Simulation-based Decision Support System for Real-time Disaster Response Management

Transcription

1 Proceedngs of the 2008 Industral Engneerng Research Conference J. Fowler and S. Mason, eds. Smulaton-based Decson Support System for Real-tme Dsaster Response Management Shengnan Wu, Larry Shuman, Bopaya Bdanda, Oleg Prokopyev Swanson School of Engneerng Matthew Kelley, Ken Sochats School of Informaton Scences Carey Balaban School of Medcne Unversty of Pttsburgh, Pttsburgh, Pennsylvana 15260, USA Abstract We have merged agent-based modelng, dscrete event smulaton, and geographcal nformaton systems (GIS) nto one seamlessly ntegrated platform to smulate maor dsaster events n real tme. One advantage of ths hybrd archtecture s the ablty to assess the mpact of agent rules on outcomes n dsaster scenaros. A heurstc top-level framework has been developed to generate evolutonary, near-optmal dspatchng decsons for the responders. The model consders multple obectves and can dynamcally drve the overall system towards a better performance over tme. Because the users can nteract wth the smulaton platform at a very hgh level lnked to famlar nterface features such as maps, t s accessble to end-users such as ncdent managers and decson makers wth lttle smulaton experence. Keywords Dsaster management, emergency response, smulaton optmzaton, decson support system, real-tme decson makng 1. Introducton Effectve decson support for dsaster plannng and response management requres smulaton of a large number of tme-varyng factors and agents. These problem features render any purely analytcal methods ether neffectve or neffcent. Smulaton s an attractve alternatve approach to model the behavor of the large-scale stochastc systems. We have used agent-based dscrete event smulaton as a prmary tool to model the frst and secondary responses to catastrophc dsasters. The ntegrated system ncludes comprehensve capabltes to smulate the responders operatons/actons and nteractons wth envronmental factors such as weather patterns, traffc congeston and vctm deteroraton. The system has been valdated by comparsons wth hstorcal data and revew of results by experts. Although smulaton s useful for modelng the expected behavor of complex operatonal systems, one must mantan the caveat that t s a prescrptve tool that may not necessarly be compatble wth optmzaton procedures drectly. One great advantage of our smulaton system called Dynamc Dscrete Dsaster Decson Support System (D 4 S 2 ) s the seamless ntegraton of the smulaton archtecture wth other components ncludng a geographcal nformaton system (GIS) nfrastructure data, user-frendly graphcal nterfaces and dsaster nformaton databases [1-4]. The computatonal flow n the system archtecture s also based upon the recognton that dsaster responses are an evolutonary decson process. The facts that decsons are nfluenced by events and mplementaton of decsons wll alter subsequent events are mplct n the teratve and nteractve updatng of the data bases durng the smulaton, whch effectvely reset the ntal condtons for the next decson teraton. We have also ncorporated a Mxed Integer Program (MIP) model formulaton (see secton 3) to set ntal condtons for local optmzaton of solutons, whch greatly reduces computaton tme and resources. 58

