11
Click here to load reader
Click here to load reader
European Journal of Operational Research 238 (2014) 363–373
Contents lists available at ScienceDirect
European Journal of Operational Research
journal homepage: www.elsevier .com/locate /e jor
Innovative Applications of O.R.
Mass-casualty triage: Distribution of victims to multiple hospitals usingthe SAVE model
http://dx.doi.org/10.1016/j.ejor.2014.03.0280377-2217/� 2014 Elsevier B.V. All rights reserved.
⇑ Corresponding author. Tel.: +1 207 780 4854.E-mail addresses: [email protected] (M.D. Dean), [email protected]
conn.edu (S.K. Nair).
Matthew D. Dean a,⇑, Suresh K. Nair b
a Business Administration, School of Business, University of Southern Maine, PO Box 9300, Portland, ME 04104-9300, United Statesb Ackerman Scholar and Dun & Bradstreet CITI Research Fellow, OPIM Department, School of Business, Unit 1041, University of Connecticut, Storrs, CT 06269-1041, United States
a r t i c l e i n f o a b s t r a c t
Article history:Received 15 February 2013Accepted 17 March 2014Available online 26 March 2014
Keywords:OR in service industriesRisk managementDisaster managementHealth careVictim distribution
During a mass casualty incident (MCI), to which one of several area hospitals should each victim be sent?These decisions depend on resource availability (both transport and care) and the survival probabilities ofpatients. This paper focuses on the critical time period immediately following the onset of an MCI and isconcerned with how to effectively evacuate victims to the different area hospitals in order to provide thegreatest good to the greatest number of patients while not overwhelming any single hospital. Thisresource-constrained triage problem is formulated as a mixed-integer program, which we call the Sever-ity-Adjusted Victim Evacuation (SAVE) model. It is compared with a model in the extant literature andalso against several current policies commonly used by the so-called incident commander. The experi-ments indicate that the SAVE model provides a marked improvement over the commonly used ad-hocpolicies and an existing model. Two possible implementation strategies are discussed along with mana-gerial conclusions.
� 2014 Elsevier B.V. All rights reserved.
1. Introduction 3. Recovery.
Effective disaster management has gained the attention of thepublic due to numerous recent natural catastrophes. However, inorder to succeed at achieving effective disaster management, thedefinition of the term ‘‘disaster’’ must first be agreed upon. Surpris-ingly, experts in the disaster management field disagree on an ex-act definition of the term. However, several common elementsappear in most definitions. This paper utilizes the definition of amass casualty incident (MCI) as defined by the World Health Orga-nization (WHO) and the terms disaster and MCI are used inter-changeably throughout. The WHO defines a mass casualtyincident (MCI) as ‘‘an incident which generates more patients atone time than locally available resources can manage using routineprocedures’’ (WHO, 2007). Examples of MCI include disasters dueto natural hazards (e.g., floods, earthquakes, etc.) or manmadedisasters such as a bioterrorism attack.
Effective response to a disaster, whether man-made or natural,follows a cyclical, four-step process. These steps include:
1. Preparedness.2. Response.
4. Mitigation.
Preparedness refers to the actions taken before the disaster toallow effective response. Response refers to the emergency actionstaken just before, during, and just after the onset of a disaster toreduce casualties, damage, and disruption. The actions taken aftera disaster to repair, rebuild, and restore community life to nor-malcy is the recovery stage. Mitigation refers to the actions takenboth after one disaster and before another to reduce the physicalimpacts of hazards on a community.
The focus here is on the critical time period immediately follow-ing the onset of an MCI. After victims have been rescued fromimmediate danger, they must be triaged and evacuated to a defin-itive care facility, such as a hospital. The focus of care must be onthe population as a whole rather than the individual, providingthe greatest good for the greatest number of people (Frykberg,2005). Triage plays a vital role during this process. It is the processof assigning treatment and evacuation priorities to victims of anMCI and is used to guide the allocation of the limited health careresources. In effect, it helps determine who will be transportedto which hospital. (For more details on the principles and practiceof triage see Frykberg (2005).)
Once the casualties have been triaged, the orderly distribution ofvictims among different hospitals must take place. However, man-aging the patient load during a disaster presents a major challenge
364 M.D. Dean, S.K. Nair / European Journal of Operational Research 238 (2014) 363–373
to hospitals and disaster response managers. Patient allocationdecisions are typically made by the so-called ‘‘Incident Command’’based on resource availability, situation details (mechanism ofinjury, etc.), and triage data. In urban areas, the possibility of send-ing victims to one of several hospitals adds an additional layer ofcomplexity to the decision process. Initially the goal is to move allvictims out of the immediate vicinity of the disaster scene to a casu-alty collection area. The location of the casualty collection areashould be situated away from the disaster scene due to the dangersit can pose to both health care providers and the survivors(Frykberg, 2002). Patients sent to the casualty collection area aretriaged, treated for immediately life threatening injuries, and trans-ported to area hospitals.
