MTS) and partall make-toorder (MTO), consstent wth man manufacturng envronments. The producton schedule s based on forecasts and then updated as more orders are receved. The producton horzon s broken nto three man sectons: producton schedulng (PS), module producton (MP), and fnal assembl (FA). There s also provson made for remote sourcng (RS). PS, MP, and FA are dvded nto dscrete tme buckets. If an order has a due date greater than the furthest perod n the producton-plannng phase, t s rejected from the sstem. It s assumed that these orders are beond the reasonable scope of the tme horzon. Suppose there are multple products, each wth unque bll of materals. Each product contans a combnaton of modules. We assume that the manufacturng horzons for modules and fnal assembl of all products are the same. Inventor s held for modules and fnshed goods. Customer orders are for multple products wth a common due date. Each order comes nto the sstem wth a due date sgnfng a future tme when the customer requests to receve the goods. Thus, a sngle order wth demand quanttes for multple products s entered nto the model. If customers requre dfferent due dates for dfferent products, t s assumed these products are consdered as separate orders. When consderng avalablt, f an entre order cannot be flled t s rejected from the sstem. In ths model we do not consder the possblt of splt orders. The model assumes a fxed prce per unt; there are no economes of scale n orderng. There s no prce dependenc based on current avalablt or urgenc of the order. 5

6 The followng secton descrbes the foundatons of the analtcal formulaton of the model. We present a mxed nteger program (MIP). The objectve functon and constrants sets are detaled to reflect the fulfllment possbltes. 4. MIP MODEL We begn b nvestgatng the form of the MIP requred to capture the acceptance and fulfllment decsons at the moment the order s receved. The model consders a sngle customer order, consstent wth the real-tme nature of the problem. Ths model s event drven. Thus, upon entr of a customer order, the model utlzes data avalable at that moment, basng the decson on the current crcumstances of the sstem. The tme horzon n ths model s dvded nto three dstnct sectons, each representng part of the producton process (See Fgure 1): 1. Producton Schedulng (T-N tme unts) 2. Module Producton (N-n tme unts) 3. Fnal Assembl (n tme unts) The total tme horzon s T tme unts, where t represents the perod under consderaton. There s also provson made for remote sourcng where S s the mnmum requred tme for remotel sourced products to be delvered. Consder a set of products, I, each contanng a set of modules, j J. Each product has a unque bll of materals, where BOM j represents the quantt of the jth module n the th product. 6

7 Remote Sourcng S Customer Order: Quanttes and Due Date FGI WIP Fgure 1: Tme Horzon Fnal Assembl (FA) n N Module Producton (MP) T Producton Schedulng (PS) Customer and Sstem Inputs The model contans two tpes of nputs customer nputs and sstem nputs. The customer nputs are the demand quanttes and due date assocated wth the gven order. The sstem nputs represent the avalablt of unpegged fnshed goods, subassembles, or producton schedulng at the moment the order enters the sstem. Customer Inputs d : quantt demanded of product l : due date of the order Sstem Inputs Q FGI : Quantt of FGI avalable for product. QFA (t) : Quantt of FA WIP avalable for product avalable at tme t. QMOD (t) : Quantt of module WIP for module j avalable at tme t. j QPS (t) : Quantt of producton schedule avalablt for module j at tme t. j 7

8 Decson Varables The decson varables represent a bnar decson whether or not to accept the order, and, f accepted, how to optmall allocate resources to the order. All of the decson varables have nteger values. The quantt demanded for each product s pegged aganst avalablt from fve dstnct sources: Notaton: Fnshed Goods Inventor (FGI) Fnal Assembl Module Producton (ncludng module nventor) Producton Schedulng Remote Sourcng x : order acceptance varable, 1 f order s accepted, 0 otherwse FGI : quantt of order for product sourced from FGI FA (t) : quantt of order for product sourced from Fnal Assembl WIP n perod t RS : quantt of order for product sourced from Remote Sourcng MOD j PS j (t) : quantt of module j pegged for product from Module Producton WIP n perod t (t) : quantt of module j pegged for product from Producton Schedulng n perod t Constrants The constrants enforce the phscal lmts of the sstem and tme boundares of the due date set b the customer. 8

