STRATEGIES TO SUPPORT AMBULANCE SCHEDULING WITH EFFICIENT ROUTING SERVICES

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1 Assocaton for Informaton Systems AIS Electronc Lbrary (AISeL) Wrtschaftsnformatk Proceedngs 2009 Wrtschaftsnformatk 2009 STRATEGIES TO SUPPORT AMBULANCE SCHEDULING WITH EFFICIENT ROUTING SERVICES Günter Kechle TU Wen Karl Dörner Unverstät Wen Stefan Bffl TU Wen Follow ths and addtonal works at: Recommended Ctaton Kechle, Günter; Dörner, Karl; and Bffl, Stefan, "STRATEGIES TO SUPPORT AMBULANCE SCHEDULING WITH EFFICIENT ROUTING SERVICES" (2009). Wrtschaftsnformatk Proceedngs Ths materal s brought to you by the Wrtschaftsnformatk at AIS Electronc Lbrary (AISeL). It has been accepted for ncluson n Wrtschaftsnformatk Proceedngs 2009 by an authorzed admnstrator of AIS Electronc Lbrary (AISeL). For more nformaton, please contact elbrary@asnet.org.

2 STRATEGIES TO SUPPORT AMBULANCE SCHEDULING WITH EFFICIENT ROUTING SERVICES Günter Kechle 1, Karl Dörner 2, Stefan Bffl 1 Abstract For regular patent transportaton and emergency transportaton wth ambulance vehcles a dynamc dal-a-rde (DARP) problem has to be solved. We analyze two schedulng strateges for the regular dal-a-rde orders n order to mnmze routng costs and to maxmze transportaton qualty. Furthermore, we revew practcal requrements and suggest a conceptual archtecture for a decson support system based on a customary control center system as bass for future busness servces. Major results of ths contrbuton are two promsng and effcent soluton procedures sutable for a smplfed b-objectve verson of the dynamc DARP and tested wth real-world problem nstances. 1. Introducton Many emergency servce provders, especally ambulance departments and companes whch provde non-publc mantenance servces, face the problem to provde dfferent types of servces wth one fleet of vehcles: (1) Emergency coverage for a certan regon to provde mmedate emergency servce; (2) Effcent regular servce: scheduled pck-up and delvery of patents, predetermned servce tasks, perodc pck-ups, etc. Ths s also the current stuaton for the largest Austran regonal emergency servce provders (e.g., the Austran Red Cross), where the same fleet s used to provde both emergency and regular transport servces. Dynamc emergency aspects thus drectly nfluence the schedule for the regular servce. When an emergency occurs and an ambulance s requred, the vehcle wth the shortest dstance to the emergency s assgned to serve the emergency patent. Therefore, t often happens that an ambulance vehcle that has been scheduled for a transport order of a patent, but has not yet started, serves the emergency request. Thus, another vehcle has to be reassgned to the regular patent and the overall regular servce schedule has to be re-optmzed. Ambulances that carry out emergency transports become avalable at the hosptal after the emergency servce and can then be used to carry out regular transportaton orders. Agan, the schedule for regular servces has to be reoptmzed [10]. 1 TU Wen, Austra 2 Unverstät Wen, Austra 15