In practice, managing patient allocation across a group of hospi-tals is challenging. Often the nearest hospitals are quickly over-loaded. There are at least two reasons why the nearest hospitalsbecome overwhelmed. First, critically injured patients require med-ical intervention as soon as possible. In many cases this necessitatesthat these patients go to the nearest hospital. Second, decisionsregarding the allocation of patients are complex and response man-agers do not have the ability to dedicate large amounts of resourcesto that task. An easy allocation scheme for the incident commanderis to continue to send victims to the nearest hospital until that hos-pital says it can no longer accommodate new patients.
In order to avoid this geographic effect, a systematic method ofdistribution of casualties from the casualty collection area amongavailable hospitals should occur in a manner that avoids overload-ing any single facility. One suggested approach within the urbansetting is ‘‘leap-frogging’’ of hospitals by sequential loads of trans-ported casualties (Jacobs, Goody, & Sinclair, 1983). For example,send every third victim to a specific more remote hospital. Theproblem with this type of allocation scheme is that it is oftenimplemented in a static fashion as given in the example. However,all disasters are dynamic in nature. As new information concerningthe disaster and the supporting hospitals becomes available, theallocation mechanism should adjust to this new information.
No matter the mechanism, allocation of victims to several facil-ities will depend on the overall objective. The overriding themewithin both the disaster management literature and the disastermanagement community is to ‘‘do the most good for the mostnumber of people’’. This objective is not precise. The two prevailingmethods that attempt to operationalize this vague objective areSTART (simple triage and rapid treatment) and SALT (sort, assess,life-saving interventions, treatment and/or transport). Both STARTand SALT label victims into four broad categories which are in-tended to be indicative of the how quickly a victim should receivecare. Green/Minor victims are considered ambulatory and care canbe delayed for hours. Yellow/Delayed victims generally cannot self-evacuate and the goal is for care to begin within an hour. Red/Immediate victims have life-threatening injuries and require careimmediately. Black/Deceased victims are mortally wounded andno care is required. One major drawback to both of these triagemethodologies is that the prioritization and resource allocationwithin the Immediate and Delayed categories are often subjective.Researchers have looked at the effectiveness of START (Kahn,Schultz, Miller, & Anderson, 2009) and compared the two method-ologies (Cone et al., 2009; Lerner et al., 2008). Both triage methodsare deficient in terms of not precisely defining what is meant by‘‘the most good for the most people’’. The limitations of the currenttriage methods motivated the development of the Sacco TriageMethod (STM) (Sacco et al., 2005). The STM work does provide aprecise definition for the objective and operationalizes it as the ex-pected number of survivors. The work presented here builds uponand enhances the STM model.
The proposed model, which we call the SAVE (Severity-AdjustedVictim Evacuation) model, provides several major contributions.
First, SAVE explicitly considers multiple hospitals while recom-mending evacuation decisions. Second, it handles the deterioratingcondition of victims and hence the increased care time for them asthe disaster unfolds. SAVE also takes into account the treatmentcapacities at the hospitals. When these limited resources are freeto accommodate new victims is based on both the timing and theseverity of the victim sent. The explicit consideration of ambulanceavailability based on when and where the transport was sent is alsoa contribution of the SAVE model. As is shown in the experimentalsection of the paper, all of these contributions lead to a better out-come when using SAVE to help manage the disaster. That is, theexpected number of survivors from an MCI increases with the useof SAVE.
The rest of this paper is organized as follows. A literature re-view, highlighting papers relevant to decision making during theresponse stage of disaster management is provided in the next sec-tion. Section 3 describes the resource constrained triage problem,highlights the STM model, and describes the SAVE model as away to solve the problem. Section 4 provides the explicit formula-tion of the SAVE model. The SAVE model is compared to severalheuristics currently used in the field in Section 5. Potential imple-mentation strategies are discussed in Section 6. The final sectionconcludes with a discussion of the managerial and policy implica-tions of using the SAVE model.
2. Literature review
There has been a great deal of research devoted to the generaltopic of disaster response. Not surprisingly, the bulk of thisresearch has been conducted by researchers in the fields of emer-gency medicine, emergency response, and public policy. While anabundance of useful clinical and applied knowledge has beenobtained from these studies, this literature review is focused ondisaster response literature that supports the decision-making pro-cess of the incident commander and stems from the operationsmanagement literature.
Due to the inherent uncertainty surrounding the resourcesrequired to respond to a specific mass casualty incident, a great dealof research has been focused on issues specific to certain types ofdisasters such as earthquakes (Barbarosoglu & Arda, 2004; Fiedrich,Gehbauer, & Rickers, 2000; Özdamar, Ekinci, & Küçükyazici, 2004),floods (Shim, Fontane, & Labadie, 2002), industrial accidents (Jian-she, Shuning, & Xiaoyin, 1994; Kourniotis, Kiranoudis, & Markatos,2001; Mould, 2001), nuclear events (French, 1996; Hobeika, Kim, &Beckwith, 1994; Papamichail & French, 1999), and terrorism(Reshetin & Regens, 2003; Wright, Liberatore, & Nydick, 2006).
