An optimization model for scheduling emergency operations with multiple teams

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1 Proceedings of the 2016 International Conference on Indstrial Engineering and Operations Management An optimization model for schedling emergency operations with mltiple teams Behrooz Bodaghi Faclty of Science, Engineering and Technology Swinbrne University of Technology Hawthorn, Victoria 3122, Astralia Ekambaram Palaneeswaran Faclty of Science, Engineering and Technology Swinbrne University of Technology Hawthorn, Victoria 3122, Astralia Abstract Post-disaster emergency operations are often chaotic and complex. In most cases, efficiently assigning and schedling mltiple teams of resorces are essential for qick and effective disaster relief. Or ongoing research has identified nmeros heristics and mathematical models for resorce schedling, of which only a few incorporate synchronization and optimization of mlti-team resorce schedling contexts. This paper presents a novel mixed integer linear programming model to minimize the relief operation completion times reqired for all incidents by optimally assigning and schedling varios teams of non-expendable resorces. Key parameters of the model inclde: nmber of incidents, severity level of each incident, nmber of relief teams of non-expendable resorces, type and capability of relief teams, resorce reqirements at each incident, travel times, process times and release times. Or primary evalation of the model considered a case stdy simlation of resorce schedling for some hypothetical fire emergency operations in a central district of the Melborne metropolitan area. The reslts are encoraging for practical applications in potential emergency operation management. Keywords Emergency operation, Resorce schedling, Optimization, Synchronization 1. Introdction Emergency operations management dring natral or other disasters is often a complex challenge, which involves nmeros individals and organizations as well as diverse chaos, priorities and limitations. Failres to assign relevant resorces sfficiently in a timely manner may worsen the disaster impacts and escalate casalties (Rolland, Patterson, Ward, and Dodin, 2010). Or ongoing research revealed that several practices adopt discrete makeshift approaches to coordinate the emergency tasks of recovery responses for disaster impacts. One of the complex decisions in the emergency operation management dring the post-disaster response phase is how to swiftly assign and schedle mltiple teams of non-expendable resorces (e.g. resce nits, and volnteers) to the emergency tasks. Or literatre review revealed an array of stdies on emergency operation management (Anaya-Arenas, Renad, and Riz, 2014; Canhye, Nie, and Pokharel, 2012; Galindo and Batta, 2013; Özdamar and Ertem, 2015). However, there is only limited research on assigning and schedling varios teams of non-expendable resorces according to severity levels of emergency disaster relief works. For example, Falasca and Zobel (2012) and Lassiter, Khademi, and Taaffe (2015) introdced cost objective integer programming models for allocating and schedling volnteers for disaster emergency operations. The time-based objective optimization problem was considered by Felix Wex, Schryen, Feerriegel, and Nemann (2014), who proposed a non-linear programming model with a set of heristics to allocate and schedle resce nits to minimize the completion time of incidents as per weighted consideration of 436