9 1. BOM Balancng Constrants These constrants ensure the modules sourced from the module producton and producton schedulng sectons of the manufacturng horzon wll create whole products. To defne ths constrant, we must add the followng notaton. We defne a constant, IBOM whch s the nverse of the number of module j requred to produce one unt of product. It s descrbed explctl b the equaton ( BOM ) where BOM j represents the number of modules j n product. 1 j j (1.1) N t= n IBOM j MOD T + IBOM j PS =, j j λ j t= N + 1 λ s an nteger decson varable equallng the quantt of product sourced from module WIP and producton schedulng. Snce λ s onl ndexed over, sourcng an equvalent number of each module based on the BOM wll be enforced b these constrants. These constrants ensure complete products are manufactured, whle allowng module WIP and producton schedulng to both be used when sourcng a product. 2. Demand Constrant The demand constrant set ensures that demand s completel satsfed. It guarantees that the entre order wll be flled, whle preventng product from exceedng the requested quantt. (2.1) FGI n + t = 1 FA + RS + λ d x = 0 Each ndvdual constrant n the set refers to a sngle product. However, the are lnked b a common bnar order acceptance varable x. Thus f demand cannot be flled for one tem, 9

10 then the entre order s rejected. λ, as prevousl defned, ensures a suffcent quantt of modules to satsf demand, as requred. 3. Due Date Constrants The due date constrants are based on the latest due date the customer specfes. These constrants guarantee that an order cannot be allocated from a source that wll not have avalablt n the requested tme frame. (3.1) (3.2) j j PSj MODj = 0 = 0 t > l t > l (3.3) RS = 0 S > l (3.4) FA = 0 t > l If the tme perod under consderaton s beond the horzon of the customer requested due date, then fulflment for ths sourced f forced to be zero. Smlarl, f the mnmum amount of tme requred for remote sourcng s greater than the customer due date, remote sourcng s not possble. 4. Maxmum Avalablt Constrants (4.1) (4.2) (4.3) (4.4) FGI FA Q Q MODj PSj FGI FA Q Q, t PS j MOD j j, t j, t The maxmum avalablt constrants ensure that product s not over promsed. These constrants allow orders to be promsed based on currentl unpegged fnshed goods, 10

11 work-n-process, or producton schedulng capact. The values used n these constrants are pulled from avalable nformaton sstems such as producton schedulng/nventor management sstems. The frst constrant (3.1) refers to fnshed goods nventor that s not currentl pegged to an order. The second constrant (3.2) allows orders to be promsed b peggng unpegged fnal assembl work-n-process over the FA horzon. The thrd and fourth constrants (3.3 and 3.4) n ths set assgn modules to requested orders. The thrd constrant assgns orders to unpegged modules n the module producton porton of the tme horzon. Fnall, the fourth constrant refers to the producton-schedulng horzon. The values used n ths constrant would most lkel represent unassgned producton capact for that tme perod or raw materals avalablt. However, an of these values could also represent a constrant based on labour avalablt or other constraned resources n the sstem. Objectve Functon Ths formulaton allows us to capture the tradeoffs between the cost of acceptng versus the cost of rejectng an order. Snce the producton envronment s mxed MTS/MTO, we assume that costs have alread been ncurred for products and modules that are n producton. Costs The followng denotes the costs used n the objectve functon. Unless otherwse noted, the are on a per tem bass. h 1 : nventor holdng cost for FGI h 2j : ntermedate nventor holdng cost for module j 11

12 p j : producton cost for module j f: cost of remote source per unt of product c FGI : cost assocated wth unpegged FGI of product c FA : cost assocated wth unpegged FA of product c MOD j : cost assocated wth unpegged module WIP of module j a f : fxed admnstratve cost of acceptng an order a v : varable admnstratve cost of acceptng an order r f : fxed cost of rejectng an order r v : varable cost of rejectng an order Objectve Functon mn T t= N + 1 [ ( l t) h ) + p ] n N cfgi FGI + cfa FA + c t= 1 j t= n+ 1 a f ( x) + a lh1 v 2 j ( x)( FGI PSj + t= 1 d ) + r n ( l t) h f j PSj 1 FA + + f (1 x) + r (1 x)( v RS j MOD j t= n+ 1 ( l t) h ( ) MOD t + j d ) N 2 j MODj + The frst four terms refer to nventor holdng costs. Once an order s accepted, nventor-holdng costs wll be ncurred untl the order s released. The frst term refers to FGI. If the order s mmedatel sourced from FGI, then we hold nventor untl tme l, the customer due date. The second and thrd terms refer to the module producton and producton schedulng portons of the manufacturng horzon. As descrbed b the due date constrants, t s not possble to source product from tmes perods greater than the customer due date. 12