There has also been much research focused on supporting deci-sion-making and interactive methods to aid response and reliefefforts. Barbarosoglu, Özdamar, and Çevik (2002) developed aninteractive approach for the hierarchical analysis of helicopterlogistics for disaster relief operations. Brown and Vassiliou(1993) studied real-time allocation and assignment of responseunits in the context of disaster relief, allowing the human decisionmaker to intervene in the underlying optimization and simulationprocesses. The integration of simulation and geographic informa-tion systems to develop spatial decision support tools to aid inrecovery operations was studied by de Silva and Eglese (2000).Other research is again specific to the problems that arise in thecontext of certain types of disasters. For example, Lee, Mahesh-wary, Mason, and Glisson (2006a, 2006b) develop a decision sup-port system that evaluates facility layout and staffing allocationsfor emergency large-scale dispensing of pharmaceuticals followinga disease outbreak.
Response logistics has also seen a fair amount of research. Thesetypes of decisions include, among other things, transportation and
M.D. Dean, S.K. Nair / European Journal of Operational Research 238 (2014) 363–373 365
evacuation after a mass casualty event occurs. The article by Bar-barosoglu et al. (2002), which explores helicopter logistics, fallsinto this category. The work by Jotshi, Gong, and Batta (2009)investigates dispatching and routing emergency vehicles with thesupport of data fusion during the aftermath of an earthquake.Christie and Levary (1998) model the transportation of the criti-cally injured patients to hospitals as a multi-server queuing systemand show that the length of time that patients wait for an ambu-lance increases rapidly with the increase in the inter-arrival rateof patients to the initial treatment/waiting area. A more exhaustivelist of OR/MS research in disaster operations management up until2004 can be found in Altay and Green (2006). A more recent com-prehensive literature review of optimization models in emergencylogistics can be found in Caunhye, Nie, and Pokharel (2012). Theirreview is broken into three parts: facility location, relief distribu-tion and casualty transportation, and other operations.
The work presented here is inherently related to the broaderarea of scheduling. Rather than review the volumes of work sur-rounding scheduling, the interested reader may wish to consultthe following books: Baker and Trietsch (2009), Pinedo (2009),and Leung (2004).
3. Resource-constrained triage
The very definition of an MCI (WHO, 2007) implies a resource-constrained environment. In particular, the major resources thatmust be considered are availability of transportation (e.g., ambu-lances) and the capacity for the various severities of casualties ateach of the hospitals. For simplicity, throughout the paper definitivecare facilities are referred to as ‘‘hospitals’’. Similarly, the hospitalcapacity is referred to as ‘‘beds’’ even though there are numerousinter-related resources that go into treating and stabilizing a victimof an MCI, such as X-ray and MRI equipment, emergency and oper-ating rooms, the number of physicians and nurses. To reference atransportation vehicle, the term ‘‘ambulance’’ is simply used.
In order to make effective evacuation decisions, triage is firstused to separate victims into distinct categories, classes, or groups.The term ‘‘victim class’’ and ‘‘score level’’ are used interchangeablythroughout the paper and indicate the classification scheme used todelineate the differences between the multiple victims of an MCI.The decisions are how many of each victim class to send from thecasualty collection area to which specific hospital at each decisionpoint. Similar to the STM model (described below), the objectiveof doing the most good for the most people is operationalized asmaximizing the expected number of survivors. In particular, thegoal is to maximize the expected number of survivors with respectto restrictions on the timing and availability of ambulances neededfor transport and the treatment resources available at the hospitals.
In order to calculate the expected number of survivors from anMCI, both an estimate of the survival probability and how that sur-vival probability deteriorates over time are needed. One way toaccomplish this is to assign each victim a ‘‘score’’ that is indicativeof his current condition, and this score deteriorates with time asvictims wait to be transported. In general, a victim’s initial severityand type of injury directly influences his deterioration rate.
The time horizon for the decision-making environment startsafter the immediate onset of the MCI and ends when all the victimshave been evacuated. The type of disaster dictates the length of thetime horizon. This paper focuses on a disaster that results in blunttrauma victims, but the overall process and methodology can beused for any type of disaster.
The setting for this paper, and experiments developed within,takes place at an airport. The motivation for the setting stems fromthe authors’ collaboration with a local airport and their disastermanagement and response teams. The MCI is an airplane running
off the end of a runway when landing at the airport, resulting inblunt trauma victims. The management of such a disaster would in-volve a centralized command-and-control. The details of the flightwould also provide a very good estimate for the number of victims.In short, this type of setting is very amenable to the SAVE model.
3.1. Brief introduction to the STM model
One paper that attempts to address the resource-constrainedproblem with a specific objective is the work by Sacco et al.(2005). Their main motivation is to provide a mixed integer pro-gramming model and process that addresses how to specificallyarticulate the oft-cited objective of ‘‘do the most good for the mostpeople’’. One of their main contributions is the recommendation touse a ‘‘score’’, which can be computed based on a victim’s severityand is predictive of his survival probability, as the basis to quantifythe objective. They suggest using the ‘‘RPM’’ score, which includesthe respiratory rate, pulse rate, and motor response. They show thatby using RPM scores and associated survival probabilities for bluntinjured victims, the STM model performs better than the traditionalSTART method used for triage in all of their simulations, withmarked improvements as the resources to transport are tightened.