2 Wu, Shuman, Bdanda, Prokopyev, Kelley, Sochats and Balaban 2. Evolutonary Decson General Framework Most large-scale systems and complex processes evolve over tme frames rangng from hours to days to even longer perods. The response of agences to catastrophc dsaster s a typcal example of a large-scale complex system because a maor dsaster normally nvolves a large number of vctms, multple response partes from each agency and multple response agences (governmental and non-governmental sectors). Durng the course of the event, no sngle decson path s unversally applcable to all scenaros: new, unexpected condtons may arse for whch prevous response decsons must be modfed. Fgure 1 llustrates a basc smulaton-based evolutonary decson process. Fgure 1: Evolutonary decson process The evolutonary decson procedure s descrbed as follows: At tme t : Deploy a new decson D whch was made n the last teraton of the process. If t 0 (start of the event), an experence-based expert decson D s preferred because there s no tme for detaled 0 analyss. Ths decson must be vald for all hazards, n the sense that t must (1) not exacerbate the stuaton drectly (.e., produce a deleterous outcome) and (2) not create deleterous bottlenecks or constrants on ensung decsons. Real-tme, actual data of current tme can be nput as ntal condtons for the frst teraton of the decson process. Durng tme t ~ t : Run the smulator to the next decson pont (smulaton tme) t. Store the smulaton results of tme t as SR. Solve a closed-form Mxed Integer Program (MIP, see secton 3 below) formulaton whch can ~ approxmate the smulaton system to rapdly obtan a near-optmal soluton D at tme t. SR 1 and/or earler smulaton results wll be used to form the MIP model. The obectves are evaluated for tme perod t ~ t. From D ~, we perform smulaton-based local searches to mprove the soluton. The best soluton becomes D. The smulator runs from t to t (smulaton tme) usng SR as the ntal condtons. At tme t : Deploy D and begn the next teraton. 3. Mxed-Integer Program (MIP) Formulaton The dsaster response smulaton system can represent the real system better than analytcal models but at great expense n computaton tme. However, because dsaster response decsons are normally extremely urgent, a tmeconsumng smulaton process to search for optmal soluton(s) s mpractcal and undesrable. An analytcal MIP model has been developed to streamlne the process of obtanng optmal solutons. The MIP model provdes a rapd soluton to gude the search nto a promsng neghborhood n the soluton space. If ntal search condtons are establshed by hgh-qualty (near-optmal) ntal solutons from the MIP formulaton, only a few full smulaton runs are needed for local optmzaton. Solutons to complex decson problems often requre a counterbalancng (or tradeoff) of multple, partally ncompatble obectves. For example, n our case, t s desrable to dspatch more emergency vehcles to the scene n 59

3 Wu, Shuman, Bdanda, Prokopyev, Kelley, Sochats and Balaban order to ncrease the vctm evacuaton capacty. However, the ntroducton of too many vehcles nto the response process (1) ntroduces sgnfcant congeston that can negatvely mpact access for other responders and the evaculaton of casualtes and (2) reduces the capacty to respond to baselne demands for responses to events such as heart attacks and traffc accdents. In some mult-obectve cases, all obectves can be quantfed n the same unts (e.g., monetary unts for economc consequences) to determne the tradeoffs automatcally. Otherwse, one must fnd a set of canddate solutons and let a human decde. Whch solutons should we nclude n the canddate decson set? A soluton s Pareto-optmal f there are no feasble solutons that are at least as good n every obectve. The set of Pareto-optmal solutons s called the effcent fronter or the tradeoff curve. A soluton s domnated f there s another soluton better n one obectve and at least as good n the rest. One approach to fnd Pareto-optmal ponts s to combne the obectves wth some weghts. If all weghts are postve, the combned sngle-obectve program would gve a Pareto-optmal pont, f an optmal soluton exsts [5]. The weghts are normally decded by the expert model users after evaluatng the relatve mportance of all the obectves. Frst, we formulated a nonlnear mxed-nteger program (NMIP), termed a D 4 S 2 -NMIP, by closely nvestgatng the nternal structure of the smulaton model. The model has eght man obectves as lsted below: Ob1. Maxmze scene evacuaton of lfe-threatenng vctms Ob2. Maxmze scene evacuaton of severe vctms Ob3. Maxmze scene evacuaton of moderate vctms Ob4. Mnmze scene fataltes Ob5. Mnmze EMS normal response degradaton Ob6. Mnmze penalty cost for callng mutual ad responders Ob7. Mnmze penalty cost for changng tasks Ob8. Mnmze dspatchng dstance (or tme) Note that all the obectve values are evaluated for the tme perod of defned n Fgure 1. Emergency response plannng s bascally an assgnment problem. Emergency vehcles (e.g., ambulances) are modeled as agents n the smulaton model (agent-based smulaton). These agents are (1) advanced lfe support (ALS) ambulances, (2) basc lfe support (BLS) ambulances, and (3) fre trucks. We want to assgn one of the three possble tasks to each of the agents: (1) respondng to the dsaster, (2) respondng to normal ncdents, and (3) respondng to an external servce area (for mutual ad partners). The model D 4 S 2 -NMIP s presented below. D 4 S 2 -NMIP = Mn. w Q X X Subect to: xk N (1) k x 0 S 3 MutAd (2) S S 1 1 x 1 (3) 2 S S x k 1 x 1 (4) f agent s assgned to response task k 0 otherwse Let N be the set of all n emergency vehcle agents n the system. All agents are dvded nto r subsets. Type agents ( 1,2,...,r) are ncluded n subset S such that S N, S N, and S S,, 1,2,..., r. In our problem, there are three types (r = 3 subsets) of agents: S {ALS ambulances}, S {BLSambulances} and 1 2 S {Fre trucks}. 3 The obectve functon aggregates several ndvdual obectves Q by mposng postve weghts w for each obectve, based upon ther relatve mportance. Note that all the obectve weghts should be postve n order to obtan Pareto-optmal solutons. Wthout loss of generalty, we have mnmzed the aggregated obectve functon. If 60