13 Thus, for t > l the decson varables are forced to be zero, thus avodng negatve charges n the objectve functon. The ffth term descrbes the producton costs assocated wth an tem that s newl placed n the producton schedule. The 6 th term s the unt cost of product that s sourced remotel. The followng three terms (7, 8, 9) descrbe the revenue that covers the correspondng producton costs. For example, f the current order under consderaton s sourced from FGI, then ths order wll absorb the assocated producton costs. Thus, t s reasonable that ths cost s credted back n the objectve functon f ths fulfllment source s emploed. These costs would smlarl be ncurred and credted for Fnal Assembl (FA) and Module Producton (MOD). Next, there are fxed and varable admnstratve costs for acceptng an order. These ma be vewed as setup costs specfc to the current order. The fnal terms refer to the fxed and varable costs of rejectng an order. Smlar to the admnstratve costs, we allow for a two-part rejecton cost. These costs are n essence a penalt or opportunt cost of rejectng the order. The objectve functon captures the tradeoffs of acceptng versus rejectng an offer. An order would be rejected f there was no sourcng possbltes, or f the cost of acceptng ths offer was greater than the cost of rejectng. The next secton descrbes the smulaton model. 5. SIMULATION MODEL The smulaton model presented n ths research represents an enterprse perspectve of a manufacturng envronment. The purpose of ths model s to create a settng n whch to observe the long-term effects of real-tme ATP. Dfferent sstem parameters are consdered, as well as varous behavour patterns of the customers (.e. hgh/low demand varablt, short/long leadtmes). Ths model contans three crtcal sstem characterstcs: dnamc 13

14 order arrvals, real-tme order acceptance and fulfllment peggng, and real-tme sstem updatng. When an order enters the sstem, the ATP optmzaton model s trggered (see Fgure 2). An nstantaneous snapshot of the producton sstem provdes data for ths nstance of the model. A decson s made whether to accept or reject the order, based on the model results, as well as how to fulfll the order. Ths nformaton s recorded and the producton-schedulng and nformaton sstem s updated to reflect the current order. For each producton perod, the number of orders, product quanttes, and customer due dates are randoml generated as follows: 1. The number of orders per da are generated from a Posson dstrbuton 2. The magntude of each order s generated b a m-erlang dstrbuton 3. The customer due date s generated from a trangle dstrbuton centered on the average customer leadtme. Data persstence s an accepted ndustr term that relates to the mantenance of dentcal data across producton-schedulng platforms, nventor management sstems, and order management processes. Thus, when a customer order s promsed, the sstem s updated to reflect the peggngs from that order. Ths ensures that there wll be no nconsstences or dscrepances between the order taker s nformaton and the actual enterprse-wde resource avalablt. At the end of a producton perod, the sstem s updated and rolled ahead for the next perod. Quanttes of pegged and unpegged nventores and WIP are adjusted to match the current producton perod. In vew of the fact that fulfllment decsons are based on nstantaneous snapshots of the sstem, the overall objectve value of the sstem can be consdered as a pece-b-pece construct from the objectve values of each ndvdual order. 14

15 Randoml generated lst of customer orders and due dates, and number of orders per perod. Producton Sstem Sstem Detals Customer Order ATP Model Order Accepted? No Yes 1. Input Order Detals 2. Update Sstem to reflect current order 1. Reject Order 2. Input Order Detals (for performance trackng purposes) Fgure 2: Smulaton Model Flow Chart The performance crtera used n ths analss are percentage of orders accepted and average cost per unt ordered. Percentage of orders accepted refers to the number of orders accepted as a percentage of the total number of orders that have entered the sstem. The average cost per unt ordered conssts of the average producton and nventor costs per unt per accepted order. Each of these component costs wll also be consdered ndependentl. Both of these measures are used to evaluate the performance of the sstem; one would not be reasonable f used n the absence of the others. 15