3.2. Limitations of STM
Overall, the STM can be viewed as a ‘‘static macro’’ model. Forexample, the model assumes up front that the decision makerknows how many resources will be available for transporting vic-tims for each time period, independent of how many victims mayhave been transported in the previous period, thus implicitlyassuming that each to and from trip takes one period. Thereforethe model can be solved as a simple assignment model – assigningvictims to each period of evacuation, given limited transport re-sources that are known at the beginning of the planning and are sta-tic. However, if multiple hospitals are involved, the time it takes toevacuate casualties will depend on which ambulances are sent tospecific hospitals in each period. These decisions influence thenumber of ambulances available in each subsequent period becausesome ambulances may still be in transit due to traveling to a moredistant hospital. The STM approach would work if only one hospitalexists and the ambulances will be back by the next decision epoch.
The decisions from the STM model are not specific; they simplyidentify the number of victims in each class to treat. Instead, theSAVE model presented here considers sending patients to multiplehospitals and prescribes where to send each victim of the variousvictim classes at each decision period. The STM model does nottake into account the hospital capacity for the different victim clas-ses and when those hospital resources become reusable for treat-ing another victim. The SAVE model uses score-based treatmentestimates as they relate to the timing of the decision. It also explic-itly considers available hospital and transportation capacity whenrecommending evacuation decisions.
3.3. The Severity-Adjusted Victim Evacuation (SAVE) model
Explicitly taking into account the capacity at the hospital can al-ter evacuation decisions and improve the expected number of sur-vivors. This, however, is just one aspect that the SAVE modelimproves. In our approach, four major enhancements are addedto the STM model.
1. Multiple hospitals are considered.2. The time needed to treat/process a victim at a hospital varies
depending on the severity of the injury to the victim. Care timesfor a particular victim will increase as his score decreases (getsworse).
366 M.D. Dean, S.K. Nair / European Journal of Operational Research 238 (2014) 363–373
3. Treatment capacities of the area hospitals are explicitlyconsidered.
4. The availability of ambulances for evacuating victims dependsupon where and when it was sent.
The first enhancement is logical progression over the STM mod-el for making more realistic evacuation decisions. The secondenhancement is also straight-forward. As a victim waits at thecasualty collection area for evacuation, his condition will worsen(according to some deterioration rate). As his condition worsens,more resources and time will generally be needed to stabilize thepatient once he arrives at the hospital. While the STM model doesconsider deterioration rates of patients, it uses them only for calcu-lating the appropriate objective function coefficients.
The treatment capacities for each score at each hospital are con-sidered explicitly in the SAVE model. The decision methodologymust be cognizant of the ability of the hospitals to be able to acceptand process victims at a score-based level. In particular, it ensuresthat a hospital has the capacity to accept a patient with his up-dated score level before sending the patient to that hospital. Recallthat a patient’s condition deteriorates over time, meaning that hewill switch score levels as time progresses. The SAVE model makessure that the hospital can accept a patient with the updated scoreat the decision point rather than a patient with the initial score.One way to accomplish this is by building it into the underlying lo-gic of the software used to implement the SAVE model (as wasdone in for this study). The implementation must understand thedeterioration rates and increased care times for each patient classand then build the model properly. The STM model does not in-clude treatment resources.
The final enhancement of the SAVE model considers how avail-able ambulances affect recommended decisions and vice versa. Be-cause multiple hospitals are considered, an ambulance that travelsto a ‘‘remote’’ hospital will be unavailable longer than one sent to a‘‘local’’ hospital. Resources for evacuation of victims are handleddifferently in the STM model. There, they simply assume a fixednumber of ambulances and that all of the vehicles return by thenext decision epoch. (They use 30-min decision epochs.)
4. Formulation of the SAVE model
4.1. Notation
Data
S set of victim score levels (e.g., RPM values) s score index H set of area hospitals h hospital index T the set of time periods t time period index Dh one-way trip distance (in time periods) to hospital h fromthe casualty collection area
Csh
the amount of care time needed to ‘‘process’’ a victim ofscore s at hospital hA
the initial number of ambulances available Bsh
the initial number of ‘‘beds’’ available at hospital h forscore sPst
the probability of survival of a victim with score s at time tVs
the number of victims of score s awaiting transport fromthe casualty collection to one of the hospitalsVariables
xsht
number of patients with score s to send to hospital hduring time period tat
the number of ambulances available at time period tbsht
The number of patients with score s that can be cared forat hospital h during time period t (e.g., the number ofresources such as beds available for victim score s athospital h during time period t)
4.2. Formulation
maxX
h2H
X
t2T
X
s2S
Pstx
sht ð1Þ
subject toX
s2S
X
h2H
xsht 6 at 8t 2 T ð2Þ
xsht 6 bs
ht 8h 2 H; 8t 2 T; 8s 2 S ð3Þ
a1 ¼ A ð4Þ
at ¼ at�1 �X
s2S
X
h2H
xsht�1 þ
X
s2S
X
h2H
xsht�2�Dh
8t > 1 2 T ð5Þ
bsh1 ¼ Bs
h 8h 2 H; 8s 2 S ð6Þ
bsht ¼ bs
ht�1 � xsht�1 þ xs
ht�ðDhþCshÞ
8h 2 H; 8t > 1 2 T; 8s 2 S
ð7ÞX
h2H
X
t2T
xsht 6 Vs 8s 2 S ð8Þ
xsht 2 Zþ 8h 2 H; 8t 2 T; 8s 2 S ð9Þ
The objective function expressed in (1) indicates the goal ofmaximizing the number of expected survivals from the MCI. Con-straint (2) enforces the restriction that more victims than ambu-lances cannot be sent to hospitals. To ensure that the capacitiesof the hospitals are not violated, constraint set (3) is used. Con-straints (4) and (6) simply set the initial values of the ‘‘state’’.The availability of ambulances at each time period beyond the ini-tial period is defined by (5). Similarly, (7) defines the capacityavailability of the hospitals during each time period beyond thefirst one. It should be noted that the way (7) is formulated implic-itly assumes that a bed is reserved at the hospital once the decisionis made to send a victim there. This is expressed in the final termand the second subscript on the x variable: t � ðDh þ Cs
hÞ. The Dh ex-presses the time it takes the ambulance to get to the hospital and isadded to the care time at that hospital, forcing the bed to remain‘‘in use’’ during that time. Constraint (8) ensures that victims of aparticular score sent to the hospitals are less than the number thatactually exists. Finally, integer restrictions are expressed in (9).