4 any ndvdual obectve weght term w postve. Wu, Shuman, Bdanda, Prokopyev, Kelley, Sochats and Balaban Q needs to be maxmzed, the Q should be flpped sgn to negatve n order to keep the The decson varables x are bnary. They ndcate the response assgnment for each vehcle agent. Because the task responses are mutually exclusve and collectvely exhaustve, the ntegrty constrant (1) s necessary. Further, gven that the type 3 task s only for mutual ad vehcles, constrant (2) specfes that the n-area vehcles cannot be assgned to a type 3 task for ths dsaster. S s the agent subset of all mutual ad vehcles that are avalable for MutAd the dsaster responses. Constrants (3) and (4) preserve basc EMS coverage by specfyng that at least one emergency medcal servces (EMS) unt, ether ALS or BLS, should respond to the maor dsaster event and the normal emergency events, respectvely. The obectve functons Q have formulated by carefully nvestgatng the nternal operatons of the smulaton model; space lmtatons preclude ther ncluson n ths paper. 4. Computatonal Experment A relatvely small network wth 20 nodes was desgned as a plot study to test the performance of the D 4 S 2 -NMIP smulaton-based approach for dsaster management plannng. It s depcted n Fgure 2. Although the network s small, both the smulaton and optmzaton are fully functonal. Fgure 2: 20-node testng network The network s completely connected (.e., a vehcle at any one node can access to any other node through a fnte path wthn the network). One-way streets are drawn as sngle-arrow connecton lnes; two-way streets are drawn as bdrectonal arrows. Medcal resources (e.g., hosptals, fre statons) are dstrbuted on the network nodes and agentbased emergency vehcles can travel along the network from start nodes to destnaton nodes. The smulaton-based optmzaton procedure s mplemented n VB.NET. The MIP model was generated and solved by the CPLEX Wndows API wth.net. The smulaton-related data were exchanged between the.net program and Rockwell Arena smulaton model through a database. A specfc dsaster scenaro was used to demonstrate the effectveness of the evolutonary decson makng procedure; 260 lfe-threatenng, 346 severe, 223 moderate casualtes occurred n an event at node #4. There were 120 deaths ntally. The hosptal and responder staton nformaton s lsted n Table 1: there were four hosptals and 20 ALS, 8 BLS and 10 Fre responders avalable. The dsaster decson support system generated decsons hourly untl the scene was cleared. The dynamc response solutons were compared wth fxed solutons provded by the experts and/or protocols. Fgure 4 compares the aggregate mult-obectve value between the dynamc solutons obtaned by the evolutonary decson procedure and the fxed expert decsons n the whole tme seres. For ths mnmzaton problem, the dynamc response solutons always obtaned better overall performance. It s hard to nterpret the aggregate obectve values because they do not have physcal meanngs. To better understand the dynamc solutons and ther effectveness, some key ndvdual obectves are extracted n the 61