16 6. EXPERIMENTAL DESIGN The ntent of ths desgn s to determne under whch condtons real-tme ATP wll lead to better performance of the sstem. The followng factors characterze the dmensons of the desgn. Ths s a two factoral desgn, wth each factor assgned hgh and low levels. Expermental Factors: 1. Objectve Functon a. Hgh: Mnmzaton objectve functon b. Low: Feasblt objectve functon 2. Varablt of Demand a. Hgh: Fluctuatng demand pattern b. Low: Stable demand pattern 3. Capact Utlzaton a. Hgh: Tght Capact b. Low: Loose Capact 4. Order Magntude a. Hgh: Multple unts per order b. Low: Low number of unts per order 5. Number Of Orders Per Da a. Hgh: Heav load b. Low: Lght load 6. Average Customer Leadtme a. Hgh: Long leadtme b. Low: Short leadtme Table 1: Expermental Factors These expermental factors requre further explanaton. The objectve functon drves the optmzaton model that determnes acceptance and sourcng decsons for each customer order. The hgh level of ths factor wll be the ncremental cost objectve functon, as 16

17 descrbed n the model formulaton secton. Ths objectve results n a cost-beneft balance assocated wth the addton of the current order, thus allowng orders to be rejected based on cost rather than on feasblt. When ths objectve functon s emploed, the producton schedulng decsons wll be made such that the fulflment sources match the customer due date as closel as possble. As such, the sstem s back scheduled so that the due date s not volated. The low level s a feasblt functon, allowng all orders to be accepted f sourcng were possble. Customer orderng patterns can be rregular or relatvel flat. These two cases are captured n the varablt of demand factor. The hgh level reflects a fluctuatng demand pattern, whereas the low level represents a more stable demand pattern. Capact Utlzaton refers to how closel suppl matches demand. In the tght capact case, we are lookng at a constraned scenaro where demand and suppl are ver close. In the loose capact case, suppl exceeds demand. The next two factors descrbe the volume and magntude of the orders. The magntude of each order descrbes whether the products are hgh or low demand tems. In one crcumstance, we assume that the expected order sze for each product wll be one or two unts. In the other scenaro, we consder orders for multple unts of each product. Changng the number of orders per da allows us to nvestgate the effects of volume and load on the sstem. At the hgh level, there s a heav loadng of orders n the sstem; the low level s a lghter demand level wth onl a few orders per perod. The average customer leadtme s the expected amount of tme requested b the customer for the due date of a partcular order. A short leadtme suggests that customers requre product almost mmedatel, whereas a long leadtme ndcates the majort of orders can be scheduled n producton schedulng f necessar. 17

18 We offer a bref descrpton of our numercal stud. We assume that there are two products each contanng two tpes of modules. Product 1 contans one of the frst module and two of the second module. Product 2 contans two of each module, and as such s the hgher cost tem. The producton horzon s 6 perods: 2 PS, 2 MP, 2 FA (refer to Fgure 1). The factors are characterzed as follows: Expermental Factor Values: 1. Objectve Functon a. Hgh: Mnmzaton objectve functon b. Low: Feasblt objectve functon 2. Varablt of Demand a. Hgh: 2-Erlang b. Low: 10-Erlang 3. Capact Utlzaton a. Hgh: Expected Mean ⅓ Std. Dev. b. Low: Expected Mean + ⅓ Std. Dev. 4. Order Magntude a. Hgh: Expected Order Sze 2 b. Low: Expected Order Sze Number Of Orders Per Da a. Hgh: Posson (30) b. Low: Posson (3) 6. Average Customer Leadtme a. Hgh: 5 da Expected Leadtme b. Low: 1 da Expected Leadtme Table 2: Expermental Values Alternatves are compared usng a full factoral desgn wth streams of common random numbers. We used ANOVA to make vald comparsons to determne whch ndependent varables had the greatest mpact. For ths expermentaton, we requred an 18

19 mplementaton envronment that would allow smulaton and optmzaton to easl nteract. We requred suffcent functonalt to solve a complcated MIP n a reasonable amount of tme. Addtonall, we needed to smulate a manufacturng suppl chan that would call multple nstances of the MIP. ILOG s OPL Studo was chosen as the modelng envronment for ths research because of ts ablt to ntegrate optmzaton and smulaton wth ts scrptng language. The optmzaton model was created usng OPL s propretar optmzaton language. The smulaton envronment was developed usng OPL Scrpt, a scrptng language that nteracts drectl wth the optmzaton code. Thus, multple consecutve nstances of the ATP/CTP model were nvoked. To effectvel mplement the model n OPL, slght modfcatons were requred for the constrant sets, wthout affectng ther functon. 7. RESULTS A full factoral set of experment runs, 2 6, was conducted. The results of these smulatons show that for each of the cost performance measures, the demand varablt, capact utlzaton, and orders per da factors are sgnfcant to 95% (see Table 3 and Table 4). Complete results of the experments can be found n the appendx. Table 3 shows the sgnfcant factors and nteractons for the nventor cost per unt ordered performance measure. Dependent Varable: Inventor Cost Per Unt Ordered Source Tpe III Sum of Squares df Mean Square F Sg. Demand Varablt Capact Utlzaton Orders Per Da DemVar * CapUtl CapUtl * OrdPerDa Table 3: Results for Inventor Cost performance measure 19