4.3. SAVE model’s performance versus STM model
A comparison of the STM and SAVE models is depicted in Fig. 1,indicating an increased number of expected survivors by using theSAVE model. To understand how these improvements are possibleand to help motivate the use of the SAVE approach, an illustrativeexample is now provided. As described earlier there are severaldeficiencies with the STM model. This example, however, focuseson the issue that STM does not explicitly take into account thecapacity for each victim class at the hospital. To provide an objec-tive comparison between the two approaches, a single hospital isused and we assume an ambulance can make a roundtrip betweenthe casualty collection area and the hospital within a single time
Fig. 1. Comparing the STM and SAVE models for a fixed capacity while varying theambulance capacity.
M.D. Dean, S.K. Nair / European Journal of Operational Research 238 (2014) 363–373 367
period. This assumption allows us to focus on the hospital capacityas the sticking point when comparing the two methods.
Assume there are a total of 45 victims, fifteen each falling intoone of three victim classes, and a single hospital. For simplicity,the three victims classes are described as red, yellow, and green,where red is the most severely affected and green the last. (This cat-egorization scheme was chosen to mimic the START triage method.)Each model is run until all victims have been evacuated. Table 1shows the survival probabilities of each victim class as time pro-gresses. For simplicity, after 15 time periods, the survival probabil-ity is assumed to be stable. Table 2 shows the care times for eachvictim class. Again, for time periods greater than fifteen, the caretime is assumed constant. Fig. 1 shows the comparison betweenthe two models when holding the hospital capacity fixed at fivebeds for each victim class and varying the ambulance capacity.
Looking at Fig. 1, focus on the final point in the two series. Herethere are five ambulances available at the beginning of the time
Table 2Care times, measured by the number of time periods, for each victim class for the time ho
Victim class Time period
1 2 3 4 5 6 7
Red 6 6 6 6 7 7 7Yellow 4 4 4 4 4 4 5Green 2 2 2 2 2 2 2
Table 1Victim class survival probability progression.
Victim class Time period
1 2 3 4 5 6 7
Red 0.630 0.588 0.490 0.432 0.350 0.287 0.230Yellow 0.900 0.878 0.840 0.812 0.769 0.750 0.703Green 0.970 0.965 0.957 0.940 0.925 0.914 0.900
Table 3Decisions from the STM model.
Victim class Time period
1 2 3 4 5 6 7
Red 5 5 5 0 0 0 0Yellow 0 0 0 5 5 5 0Green 0 0 0 0 0 0 5
horizon and they are all dedicated to evacuating victims from thisMCI until all victims have been transported. Each victim class hasan initial capacity of five beds at the hospital. Running the STMmodel on this data, we get the following results shown in Table3. Because the STM model does not take into account the capacityconstraints at the hospital, it will send five more victims during thesecond time period, even though there are no available resourcesat that time to accommodate them. In reality, this situation wouldmanifest itself as a build-up of victims at the hospital. Because ofthis, to calculate the objective function the resulting evacuationdecisions are treated as a queuing problem with the probabilityof survival being added when the each victim is actually treated.The objective function results in 25.450 expected survivors. Usingthe SAVE model on the same data, the objective function improvesto 28.889 expected survivors, a 13.51% improvement. The corre-sponding decisions for the SAVE model are shown in Table 4.
Based on the set-up, the improvement stems from the STM’sshortcoming of not considering treatment resource availability.In contrast, the SAVE model explicitly handles this situation. Asthe results above indicate, the SAVE model may help increase thenumber of survivors. In order to get an idea of the possibleimprovement by using the SAVE model rather than the STM model,a small experiment was conducted. To get a better picture of howSAVE reacts in various settings, the number of available ambu-lances and the capacity levels were varied. The number of availableambulances was incrementally changed from two to five and thecapacity levels for each score level ranged from two to five bedsat the hospital. To provide a fair comparison, a single hospital isused and it is assumed that an ambulance can make the roundtripfrom the casualty collection area to the hospital route within a sin-gle time period. (Note that these restrictions are in place because ofthe drawbacks to the STM model mentioned earlier. As shown la-ter, the SAVE model overcomes these deficiencies.) The SAVE mod-el’s objective function was then compared to the STM model. Overthese 16 comparisons (four levels of bed capacity at the hospitaland four levels of ambulances), the SAVE model demonstrates an
rizon.