5 Wu, Shuman, Bdanda, Prokopyev, Kelley, Sochats and Balaban followng. Fgure 5 shows the number of vctms wth lfe-threatenng (LT) nures at the scene as a functon of tme after the catastrophc event. Wth the dynamc solutons, LT patents can be cleared at the 11 th hour, compared wth about 19 hours usng the fxed rule solutons. Table 1: Hosptal and responder statons Hosptal Info Responder Staton Info Locaton (Node) Capacty Node ALS# BLS# Fre# Node ALS# BLS# Fre# #1 Unlmted #1 1 # #2 Unlmted #2 1 1 # #5 Moderate only #4 1 # #17 Unlmted #5 1 1 # #6 2 #16 2 #7 3 # #8 1 #18 1 #9 1 1 # # Aggregate Obectve Value Dynamc MIP Fxed Rule Tme (Hour) Fgure 4: Comparson of aggregate obectve value Dynamc MIP Fxed Rule 200 Scene LT Tme (hour) Fgure 5: Comparson of scene lfe-threatenng vctm evacuaton 62

6 Wu, Shuman, Bdanda, Prokopyev, Kelley, Sochats and Balaban The number of fataltes at the scene s another mportant measure of the response effectveness. Fgure 6 compares the numbers of fataltes between dynamc solutons and fxed solutons. Although the death rate for dynamc solutons s hgher durng the frst nne hours after the response, there s a cumulatve savng of fve lves because the lfe-threatenng vctms are evacuated more rapdly. Further, although the fre responders can help treat/stablze the severe vctms, ther appearance at the scene causes congeston that delays the EMS evacuaton actvty. Thus, the dynamc decson system dspatches the space-consumng fre trucks more conservatvely to tradeoff rapd evacuaton aganst an ncreased on-ste deteroraton rate of severely nured patents Dynamc MIP Fxed Rule Scene Fataltes Tme (hour) Fgure 6: Comparson of scene fataltes 5. Conclusons Ths paper brefly presents a smulaton-based evolutonary decson makng procedure and apples heurstc methods to solve a real-tme dsaster response management problem. The computatonal results from a plot case study have shown the advantage of usng the dynamc decson support system to obtan tme-dependent solutons compared wth fxed expert/rule decsons. Acknowledgements The authors would lke to thank Offce of the Provost at the Unversty of Pttsburgh for the support provded to ths research. Many ndvduals and organzatons offered nsghtful knowledge to the D 4 S 2 proects. Ther nputs are also apprecated. References 1. Wu, S., Shuman, L., Bdanda, B., Kelley, M, Sochats, K., and Balaban, C., 2007, Dsaster Polcy Optmzaton: A Smulaton Based Approach, Proc. of the 2007 Industral Engneerng Research Conference, Nashvlle, TN, Wu, S., Shuman, L., Bdanda, B., Kelley, M., Sochats, K., and Balaban, C., 2007, Embeddng GIS n Dsaster Smulaton, Proc. of the 27th Annual ESRI Internatonal User Conference, San Dego, CA, paper no. UC Wu, S., Shuman, L.J., Bdanda, B., Kelley, M., Sochats, K., and Balaban, C.D., 2007, System Implementaton Issues of Dynamc Dscrete Dsaster Decson Smulaton System (D 4 S 2 ) Phase I, Proc. of the 2007 Wnter Smulaton Conference, Washngton, DC, Wu, S., Shuman, L., Bdanda, B., Kelley, M., Sochats, K., and Balaban, C., 2008, Agent-based Dscrete Event Smulaton Modelng and Valdaton for Emergency Responses, Proc. of the 2008 Industral Engneerng Research Conference, Vancouver, Brtsh Columba (accepted for press). 5. Ehrgott, M., 2005, Multcrtera Optmzaton, 2 nd Edton, Sprnger, New York. 63