20 The results of the analss usng the producton cost per unt ordered as the performance measure (Table 4) reveal that n addton, the order magntude factor s also sgnfcant to 95%. There are addtonal nteracton effects present as well. Dependent Varable: Producton Cost Per Unt Ordered Tpe III Sum of Source Squares df Mean Square F Sg. Demand Varablt Capact Utlzaton Magntude per Order Orders Per Da DemVar * CapUtl CapUtl * MagOrd DemVar * CapUtl * MagOrd CapUtl * OrdPerDa MagOrd * OrdPerDa DemVar * CapUtl * MagOrd * OrdPerDa Table 4: Results for Producton Cost performance measure The percentage of orders accepted showed smlar results. Demand varablt, capact utlzaton, magntude of order and orders per da were all statstcall sgnfcant to 95%, as presented n Table 5. Dependent Varable: Percentage of Orders Accepted Tpe III Sum of Source Squares df Mean Square F Sg. Demand Varablt Capact Utlzaton Magntude per Order Orders Per Da DemVar * CapUtl DemVar * MagOrd CapUtl * MagOrd CapUtl * OrdPerDa MagOrd * OrdPerDa MagOrd * AvgCLT DemVar * CapUtl * MagOrd CapUtl * MagOrd * OrdPerDa CapUtl * MagOrd * AvgCLT Table 5: Results for Percentage Accepted Performance Measure 20

21 On the whole, these results are not unexpected. Each factor s detaled n the followng paragraphs. All of the results show that that the model s most senstve to capact utlzaton. Estmates of the sze of the effect reveal that the nventor costs per unt ordered ncreased b a factor of 6.5 when movng from tght to loose capact utlzaton. The producton costs also ncreased b approxmatel thrt percent. Correspondngl, the percentage of orders accepted ncreased from 80% to 100%. The capact utlzaton factor shows sgnfcant nteracton effects wth all the other factors wth the excepton of the objectve functon factor, as seen n the tables above. All of these results are consstent wth the suppl-demand envronment. When suppl exceeds demand, total order satsfacton s expected. The extra nventor n the sstem wll ncrease costs overall. Interestngl, the model results are ndfferent between the mnmzaton and feasblt objectve functons. None of the performance measures show a sgnfcant dfference between the two objectve functons. Thus, n ths tpe of envronment, the ease of the feasblt objectve functon would be favored n an mplementaton. It does not have as hgh a level of data requrements (.e. cost data) as the mnmzaton objectve functon and requres much less computaton tme. Fgure 3 shows the percentage of orders accepted versus the per unt nventor cost. As the percent accepted orders ncreases, the nventor costs ncrease. The dashed trend lne (R 2 =0.74) shows the exponental ncrease n nventor costs. The obvous dvson n the data spread s due to the splt between scenaros nvolvng loose and tght capact. 21

22 $25.00 $20.00 Per Unt Inventor Cost $15.00 $10.00 $5.00 $ R 2 = Percentage Accepted Fgure 3: Percentage of Orders Accepted vs. Per Unt Inventor Cost Loose capact scenaros have a 100% order acceptance wth a wde range of per unt nventor cost, dependng on the other factors of the scenaro. For tght capact scenaros, the data ponts n are the 65%-95% order acceptance range. These data show a mostl flat result, wth a slght postve trend (R 2 =0.1) n the nventor costs. Ths suggests that per unt nventor costs reman stable despte acceptng and fulfllng more orders. Demand varablt, number of orders per da, and magntude of each order do not reveal an unexpected results. All three factors show sgnfcant dfferences on the performance measures. Table 6 summarzes ther nfluences. 22