8 9 10 11 12 13 14 15
7 8 8 8 8 9 9 95 5 5 5 5 6 6 62 3 3 3 3 3 3 3
8 9 10 11 12 13 14 15
0.196 0.150 0.118 0.089 0.073 0.052 0.011 0.0050.630 0.588 0.490 0.432 0.350 0.287 0.230 0.1960.878 0.840 0.812 0.769 0.750 0.738 0.703 0.630
8 9 10 11 12 13 14 15
0 0 0 0 0 0 0 00 0 0 0 0 0 0 05 5 0 0 0 0 0 0
Table 4Decisions from the SAVE model.
Victim class Time period
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Red 2 3 0 0 0 0 2 3 0 0 0 0 0 2 3Yellow 3 2 0 0 3 2 0 0 3 2 0 0 0 0 0Green 0 0 5 0 2 3 2 2 1 0 0 0 0 0 0
368 M.D. Dean, S.K. Nair / European Journal of Operational Research 238 (2014) 363–373
increase in the expected number of survivors, as we expected a pri-ori. The overall average improvement of the SAVE model over theSTM model is 17.26%. The full results of the improvement SAVEprovides over the STM model are shown in Table 5.
Fig. 2 provides a look at how the models react when holding onevariable constant and varying the level of the second. The graph onthe left fixes the capacity of the hospital to four beds and varies thenumber of ambulances between two and five. The rightmost graphholds the number of available ambulances constant at four andvaries the hospital’s capacity from two to five beds.
5. Experiments
5.1. Heuristics used in practice
One point of interest is to determine how well the SAVE modeldoes in comparison to several heuristics that are currently used in
Fig. 2. Model reactions to varying am
Table 5The full improvement results using the SAVE model versus the STM model.
Capacity Ambulances STM’sobjectivefunction
SAVE’sobjectivefunction
Improvement(%)
2 2 17.277 19.943 15.433 16.755 20.448 22.044 17.393 20.543 18.115 17.659 20.625 16.80
3 2 18.988 21.691 14.243 18.900 23.358 23.594 19.578 23.918 22.175 20.256 24.139 19.17
4 2 20.607 22.501 9.193 20.734 25.345 22.244 21.763 26.295 20.825 22.853 26.712 16.89
5 2 21.726 23.033 6.023 22.562 26.543 17.644 23.866 28.252 18.385 24.450 28.889 13.51
Average 17.26
real life. Three of the most common ‘‘rule of thumb’’ approachesused in practice are:
1. Closest-first – send as many victims as possible to the closesthospital first. When that hospital reaches capacity, send victimsto the next closest hospital.
2. Furthest-first – send as many victims as possible to the furthesthospital first. When that hospital reaches capacity, send victimsto the next furthest hospital.
3. Cyclical – send victims in a round-robin fashion to the areahospitals.
The logic behind using the closest-first heuristic is to evacuatethose victims which have been triaged and shown to be the mostseverely afflicted to a hospital as quickly as possible to receivetreatment. The furthest-first heuristic is also used at times. It isknown that victims deteriorate over time. If a large number ofseverely injured casualties is expected, then the first ones found(often the ones with less severe injuries) are sent to the furthesthospital because the assumption of the incident command is thatthese victims can survive the longer transport distance. After sometime passes the next batch of casualties will have deteriorated andthe ‘‘reserved’’ capacity at the closer hospital is a benefit becausethose victims could not survive the wait and an extended traveltime. The final common heuristic considers sending victims in analternating fashion to the different area hospitals. The benefit ofthis heuristic is that some ‘‘breathing room’’ is provided for eachhospital. That is, it essentially assumes that no victims will geteffective care if a hospital is overwhelmed by incoming patients,impairing its ability to respond.
Each of these heuristics can be implemented several ways. Themost common implementation in use is to evacuate the most crit-ical, non-expectant victims first. Intuitively, this seems like thebest approach. However, as is shown below, this may not resultin the best outcome if the measure is the total number of expectedsurvivors. In direct contrast, another implementation possibility isto transport the least critical victims first, leaving the most se-verely injured patients for transportation later. Obviously, theseare the two extremes and various other schemes could be used.
bulances and hospital capacity.
Table 7The probability survival estimates for RPM values and theassociated care time. Sacco et al. (2005) is the source of first twocolumns.
rpm value Survival probability Care time (minutes)
0 0.052 1801 0.089 1702 0.15 1603 0.23 1504 0.35 1405 0.49 130
M.D. Dean, S.K. Nair / European Journal of Operational Research 238 (2014) 363–373 369
The cyclical heuristic has even more flexibility in terms ofimplementation possibilities. When alternating between differentarea hospitals, how many victims are sent to each hospital beforeswitching the destination to a different hospital is one way to varyhow the heuristic is implemented. For example, it could prescribesending one victim to the first hospital, the next victim to the sec-ond hospital, etc. Alternatively, it could be implemented to sendthe first two victims to the first hospital, the next two victims tothe second hospital, and so on. Again, there exist many differentways to implement the cyclical heuristic.