3 Regular transportaton servces are offered for handcapped persons or patents wth mnor dseases, who could not use tax servces. Thnkng of optmzaton for ambulance schedulng, we have to consder at least two perspectves. From the perspectve of a transportaton provder, the objectve s to mnmze cost of operatons. On the other hand, to maxmze qualty of servce s the objectve from a patent s pont of vew. Although both objectves comprse a multtude of factors, a smplfed model of realty s subject to our nvestgatons. Bascally, we use the length of a tour n terms of drvng tme to model costs and watng tme of patents to model transportaton qualty. A tour or route s defned as the overall movements of a vehcle over a day of operaton. Ths paper revews some of the results and experences from the Ambulance Routng research project, whch deals wth dfferent perspectves on the ambulance schedulng, e.g. consderaton of expected transportaton requests n vehcle schedulng determned from experences n the past or watng strateges for maxmzng coverage to reduce response tmes for emergency servces. In ths contrbuton we wll concentrate on regular transportaton servces, where a mnor part of transportaton requests arses dynamcally and most of the requests are known beforehand. Emergency requests dsturb regular operatons, but may be modeled as dynamc requests wth hgh prorty. Some related work has been publshed where pck-up and delvery requests occur dynamcally (see [1], [5] and [11]). Lkewse, a range of optmzaton algorthms has been developed and evaluated for varatons of ths problem (see [1], [4], [5], [11] and [12]). To our best knowledge, a dynamc changng fleet sze and ths type of dsrupton caused by emergency requests have not been consdered so far but seem partcularly desrable to mprove the capablty of decson support systems to provde future busness servces n real-world contexts. A major goal of the Ambulance Routng project s to demonstrate potental advantages of optmzaton algorthms n a decson support plot system for ambulance schedulng. Related work n the feld of decson support systems has demonstrated the practcal use of optmzaton for real-world vehcle routng problems (see [2] and [9]). Provdng dynamc routng servces requres a certan nformaton system nfrastructure that ntegrates Postonng Systems, Wreless Communcaton, and Geographc Informaton Systems to process necessary nputs for optmzaton and decson support (see [6][7]), whch n turn can provde busness servces useful for dspatchers. The contrbutons of ths paper are twofold. On the one hand, we descrbe two promsng and effcent soluton procedures sutable for a smplfed b-objectve verson of the dynamc dal-a-rde problem (DARP) and evaluate the effcency of these procedures wth real-world problem nstances n secton 4. On the other hand, we revew restrctons and constrants for the development of a decson support extenson for ambulance schedulng n secton 3 and suggest a system archtecture for ntegraton of our soluton procedures nto an exstng control center system to provde nterfaces for future busness servces n secton Problem descrpton The regular patent transportaton problem can be consdered as a varaton of the DARP wth addtonal real-world constrants regardng customer preferences or requrements. A comprehensve descrpton of the DARP s gven n [3] and partly repeated here to set a common ground for specfc varatons later on. 16

4 Let G = (N, A) denote a graph consstng of a set of nodes N and a set of arcs A. The set of nodes N holds all pck-up locatons P = {1,..., n}, all delvery locatons D = {n+1,..., 2n} and two copes of the depot 0 and 2n+1. N { 0, 2 + 1} = P D n For each arc n set A, a weght t j s gven and represents the drvng tme between two locatons. The DARP conssts of desgnng vehcle routes and schedules for n customers or patents who specfy pck-up and drop-off requests between orgns and destnatons. Note, that the number of customers n equals the number of pck-up locatons and also the number of delvery locatons. A typcal stuaton s that the same patent wll have two requests durng the same day or wthn a certan perod an outbound request, usually from home to a hosptal, and an nbound request for the return trp. Each transportaton order (or request) ncorporates a pck-up locaton out of set P and a delvery locaton +n out of set D. Furthermore, let g be a bnary value ndcatng whether a request s nbound or outbound. We set g to 0 for nbound and g to 1 for outbound requests. In addton we defne tme wndows [e, l ] and [e +n, l +n ] as well as servce (or loadng) tmes s and s +n for each pck-up and delvery locaton. Regardng tme wndows, we have two stuatons on the one hand, patents should be pcked-up as late as possble from ther home when they are beng transported to hosptals; on the other hand, patents should be pcked-up as early as possble when they are transported from the hosptal back home. Devatons from the desred pck-up and drop-off tmes wthn the specfed tme wndow are consdered n the objectve functon as watng tme. Tme wndows for each request are defned ether by a desred delvery tme l +n * for outbound requests or a desred pck-up tme e * for nbound requests whle remanng start and end values of each related tme wndow are computed as follows: l = e + W l+ n l + t, e e + t = + n + n =, + n P D + s P + s P In the standard case dscussed n the lterature, a homogeneous fleet of vehcles s consdered. The objectve s to plan a set of mnmum-cost vehcle routes whle servng as many customers as possble under a set of constrants. The man dfference between the DARP and most classcal routng problems s the fact that n the DARP human bengs are transported nstead of goods as n the other problems. Thus, addtonal constrants, e. g., maxmum rde tmes for the patents, no watng tmes wth a patent on board, preferred pck-up and drop-off tmes are consdered (see [3]). Our realworld DARP s extended n two ways: patents have an ndvdual maxmum watng tme W gven and vehcles may carry up to an ndvdual number of C k patents concurrently, assumng a set K of vehcles wth a fxed number of vehcles n operaton. To fnd a soluton for the descrbed problem two decsons have to be made. On the one hand, the relatve order of pck-up and delvery locatons on a tour has to be set. We use the bnary decson varable x j k to denote whether the locatons and j are vsted from vehcle k drectly one after another. 17