2 Proceedings of the 2016 International Conference on Indstrial Engineering and Operations Management severity levels. Only a few stdies have considered that each incident reqire mltiple teams of resorces and synchronizing the emergency operations according to their availability. For example, Wex, Schryen, and Nemann (2013) and Schryen, Rachecker, and Comes (2015) developed non-linear mathematical models for assigning and schedling resce nits to incidents, which take into accont the fact that each incident may reqire a single resce nit or a collaboration of resce nits may be needed for each incident. Still, both these models inclde certain heristics to solve and compare the soltion with some practice otcomes. This paper presents a novel mixed integer linear programming model to minimize the completion times of emergency relief operations at all incidents/ demand points by optimally synchronizing assignment and schedling of varios teams. This model can be sefl for decision makers seeking to optimize the relief operation completion times by: (1) effectively considering: (a) simltaneos incidents with different severity levels, (b) availability of varios teams with different capability; and (2) efficiently assigning and schedling mltiple teams of non-expendable resorces with optimal synchronization to address: (a) diverse demands at different incidents or demand points/ locations, (b) different sorces/ base station locations (for teams) and travel times. 2. Model development Primarily, or model development considered that the problem of the disaster response sitation is deterministic/ static. Figre 1 portrays a set of incidents. Frthermore, we examined the disaster response sitation with scarce resorces in which the incidents that need to be served by mltiple teams of non-expendable resorces are mch higher than the availability of teams. There is a given processing time for each incident once the relief operation for specific point starts. The processing time varies for each incident and depends on each team of non-expendable resorces (each team has a niqe processing time to process each incident). Similarly, transportation time for teams is varied and depends on each team. When the process for the incident has been completed, the teams are released for the next incident on their rote. For the objective fnction, we try to minimize the total weighted completion times over all incidents. The weighted factor depends on the severity level of damage and the total nmber of casalties that reqire relief on each incident. Hence, synchronization of the teams of non-expendable resorce dring the disaster response is reqired to lessen the incident s completion time and delay on the releif reqired on each incident. In addition, the following assmptions are considered: Different teams sch as medical nits, fire brigades, and volnteers (e.g. Victoria State Emergency Service team) are available for emergency operations. The size and capabilities of each team may be different. The demand at each incident may be different. Each incident may reqire different teams. However, an incident cannot reqest more than one team of the same type. If the demand at a demand point/ location is more than the capability of a single available team of a particlar type, then simltaneos occrrence of mltiple incidents at the same demand point/ location will be sitably considered by the model The service starting time is driven by the latest team arrival time. The incident processing after commencement will not be interrpted (non-preemption).... Notation An incident at a demand point/ location A non-expendable resorce team base station Seqence and rote of Team 1 Seqence and rote of Team n Figre.1 A network conceptalization of emergency relief operations 3. Mathematical formlation The mixed integer linear programming model described in this paper aims to find the optimal schedle and assignment of resorces to incidents. The notations sed in this model are consolidated in Table

3 Proceedings of the 2016 International Conference on Indstrial Engineering and Operations Management Table 1. Notations sed in the mixed integer linear programming mathematical model Notation Description n Total nmber of incidents, with set i = {1,, n} t ij Travel time reqired by team to move from incident i to incident j, for all i, j I, U M Sfficiently large nmber U Total nmber of teams with set = {1,, UU} p i Time reqired by each team to process to process incident ii for all ii II, UU r Release time of team at its depot for all UU ω i Severity level of incident ii t Type of team of non-expendable resorces (e.g. medical team, fire fighters) with set t = {1,, T} α it Reqirement of team type tt on each incident, where αα iiii = 1 if the incident ii reqires the team type tt; otherwise is zero. β t Capability of team for skill type tt. Where ββ = 1 if the team capable for skill type tt; otherwise is zero. The decision variables of the model are: X ij {0,1} Seqence of incidents visit by non-expendable resorces. XX iiii = 1 if incident ii is processed by team immediately before processing incident jj;0 otherwise for all ii, jj II, UU S i Starting time of service at incident ii, for all ii II Completion time of service at incident ii, for all ii II C i With these notations and variables, the mathematical model (P1) can be transcribed as below: n Min Z = ω i C i i=1 (1) Sbject to: n+1 U β t X ij = 1 j=1 =1 n+1 X 0(j) j=1 = 1 i I; t T; α it 0 (2) U (3) U U X ij + X ji =1 =1 1 i I ; j J (4) n n+1 X il X lj = 0 i=0 j=1 l I; U (5) X ij = 0 i I ; j J; U; i = j (6) S i + p i + t ij S j + M 1 X ij i I ; j J; U (7) C i S i + (p i X ij ) i I ; j J; U (8) 438