6 0.63 1207 0.75 1108 0.84 909 0.90 60
10 0.94 5011 0.97 4012 0.98 30
Table 8The deterioration of RPM scores in 30-min time intervals. Adapted from Sacco et al.(2005).
Initial RPM Time interval
1 2 3 4 5 6 7 8 9 10 11 12
0 0 0 0 0 0 0 0 0 0 0 0 01 0 0 0 0 0 0 0 0 0 0 0 02 0 0 0 0 0 0 0 0 0 0 0 03 1 0 0 0 0 0 0 0 0 0 0 04 2 1 0 0 0 0 0 0 0 0 0 05 3 2 1 0 0 0 0 0 0 0 0 06 4 3 2 1 0 0 0 0 0 0 0 07 6 5 4 3 2 1 0 0 0 0 0 08 8 7 6 5 4 3 2 1 0 0 0 09 9 8 8 7 6 5 4 3 2 1 0 0
10 10 9 9 8 8 7 6 6 5 5 4 411 11 11 10 10 9 8 8 7 7 6 6 512 12 12 11 11 10 10 10 10 9 9 8 8
5.2. Experimental setup
While certain restrictions had to be placed on the setting whenthe SAVE model was compared to the STM model in Section 4.3,they can be relaxed now when comparing the SAVE model to com-monly used heuristics. One of the contributions of the SAVE modelis that it explicitly considers multiple hospitals when recommend-ing evacuation decisions. Therefore, we consider two hospitals forall of the following experiments. It should be noted, that while twohospitals are used for illustrative purposes, the SAVE model iscapable of handling many more. We are now also able to take intoaccount round-trip times for ambulances that are longer than thelength of a time period.
For all of the experiments the following setup is used. The basisof the experiment comes from conversations stemming from a cur-rent research collaboration project with an airport to implementthe SAVE model. As described earlier, the setting of a landing air-plane over running the tarmac is amenable to the SAVE model. Thistype of disaster is mostly self-contained, results in blunt-traumavictims, and the airport’s disaster response team utilizes a central-ized command-and-control approach to manage the disaster. Theexperimental setup also follows Sacco et al. (2005) in several re-gards. For victim scores, the ‘‘RPM’’ score, which includes the respi-ratory rate, pulse rate, and motor response (Sacco & Champion,1983), is utilized. The RPM score is the sum of coded values forthe three categories/rows as shown in Table 6. Additionally, it is as-sumed that the MCI caused blunt trauma victims. This assumptionallows the utilization of both the survival probabilities and the vic-tim deterioration rates derived by Sacco et al. (2005). The survivalprobabilities are shown in Table 7 and the deterioration ratesbased on 30-min intervals are shown in Table 8.
One of the enhancements of SAVE over STM is that care time isdirectly related to the current status (i.e., RPM score) of the victim.The care times used in these experiments are shown in Table 7. Thecare time is measured in minutes. It represents an estimate of howlong it would take to stabilize a patient with the associated score,thus freeing the resources to be used on another victim. As men-tioned earlier, for simplicity and exposition purposes, this paperrefers to these resources simply as ‘‘beds’’ even though there aremany other intertwined resources involved.
A fixed time horizon of 6 h after the onset of a MCI is considered.It is assumed that victims are gathered at a common collection areafrom which emergency medical vehicles depart to evacuate thevictims to a hospital. This assumption is consistent with both thediscussion in the introduction and with the way a MCI would beattempted to be handled by a centralized command-and-control
Table 6The RPM coded values. Source: Sacco et al. (2005).
Coded values 0 1 2
Respiratory rate 0 1–9 36+Pulse rate 0 1–40 41–Motor response None Extends/flexes from pain Wi
at an airport. Another assumption is that both the number of victimsand their associated distribution are known at the beginning of thetime horizon. Three different distribution patterns of victims thatare awaiting transport are investigated: a uniform distribution, aleft-skewed distribution, and a right-skewed distribution. SeeFig. 3 for a pictorial representation of the victim distributions. Eachdistribution considers the same number of overall victims: 130. Thisis approximately the number of passengers on jet airliner from theAirbus A320 family.
Transit time between each hospital is also considered. Theassumption that the transit time is deterministic, known, and thesame for both the outbound and inbound directions is used. Fourdifferent levels for the number of ambulances are examined. Twohospitals are considered: a ‘‘local’’ hospital and a ‘‘remote’’ one.Both hospitals have the same technology resources and are capableof treating each victim class. Additionally, both hospitals treat thevictims in the same amount of time. Each of the hospital’s capacityand the distance of the remote hospital from the casualty collec-tion area are varied. Table 9 shows the different levels considered.
3 4
25–35 10–2460 121+ 61–120
thdraws from pain Localizes pain Obeys commands
Fig. 3. The distributions used during the experiments.
Table 9The parameter settings for the experiments.
Parameter Levels
Initial number of available ambulances 5, 10, 15, 20Distribution of victims Uniform, left-skewed, right-
skewedLocal hospital capacity for each RPM score 2, 4, 6, 8Remote hospital capacity for each RPM
score2, 4, 6, 8
One-way distance to local hospital(minutes)
5
One-way distance to remote hospital(minutes)
8, 20
370 M.D. Dean, S.K. Nair / European Journal of Operational Research 238 (2014) 363–373
Altogether 384 different design settings are investigated. The mod-els were solved using the Gurobi solver.