23 Demand Varablt Percent Accepted Per Unt Inventor Cost Per Unt Producton Cost Hgher varablt resulted n a Hgher varablt Hgher varablt resulted n 7% decrease n the number of resulted n 37% ncrease slght ncrease orders accepted Orders Per Da There was onl a 1% dfference between hgh volume and low volume demand Hgher volume demand resulted n 60% lower per unt nventor costs Hgher volume demand resulted n an 8% decrease n per unt producton costs Magntude of each Order Larger orders resulted n a decrease of 3% n number of orders accepted over smaller order szes Larger orders result n a 15% decrease n per unt nventor costs Larger orders result n a 5% ncrease n per unt producton costs Table 6: Further Results An nterestng fndng s that when consderng total cost per unt, the effect on order magntude was neglgble. However, when consderng the ndvdual cost components, the effects are sgnfcant n both cases. The cause of ths s that the drecton of the effect n these cases was opposte thus negatng ther respectve effects when added together to determne the total cost per unt. Average customer leadtme does not have an sgnfcant effect on the percentage of orders accepted or on the per unt producton cost, but t does have a statstcall sgnfcant effect on per unt nventor cost. A longer customer leadtme results n a 12% ncrease n the per unt nventor cost. Ths s not a surprsng result gven that fnshed goods wll on average sta n the sstem for a longer perod of tme wth a longer customer order leadtme than wth a short customer leadtme, assumng equvalent producton schedules for ether level. 23

24 $50.00 $45.00 Total Cost Per Unt Ordered $40.00 $35.00 $30.00 $25.00 $20.00 $ Percentage Accepted Hgh Demand Varablt, Low Orders Per Da Hgh Demand Varablt, Man Orders Per Da Low Demand Varablt, Low Orders Per Da Low Demand Varablt, Man Orders Per Da Fgure 4: Percentage of Orders Accepted vs. Total Cost Per Unt Ordered Fgure 4 shows the smulaton results plottng Percentage Accepted versus Total Cost per Unt Ordered. Consderng the sgnfcant factors, we can determne approxmate upper and lower bounds on both of these performance measures. For the four sets of factors characterzed above, the reader can nterpret the upper bound as the greatest per unt cost n a loose capact envronment as descrbed. Smlarl, the lower bound on percentage accepted would reflect the worst stuaton n a capactated crcumstance as descrbed above. The best performance occurs for cases wth low demand varablt and hgh volume of orders per da. The lower bound on order acceptance s 83% whle the upper bound on unt cost s approxmatel $29. Note that the costs are drven b our selecton of parameters. The results are better nterpreted relatve to each other, as opposed to absolute dollar values. 24

25 Mantanng low demand varablt for cases wth a low volume of orders ncreases the unt cost b 25%. The lower bound on order acceptance drops to 78% Hgh demand varablt shows better performance wth hgh volume of orders. Ths factor combnaton overlaps wth the prevous one. The lower bound on order acceptance s 72% whle the upper bound on unt cost s approxmatel $37. Low volume orders wth hgh demand varablt show the worst performance, wth low percentage accepted (68%) and hgh per unt costs ($48). 8. CONCLUSION Ths paper has presented a model for real-tme ATP. Dnamc order promsng and order fulfllment decsons are made usng an MIP whose nput data represents an nstantaneous snapshot of the sstem at the moment the order arrves. We have nvestgated the effects of dfferent factors on the performance measures percentage accepted and total costs. Our assumptons allow us to formulate a model that s modular and flexble to capture the nformaton avalable at the moment the order enters the sstem. Ths nformaton can be customzed to reflect the constraned resources at that partcular nstance or for that specfc customer. The results of our studes suggest that order acceptance levels and costs are most senstve to capact utlzaton. The other factors that showed sgnfcant effects were demand varablt, number or orders per da and the magntude of these orders. Total costs vared sgnfcantl n loose capact cases, but were ndfferent to tght capact cases. We of course also expect that ncreased order acceptance wll lead to ncreased revenue. In our model revenue was not consdered as our ntent was to see whether ncreased nformaton and the resultng ncreased flexblt would result n ncreased order acceptance. 25