5 x k j { 0,1}, j N k K =, On the other hand, the actual pck-up or delvery tmes have to be fxed. Here we use the decson varable B k to denote the startng tme of the loadng/unloadng process of vehcle k at a pck-up or delvery locaton. B k N \{0}, k K Once the startng tme B k s set, also the end tme D k of a loadng/unloadng process whch equals the departure tme of vehcle k at a locaton may be determned. Above defned relatons for tme wndows are shown n Fg. 1 whch depcts a sngle segment of a tour. Fg. 1: Tme wndows for an outbound request. In our real-world problem t s desred to mnmze transportaton costs and to maxmze the qualty of servce for patents whle the followng constrants are consdered. Frst, the maxmum transport tme L measured from the startng of loadng B k untl the startng of unloadng B +n k s lmted to the drect drvng tme from locaton to locaton +n plus the maxmum watng tme W. L = t, + n + W P Second, a vehcle k s not allowed to wat dle whle a patent s on board. Below, we use Q k to denote the load of a vehcle k after ts vst at locaton : we force to serve the pck-up at locaton j and the delvery at locaton wthout detour or watng n between f Q k s postve after vstng locaton. B k j D k = t j x k j = 1 Q 0 k The overall objectve n our problem s to optmze two crtera: mnmze transportaton costs and maxmze qualty of servce for the regular transportaton orders. Each crteron s normalzed to a value n the nterval [0,1] and weghted wth a constant factor. Emergency transportaton orders are gnored snce they have to be served as soon as possble. Total costs of transportaton usually nclude vehcle and personnel costs lke drver wages, fuel costs, and other costs. Snce a detaled cost structure s not avalable, we consder the overall tour length stated n drvng tme to be a suffcent proxy measure for transportaton costs. The objectve of mnmzng transportaton costs s thus stated as mn x j t. k K N j N Qualty of servce for regular transportaton orders depends on customer watng tmes, relatve customer rde tme (.e., total tme spent n vehcles compared wth mnmum possble tme), and dfference between actual and desred pck-up and drop-off tmes. These crtera are nterrelated: k j 18

6 some are treated as constrants, some as part of the objectve functon. In our nterpretaton, the objectve of maxmzng qualty of servce for regular transportaton orders s thus stated as mnmzng the sum of watng tmes, where watng tmes are defned as devatons from desred pckup or delvery tme. mn k * * k ( B e ) + ( l + n B + n ) k K P g = 0 P g = 1 The weghtng factors for the dfferent objectve crtera are not subject to our observatons. We beleve that fxng ther values remans as an open poltcal and manageral challenge. 3. Decson support for ambulance dspatchng Patent transportaton and emergency servces n Austra are organzed n regonal unts. Although a number of control center solutons are used, schedulng of vehcles s done manually by human dspatchers wth all solutons. The solutons are supported by customzed nformaton systems provdng mmedate access to all relevant data about transportaton requests, vehcle states and equpments, etc. To enhance the current way of ambulance schedulng we suggest extendng exstng control center systems wth components of a model-drven decson support system (see [13]). Due to practcal ssues two sde constrants have to be consdered: (1) Exstng workflows, servce- and admnstratve processes, roles of staff, and nfrastructure are not subject to change. (2) The exstng control center systems may not provde all nterfaces to smoothly ntegrate optmzaton components, schedulng recommendatons, or even sem-automatc vehcle schedulng. Thus, decson support should work wth a mnmum set of nterface requrements to exstng systems. For a practcal case study about usng decson support elements n ambulance schedulng we collaborate wth the Red Cross n Salzburg (RCS) to use ther current processes and nfrastructure. RCS uses a modern system that features wrelessly connected moble nformaton systems on the vehcles. The system supports ntegrated order management and regularly sends vehcle postons and operaton states to the control center, whch already helped mprovng effcency of transportaton operatons (see [7]). In order to elct ways to support dspatchers n ther everyday work and to explore correspondng requrements from an end-user perspectve, two workshops wth dspatchers were organzed. Man results of those dscussons were: (1) Dspatchers face dffcultes to overlook the entre quantty of transportaton requests to fnd synerges. Thus, the most mportant feature of a decson support system s a flter (or recommendaton), whch transportaton orders could (and also should) be servced as a group. We call ths strategy to combne transportaton requests and provde a more detaled examnaton of ths ssue. (2) The fnal assgnment of a transportaton order to a vehcle s done on short notce, because emergency requests and new regular transportaton orders may come n any tme. A rough schedule mght be planned some tme n advance, but usually ths draft schedule s altered frequently. Thus, the response tme of a real-world decson support system has to be clearly less than one mnute whle the plannng horzon s typcally a few hours. 19