4 Proceedings of the 2016 International Conference on Indstrial Engineering and Operations Management S i 0 i I (9) X ij {0,1} i I ; j J; U (10) In this model, the objective fnction (1) is to minimize the weighted sm of completion times over all incidents. The constraint sets (2) (6) relate to finding the optimal seqence of incidents visited by teams of non-expendable resorces. For each team, two milestones are considered as the starting and end points (given by 0 for starting point and n + 1 for ending). The processing time for starting point is eqal to release time (PP 0 = rr ) and for the ending point is zero (PP nn+1 = 0). Regarding the transportation time, each team of non-expendable resorce needs a specific tt 0jj to arrive to particlar incident jj from its starting point. For all teams of non-expendable resorces, tt ii nn+1 = 0. Constraint (2) ensres that one relevant scceeding incident jj can be processed after completing the operations of a particlar demand point i by a team. Constraint (3) ensres that each team starts to process incidents from a base station/ depot (incident 0). Constraint (4) eliminates loop in processing of incidents by each team. Constraint (5) garantees that if an instant predecessor is available for each incident, it shold be an immediate sccessor for that nless it will be the last incident (incident nn + 1). Constraint (6) eliminates the establishment of any reflection precedence relationship. Constraint (7) ensres that the starting time of processing of each incident cannot be earlier than the earliest arrival time of the teams of non-expendable resorces. Constraint (8) calclates the completion time of the entire operation at each incident. Constraints (9) and (10) define the domains of variables CC ii, SS ii aaaaaa XX iiii. 4. Illstrative example, reslts, and discssion To evalate the model, a simlated case stdy of a hypothetical fire emergency scenario in the Melborne Metropolitan Fire Brigade (MFB) central district has been considered. It aims at demonstrating potential applicability of the model in a practical disaster emergency sitation. All information has been randomly generated de to the navailability of real data. We have considered a simltaneos occrrence of mltiple fire emergencies in the case stdy region. Frthermore, the case stdy assmed the emergency management has following resorces and demand points: (a) two medical teams, (b) two fire fighter teams and (c) 15 simltaneos incidents. Also, we have considered that the Royal Melborne Hospital and MFB Station No.1 as the primary depot for medical teams and fire brigade teams respectively. The topology and rote data sch as road network, location of hospital and MFB station have been retrieved from the Victorian Government Open data 1. Figre 2 illstrates the location of nodes in the Central district of Melborne. The shortest travel distance between nodes with average speed of 25 km/h is considered as the basis for compting the travel times of resorces between nodes. Tables 2 and 3 provide frther details of the case. The model was solved by the IBM ILOG CPLEX 12.6 solver and a smmary of the obtained soltion is portrayed in Figre 2. The reslts indicate that the model has sccessflly generated the optimal schedling plan for assigning and schedling mltiple teams of non-expendable resorces for emergency operations. In this case stdy evalation, the objective fnction of the model is and the longest path was completed at 3.30 hors. The longest path was completed at incident no.14. The details of starting and completion time of operation in each incident are consolidated in Table 4. For instance, the medical team 1 starts the relief operation from incident 7, then it passes to incident 10 and then finished the relief operation at incident 12. Likewise, the fire fighter team 1 starts the relief operation at incident 15, then passes throgh incidents and finally finishes the operation at incident 14. The optimal team rotes are portrayed in Figre 2. Table 2. Parameters of case stdy for evalationg the model Inpt Parameters Vale, range or distribtion The total nmber of incidents (nn) 15 The total nmber of team of non-expendable resorces () 4 Processing time of each incident (PP ii ) ( in hors) Uniform (0,1) Teams release time from the base (rr )( in hors) Uniform (0,1) Severity level (factor of destrction)incidents (WW ii ) Uniform (1,6)

5 Proceedings of the 2016 International Conference on Indstrial Engineering and Operations Management No. Severity level Medical nit reqirement (α it ) Table 3. Example inpts of case stdy for model evalation Processing Processing Fire fighter time for time for reqirement medical medical (α it ) team 1 team 2 1 Processing time for fire fighter team Processing time for fire fighter team 2 Wi t=1 t=2 Pi1 Pi2 Pi3 Pi Table 4. Model soltion for the case stdy scenario No. Starting time Completion time Weighted completion time i Si Ci Wi Ci Total = Or review identified that some ad hoc measres or sbjective decisions are being followed in many practices. The optimization model presented in this paper can effectively facilitate optimal schedling of emergency operations and synchronization of different essential resorces for efficient otcomes. 440

Proceedings of the 2016 International Conference on Indstrial Engineering and Operations Management Figre2. Optimal soltion of rote and seqence for the case stdy problem 5.