26 Future research areas nclude examnng the effects of dnamc reschedulng as an addtonal facet of real-tme order promsng. Allowng exstng orders to be rescheduled (and stll meet ther due dates) provdes another degree of flexblt n the order-entr process. However, ths could result n a nervous sstem. Another area of potental nvestgaton s the ncluson of dnamc prcng n the model. The next generaton of advanced plannng sstems s ncludng proftable-to-promse (PTP) as part of ther order promsng capabltes. Rather than consderng feasblt and cost, these sstems hope to make order acceptance decsons based on a proft margn per order. 9. REFERENCES Baker, K. R. and J.W.M. Bertrand (1981) An Investgaton of Due-Date Assgnment Rules Wth Constraned Tghtness, Journal of Operatons Management, Vol. 1, No. 3, pp Best Practces, LLC (2003) Suppl Chan Management: Tactcs That Keep Companes Compettve October 16, 2003 Chen, C.-Y., Zhen-Yng Zhao, and M. Ball (2002) A Model for Batch Advanced Avalable- To-Promse, Producton and Operatons Management, Vol. 11, pp Ervolna, T. and B. Detrch (2001) Movng Towards Dnamc Avalable to Promse Workng Paper, IBM Research Dvson, T.J. Watson Research Center. Greene, A. (2001) Makng Better Promses, Manufacturng Sstems, Vol. 19, No. 4, p

27 Hem, C. (2001) Don t Forget About Fulfllment, APICS-The Performance Advantage Vol. 11, No Hopp, W. J. and M. R. Sturgs (2001) A Smple, Robust Leadtme-Quotng Polc, Manufacturng and Servce Operatons Management, Vol. 3, No. 4, pp Jeong, B., Sm, S.-B., Jeong, H.-S., and S.-W. Km (2002) An avalable-to-promse sstem for TFT LCD manufacturng n suppl chan, Computers & Industral Engneerng, Vol. 43 No. 1/2, pp Kern, G. M. and H. H. Guerrero (1990) A Conceptual Model for Demand Management n the Assemble-to-Order Envronment, Journal of Operatons Management, Vol. 9, No. 1, pp Schultz, G. (2002) Promse Keepers, Manufacturng Sstems, Vol. 20, No.9, pp Talor, S. G. and G. J. Plenert (1999) Fnte Capact Promsng, Producton and Inventor Management Journal, Thrd Quarter, pp Xong, M., Tor, S. B., Khoo, L. P. and C.-H. Chen (2003) A Web-enhanced Dnamc BOMbased Avalable-to-Promse Sstem, Internatonal Journal of Producton Economcs, Vol. 84, pp