7 (3) Human dspatchers consder a broad range of hard and soft constrants n ther decsons, whch could not exhaustvely be ncorporated n a model-based approach. Nevertheless, an ntutve and fast way of processng recommendatons for assgnments of orders to vehcles s requred. (4) A decson support system should make no decsons wthout a human dspatcher ths clearly states that a sem-automatc ambulance schedulng approach s not up for dscusson. As a result of these fndngs we propose two features of the decson support system. Frst, a lst of currently possble combnatons of transportaton requests should be gven, regardless of vehcle avalablty. The lst should also value the combnatons n terms of tour length and watng tme as well as state the latest tme that the mplementaton of the combnaton has to be decded. Second, a vsual representaton of a suggested schedule for all vehcles should be shown. Wth ths llustraton human dspatchers can vew the suggested assgnment of requests to vehcles Combnaton of transportaton requests If two or more transportaton requests meet vehcle capacty and tme restrctons, they may be combned,.e., more than one patent s on board of a vehcle at the same tme. Two basc schemes of combnatons apply to our problem structure and are depcted n Fg. 2: The common sequence of requests s one after another lke shown n sub-pcture (1) where pck-up and delvery for each request are scheduled consecutvely. In the frst scheme of combnaton shown n sub-pcture (2) two pck-ups are scheduled consecutvely and the request that was pcked up later s delvered frst. The second scheme shown n sub-pcture (3) also features two consecutve pck-ups frst, but here the request pcked up later s delvered last. (1) (2) (3) Pck-up Delvery Fg. 2: Transportaton request combnaton schemes. Usng these optons for combnatons of requests may lead to shorter tour lengths or watng tmes or both, but only requests n temporal and spatal proxmty are benefcal and fulfll the maxmum transportaton tme restrcton. Certanly, these schemes of combnatons are also appled to a hgher number of combned requests Vsualzaton of a suggested schedule In order to provde an ntutve vsualzaton of calculated schedulng recommendatons we propose to use a bar chart approach for communcaton wth human dspatchers. Fg. 3 llustrates a prototype vsualzaton module that shows each vehcle and ts suggested requests on a separate lne. The pcture shows request types denoted as D for delveres (and P for pck-ups), begnnng tmes of pck-ups and endng tmes of delveres as well as combnatons of requests. 20

8 4. Soluton procedures and results Fg. 3: Vsual representaton of a schedule In order to study dfferent dspatch strateges for the problem at hand, we developed a smple and effectve soluton procedure: We mplemented a constructve heurstc approach. In the constructon phase, we explot the temporal structure of requests and use a nearest-neghbor measure nspred by [8]. Addtonally, a more sophstcated soluton approach correspondng to the plot method of [14] was mplemented and compared to the heurstc procedure. Each soluton procedure s capable to deal wth the statc and the dynamc verson of the DARP. In the dynamc case, the lst of transportaton requests changes over tme. Furthermore, dsruptons are consdered, whch are caused by emergency requests that are not known beforehand and must be served wth hgh prorty. In case of an emergency, the empty vehcle whch s closest to the emergency locaton wll be redrected and s not avalable for regular operaton any more. In ths stuaton, a re-calculaton of the schedule s necessary. The heurstc soluton procedure follows a greedy approach and constructs a vald soluton n a step-wse process: n a pre-processng step a sorted lst of requests s computed and processed startng from the earlest to the latest request untl the lst s empty. In each constructon step a further request s added to one of the tours n the current soluton. To determne the request to be added a set of most promsng tour-request pars s computed n each step. The decson crteron s the dstance from the delvery locaton of the last request to the pck-up locaton of the current request. The plot method may be characterzed as general approach to enhance a constructve heurstc procedure whle provdng a sophstcated decson rule n each constructon step. The basc dea s to avod unfavorable decsons by lookng ahead for each choce to be made. In our case the heurstc soluton procedure descrbed above s used as ntal heurstc that s extended wth the plot concept. Our plot method procedure evaluates a number of promsng optons n each constructon step whle computng a plot soluton for each opton. All plot optons are then revewed usng the overall objectve functon. The best soluton determnes the opton that s fnally fxed n each constructon step. Note that n contrast to the classc approach reported by [14] we evaluate not all but only a lmted number of promsng solutons n each step. To evaluate the soluton methods a set of 15 problem nstances taken from a larger real-world dataset of the Austran Red Cross wth a number of regular transportaton requests rangng from 152 to 286 was used. Table 1 shows the average results for all 15 nstances, where the objectves of tour length and watng tme were weghted 4:1. The results for the plot method are average values a number of 2 to 8 plot solutons were evaluated n each stop of the procedure and results for 2 and 8 plot solutons. Table 2 shows run tmes for the soluton methods calculatng complete solutons for the smallest, a medum and the bggest problem nstance on an Intel XEON CPU wth 2.8 GHz and 4 GB RAM. Note that the heurstc procedure and even the plot method wth 2 plot solutons are fast enough to provde solutons n most cases wthn the requested response tme of one mnute. Due to the dynamc nature of the problem, a rollng horzon may be appled n practce and 21