6 Proceedings of the 2016 International Conference on Indstrial Engineering and Operations Management Figre2. Optimal soltion of rote and seqence for the case stdy problem 5. Conclsion This paper presents a novel mixed integer linear programming model is presented to optimally assign and schedle mltiple teams of non-expendable resorces for emergency operations of disaster response. The proposed model considered the sitations that reqire synchronization of mltiple teams. A hypothetically simlated case stdy in Melborne s central district area was sed for verifying the performance of the model. The reslts demonstrate the optimal soltion with synchronization of resorce assignment and schedling emergency operations. The developed model is capable of potential applications in relevant real emergency operations. Or ongoing research is focsed on model constrcts inclding additional aspects sch as coordinating varios expendable and non-expendable resorces, diverse vehicles and capacities. Frthermore, it wold be valable to extend the model with aspects sch as ncertainties and dynamic changes of incident resorce demands (e.g. emergent/ volatile changes at incidents). References Anaya-Arenas, A. M., Renad, J., and Riz, A., Relief distribtion networks: a systematic review, Annals of Operations Research, vol. 223, no. 1, pp , Canhye, A. M., Nie, X., and Pokharel, S., Optimization models in emergency logistics: A literatre review, Socio- Economic Planning Sciences, vol. 46, no. 1, pp. 4-13, Falasca, M., and Zobel, C., An optimization model for volnteer assignments in hmanitarian organizations, Socio- Economic Planning Sciences, vol. 46, no. 4, pp , Galindo, G., and Batta, R., Review of recent developments in OR/MS research in disaster operations management, Eropean Jornal of Operational Research, vol. 230, no.2, pp , Lassiter, K., Khademi, A., and Taaffe, K. M., A robst optimization approach to volnteer management in hmanitarian crises, International Jornal of Prodction Economics, vol. 163, pp , Özdamar, L., and Ertem, M. A., Models, soltions and enabling technologies in hmanitarian logistics, Eropean Jornal of Operational Research, vol. 244, no. 1, pp , Rolland, E., Patterson, R., Ward, K., and Dodin, B., Decision spport for disaster management, Operations Management Research, vol.3, no.1, pp ,

7 Proceedings of the 2016 International Conference on Indstrial Engineering and Operations Management Schryen, G., Rachecker, G., and Comes, T., Resorce planning in disaster response. Bsiness and Information Systems Engineering, vol.57, no. 4, pp , Wex, F., Schryen, G., Feerriegel, S., and Nemann, D., Emergency response in natral disaster management: allocation and schedling of resce nits, Eropean Jornal of Operational Research, vol. 235, no.3, pp , Wex, F., Schryen, G., and Nemann, D., Decision modeling for assignments of collaborative resce nits dring emergency response. Proceedings of the 46th Hawaii International Conference on the System Sciences (HICSS), Hawaii, USA, Jan. 7 10, Biography Behrooz Bodaghi is crrently a fll time PhD candidate affiliated with the Centre for Sstainable Infrastrctre and the Department of Civil and Constrction Engineering at the Swinbrne University of Technology, Astralia. He earned B.S. in Indstrial Engineering from Mazandaran University of Science and Technology, Iran, and a Masters in Indstrial Engineering from University Teknologi Malaysia (UTM), Malaysia. His research interests inclde optimization, schedling, manfactring, spply chain management and lean management. Palaneeswaran Ekambaram is an Associate Professor, Postgradate Program Coordinator and Director of Constrction and Infrastrctre Management corses in the Faclty of Science, Engineering and Technology at Swinbrne University of Technology, Astralia. He completed BE and ME (Honors) degrees from India and received his PhD from the University of Hong Kong. Prior to joining in Swinbrne, he served as an academic staff at the University of Hong Kong and City University of Hong Kong. He has pblished 100+ peer-reviewed research papers and recipient of several prestigios awards/ grants inclding competitive grants from Astralian Research Concil and Hong Kong Research Grants Concil. He is affiliated with professional instittions sch as ASCE, IEEE, ISTE, and PMI. 442

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