28 Appendx: The followng table presents a summar of the results for each set of runs. Obj Functon Var of Demand Capact Utlzaton Mag. of Each Order Orders Per Da Avg. CLT Total Inventor Total Producton % Accepted Mnmzaton Low Loose 2 unts 3 orders 1 da $ 5,082 $ 10, % Mnmzaton Low Loose 2 unts 30 orders 1 da $ 33,152 $ 99, % Mnmzaton Low Loose 10 unts 3 orders 1 da $ 28,407 $ 54, % Mnmzaton Low Loose 10 unts 30 orders 1 da $ 128,955 $ 498, % Mnmzaton Low Loose 2 unts 3 orders 5 das $ 5,573 $ 10, % Mnmzaton Low Loose 2 unts 30 orders 5 das $ 39,875 $ 99, % Mnmzaton Low Loose 10 unts 3 orders 5 das $ 31,253 $ 54, % Mnmzaton Low Loose 10 unts 30 orders 5 das $ 164,214 $ 498, % Mnmzaton Hgh Loose 2 unts 3 orders 1 da $ 8,627 $ 11, % Mnmzaton Hgh Loose 2 unts 30 orders 1 da $ 57,883 $ 111, % Mnmzaton Hgh Loose 10 unts 3 orders 1 da $ 32,185 $ 58, % Mnmzaton Hgh Loose 10 unts 30 orders 1 da $ 241,995 $ 553, % Mnmzaton Hgh Loose 2 unts 3 orders 5 das $ 9,145 $ 11, % Mnmzaton Hgh Loose 2 unts 30 orders 5 das $ 64,868 $ 110, % Mnmzaton Hgh Loose 10 unts 3 orders 5 das $ 34,787 $ 58, % Mnmzaton Hgh Loose 10 unts 30 orders 5 das $ 274,331 $ 552, % Mnmzaton Low Tght 2 unts 3 orders 1 da $ 1,171 $ 7,396 92% Mnmzaton Low Tght 2 unts 30 orders 1 da $ 9,838 $ 78,440 93% Mnmzaton Low Tght 10 unts 3 orders 1 da $ 3,915 $ 33,814 79% Mnmzaton Low Tght 10 unts 30 orders 1 da $ 23,979 $ 389,240 84% Mnmzaton Low Tght 2 unts 3 orders 5 das $ 1,275 $ 7,208 88% Mnmzaton Low Tght 2 unts 30 orders 5 das $ 8,185 $ 78,230 90% Mnmzaton Low Tght 10 unts 3 orders 5 das $ 4,654 $ 33,568 80% Mnmzaton Low Tght 10 unts 30 orders 5 das $ 40,888 $ 388,706 85% Mnmzaton Hgh Tght 2 unts 3 orders 1 da $ 911 $ 5,848 79% Mnmzaton Hgh Tght 2 unts 30 orders 1 da $ 3,982 $ 66,600 77% Mnmzaton Hgh Tght 10 unts 3 orders 1 da $ 3,318 $ 29,224 69% Mnmzaton Hgh Tght 10 unts 30 orders 1 da $ 22,092 $ 333,670 73% Mnmzaton Hgh Tght 2 unts 3 orders 5 das $ 702 $ 5,724 76% Mnmzaton Hgh Tght 2 unts 30 orders 5 das $ 6,255 $ 66,026 76% Mnmzaton Hgh Tght 10 unts 3 orders 5 das $ 3,266 $ 28,781 68% Mnmzaton Hgh Tght 10 unts 30 orders 5 das $ 29,209 $ 331,462 73% Feasblt Low Loose 2 unts 3 orders 1 da $ 4,980 $ 10, % Feasblt Low Loose 2 unts 30 orders 1 da $ 33,152 $ 99, % Feasblt Low Loose 10 unts 3 orders 1 da $ 28,589 $ 54, % Feasblt Low Loose 10 unts 30 orders 1 da $ 128,955 $ 498, % Feasblt Low Loose 2 unts 3 orders 5 das $ 5,664 $ 10, % Feasblt Low Loose 2 unts 30 orders 5 das $ 39,946 $ 99, % Feasblt Low Loose 10 unts 3 orders 5 das $ 31,658 $ 54, % Feasblt Low Loose 10 unts 30 orders 5 das $ 164,751 $ 498, % Feasblt Hgh Loose 2 unts 3 orders 1 da $ 8,662 $ 11, % Feasblt Hgh Loose 2 unts 30 orders 1 da $ 57,883 $ 111, % Feasblt Hgh Loose 10 unts 3 orders 1 da $ 32,162 $ 59, % Feasblt Hgh Loose 10 unts 30 orders 1 da $ 241,995 $ 553, % Feasblt Hgh Loose 2 unts 3 orders 5 das $ 9,191 $ 11, % Feasblt Hgh Loose 2 unts 30 orders 5 das $ 64,814 $ 110, % Feasblt Hgh Loose 10 unts 3 orders 5 das $ 35,698 $ 58, % 28

29 Feasblt Hgh Loose 10 unts 30 orders 5 das Feasblt Low Tght 2 unts 3 orders 1 da Feasblt Low Tght 2 unts 30 orders 1 da Feasblt Low Tght 10 unts 3 orders 1 da Feasblt Low Tght 10 unts 30 orders 1 da Feasblt Low Tght 2 unts 3 orders 5 das Feasblt Low Tght 2 unts 30 orders 5 das Feasblt Low Tght 10 unts 3 orders 5 das Feasblt Low Tght 10 unts 30 orders 5 das Feasblt Hgh Tght 2 unts 3 orders 1 da Feasblt Hgh Tght 2 unts 30 orders 1 da Feasblt Hgh Tght 10 unts 3 orders 1 da Feasblt Hgh Tght 10 unts 30 orders 1 da Feasblt Hgh Tght 2 unts 3 orders 5 das Feasblt Hgh Tght 2 unts 30 orders 5 das Feasblt Hgh Tght 10 unts 3 orders 5 das Feasblt Hgh Tght 10 unts 30 orders 5 das $ 274,664 $ 552, % $ 1,027 $ 7,390 92% $ 5,209 $ 78,440 89% $ 4,175 $ 33,957 81% $ 24,495 $ 389,240 84% $ 1,101 $ 7,361 92% $ 7,302 $ 78,275 90% $ 4,811 $ 33,896 80% $ 32,210 $ 388,406 86% $ 681 $ 5,681 77% $ 3,815 $ 66,590 78% $ 3,269 $ 29,424 71% $ 21,711 $ 333,960 73% $ 681 $ 5,681 77% $ 4,690 $ 66,188 77% $ 2,792 $ 29,152 71% $ 22,648 $ 331,999 74% 29