9 substantally shorten run tmes. Ths means that even a hgher number of plot solutons may be calculated and the soluton procedure stll performs n tme as long as the number of consdered requests n the rollng plannng horzon s reduced properly. Table 1: Optmzaton results of 15 nstances wth 150+ to 280+ transportaton requests. Soluton method Objectve value Tour length Watng tme Heurstc procedure 100% 100% 100% Plot method (avg.) 91,7% 86,6% 120,6% Plot method (2 plots) 93,1% 87,0% 127,8% Plot method (8 plots) 91,1% 86,6% 116,0% Table 2: Run tmes n seconds. Number of transportaton requests per nstance Heurstc procedure Plot method (2 plot solutons) Smallest (152 reqs.) 0,09s 9,27s 32,8s Medum (218 reqs.) 0,25s 35,9s 129s Bggest (286 reqs.) 0,38s 69,2s 254s Plot method (8 plot solutons) Investgatng parameter settngs for the plot method, we found that watng tme declnes by far more than the tour length wth an ascendng number of plot solutons. The results gven n Fg. 4 are average values over 15 problem nstances. Results n relaton to average 107,0% 105,0% 103,0% 101,0% 99,0% 97,0% 95,0% Objectve value Tour length Watng tme Number of plot solutons evaluated n each step Fg. 4: Results of the plot method dependng on number of plot solutons used 5. Integraton of decson support servces nto a control center system In Austra, several control center solutons for ambulance schedulng are currently run by regonal branches of the Austran Red Cross. The descrbed soluton procedure has the potental to enhance effcency n any exstng control center system. Therefore, decson support functonalty to enable more effcent ambulance schedulng could and should be ntegrated nto an exstng system. It s the am of the Ambulance Routng project to demonstrate potental advantages of optmzaton algorthms n a plot settng together wth the Red Cross Salzburg. Ths case study ams at llustratng the use of optmzaton algorthms to provde busness servces n a practcal envronment. Snce one could not expect a control center system to feature all the necessary nterfaces to smoothly ntegrate schedulng recommendatons we propose a loosely coupled system archtecture that mnmzes dependences between decson support components and the rest of the system. 22

10 Fg. 5 shows an overvew of the proposed decson support system, where on the left sde an exstng control center soluton s depcted. Extensons for decson support are shown on the rght sde and color-coded dfferently. To provde schedulng recommendatons for human dspatchers the system proceeds as follows: (1) A lst of current and forthcomng requests and current vehcle states s obtaned from the Control Center System and pre-processed n the Integraton System (2) Soluton procedures are appled to the transportaton request data and a recommendaton of a promsng vehcle schedule s calculated (3) The recommended schedule s vsualzed to the human dspatcher, who can decde whether to ncorporate parts of the suggested tour plans or not. The actual decsons of the dspatcher are fed back to the schedule recommender va (1). Control Center System (1) nput data Integraton System {1} Solver {2} (3) vsualzaton (2) schedule Dspatcher Schedule Vsualzer {3} Fg. 5: Ambulance routng decson support system overvew. All nput data (1) for the decson support sub-system s gathered va a sngle web-servce nterface that provdes a complete snapshot of dspatchng status. The Integraton System {1} and the Schedule Vsualzer {3} are mplemented wth Java technology, whle the Solver {2} s mplemented n C++ for performance reasons. 6. Concluson and Outlook In ths paper we ntroduced a vehcle routng problem relevant to ambulance schedulng. The problem s based on the well-known dal-a-rde problem (DARP), but features a specal extenson that causes dsruptons because of emergency servce requests. We reported restrctons and constrants for the development of a decson support extenson for an exstng control center system. The fndngs were gathered from workshops wth human dspatchers. We developed two soluton approaches, a greedy heurstc and a plot method procedure sutable for a smplfed b-objectve verson of the dynamc DARP. We evaluated the soluton procedures wth real-world test data from an ambulance servce provder n Austra and compared the results. We found that both algorthms perform well enough n terms of runtme. Fnally, we suggested a system archtecture wth a web-servce nterface for ntegraton of our soluton procedures nto an exstng system. Next steps n the Ambulance Routng project wll be the ntegraton of all components of the archtecture nto a runnng prototype system, whch wll be used for evaluaton of our approach under real-world condtons. Expected fndngs of these nvestgatons wll be actual mprovements enabled through optmzaton as well as a measure for the qualty of our schedule recommendatons. 23

11 7. Acknowledgements We would lke to thank Stefan Achletner, Uwe Krchengast, and Mchael Sprnzl for ther contrbutons to the bar chart vsualzaton of vehcle schedules. Furthermore, fnancal support from the Austran Scence Fund (Fonds für wssenschaftlche Forschung; FWF) under grant #L286-N04 s gratefully acknowledged. 8. References [1] ATTANASIO, A., CORDEAU, J.-F., GHIANI, G., and LAPORTE, G. (2004), Parallel Tabu search heurstcs for the dynamc mult-vehcle dal-a-rde problem, Parallel Computng 30, [2] BASNET, C., FOULDS, L. and IGBARIA, M., FleetManager: a mcrocomputer-based decson support system for vehcle routng, Decson Support Systems 16, , 1996 [3] CORDEAU, J.-F., and LAPORTE, G., The Dal-a-Rde Problem (DARP): Varants modellng ssues and algorthms, 4OR 1, [4] CORDEAU, J.-F., and LAPORTE, G., A tabu search heurstc for the statc mult-vehcle dal-a-rde problem, Transportaton Research B 37, [5] GENDREAU, M., GUERTIN, F., POTVIN, J.-Y., and SÉGUIN, R., Neghborhood Search heurstc for a Dynamc Vehcle Dspatchng Problem wth Pck-ups and Delveres, Techncal Report, Centre de recherche sur les transports, Unversté de Montréal, Forthcomng n Transportaton Research C [6] GOEL, A., Fleet Telematcs Real-Tme Management and Plannng of Commercal Vehcle Operatons, Operatons Research/Computer Scence Interfaces, Sprnger, 2008 [7] GOEL, A., and GRUHN, V., Integraton of telematcs for effcent management of carrer operatons, In: Proceedngs of the IEEE Internatonal Conference on e-busness Engneerng (ICEBE 2005), , 2005 [8] JAW J.-J., ODONI, A., PSARAFTIS, H., and WILSON, N., A heurstc algorthm for the mult-vehcle advance request dal-a-rde problem wth tme wndows, Transportaton Research B 20 (3), [9] KEENAN, P., Spatal decson support systems for vehcle routng, Decson Support Systems 22, 65-71, 1998 [10] KIECHLE, G., DOERNER, K., GENDREAU, M., and HARTL, R., Patent Transportaton - Dynamc Dal-a-Rde and Emergency Transportaton Problems, Preprnts of Sxth Trennal Symposum on Transportaton Analyss (TRISTAN), 2007 [11] MITROVIĆ-MINIĆ, S., KRISHNAMURTI, R., and LAPORTE, G., Doublehorzon based heurstcs for the dynamc pck-up and delvery problem wth tme wndows, Transportaton Research B 38, [12] SAVELSBERGH, M. W. P., and SOL, M., DRIVE : Dynamc Routng of Independent Vehcles. Operatons Research 46 (4), [13] SHIM, J. P., WARKENTIN, M., COURTNEY, J. F., POWER, D. J., SHARDA, R. and CARLSSON, C., Past, present, and future of decson support technology, Decson Support Systems 33, [14] VOSS, S., FINK, A., and DUIN, C., Lookng Ahead wth the Plot Method. Annals of Operatons Research 136 (1),