5.3. Low score first not always best approach
The logic behind using the closest-first heuristic is to get criti-cally injured victims needed care as quickly as possible. This ap-proach seems intuitive: see if it is possible to provide the mostbadly injured victims help in time for them survive. However,when we quantify the probability of survival and want to maxi-mize the overall number of expected survivors, the low-score-firstheuristic may fall short of its intended outcome. Instead, this
Table 10The results of testing a low-score-first implementation versus a high-s
Lowest score considered Uniform (%) Left-skewe
2 58.6 52.33 79.7 59.44 83.6 72.75 93.8 74.26 98.4 93.0
objective may indicate that a high-score-first approach should beused when making transportation decisions. Using the experimen-tal setting described above, an exploration of which circumstanceslead to use of the low-score-first heuristic versus the high-score-first approach is conducted.
In the experimental design, victims with RPM scores of 0 and 1would most likely be dead or expected to die. Therefore, in realitythese victims would not be considered when making evacuationdecisions. This narrows the victim classes to consider down tothose with RPM scores of 2 and higher. The closest-first heuristicis implemented as low-score-first and compared to a high-score-first implementation. The lowest score considered varies from 2to 6. The results showing the percentage of the time the low-score-first is at least as good as the high-score-first, in terms ofthe objective function, are displayed in Table 10. That is, if thereis a tie, the low-score-first is considered the ‘‘winner’’. Percentagesfor each of the individual distributions are based on the 128 runsfor that particular distribution. The overall percentage (last col-umn) is over all 384 runs.
Table 10 shows that whether a low-score-first implementation isbetter depends on both the underlying distribution of victims andwhich RPM score values are considered. For example, when consid-ering an RPM score of 2 as the lowest score with a right-skewed dis-tribution, only 11.7% of the runs showed a better objective function(i.e., the expected number of survivors) using a low-score-firstapproach instead of a high-score-first implementation.
core-first implementation.
d (%) Right-skewed (%) All distributions (%)
11.7 40.936.7 58.676.6 77.688.3 85.499.2 96.9
M.D. Dean, S.K. Nair / European Journal of Operational Research 238 (2014) 363–373 371
5.4. Comparison of SAVE model to heuristics
It is also of interest to see how well the SAVE model performsagainst the commonly used heuristics. As discussed earlier, eachheuristic can be implemented in numerous ways. The cyclical heu-ristic is implemented in three specific ways: switch hospitals aftereach patient, switch to a different hospital after two patients havebeen sent to the current hospital in row, and switch to the otherhospital after sending three victims to the current one. A simplisticrandom heuristic is also implemented for comparison purposes.For each time period, if an ambulance is available, the random heu-ristic first picks the hospital with a simple flip of a fair coin. Basedon the destination hospital, it then randomly picks one of theawaiting scores for which the destination hospital has capacity.This random heuristic is included to show that the performanceimprovements of the SAVE model are not due to chance. The re-sults showing the average improvement of the SAVE model overeach heuristic are shown in Fig. 4. Both the high-score first andthe low-score first implementations for the heuristics are dis-played. (Note that the random heuristic chooses which score toevacuate in a probabilistic manner eliminating the possibility forhigh-score versus low-score, so the two bars in the graph are thesame height.) As is evident from the graph, the SAVE model handilyoutperforms the heuristics when they utilize the low-score first ap-proach. For this reason, the following analysis and Figs. 5 and 6only show a high-score-first implementation for each heuristic,
Fig. 4. The average improvement over the common
Fig. 5. The expected number of survivors of the SAVE model versus heuristics when t
giving a conservative estimate of the improvement of the SAVEmodel over each heuristic.
Other attributes about the problem were varied to determinehow the SAVE model compares to the various heuristics in differ-ent settings. First, the capacity at each hospital is held constantat six beds and the number of available ambulances varies. The re-sults are depicted in Fig. 5. Next, the number of available ambu-lances is fixed at 15, the capacity at the remote hospital is set tosix beds, and the capacity at the local hospital is varied. The resultsare shown in Fig. 6. Of the cyclical heuristics, only the cyclical-1 isshown and compared to the SAVE model in order to avoid clutteredgraphs. As indicated by Fig. 4, the cyclical-1 heuristic is very repre-sentative of the other two cyclical heuristics when using the high-score first implementation.
6. Implementation strategies
Using the SAVE model in practice may be challenging. Eventhough the STM model has been around for several years, theauthors are not aware of any real-world disaster response imple-mentations of it. Perhaps the primary challenge to implementationstems from the fact that the techniques used by the SAVE and STMmodels are generally quite foreign to incident commanders in chargeof MCI response. Two possible strategies are discussed to help over-come the possible challenges of implementing the SAVE model.
ly used heuristics when using the SAVE model.
he number of ambulance varies and the hospital capacity is held constant at six.
Fig. 6. The expected number of survivors of the SAVE model versus heuristics when the local capacity varies and the number of ambulances is held constant at fifteen.
372 M.D. Dean, S.K. Nair / European Journal of Operational Research 238 (2014) 363–373
One implementation strategy involves using the SAVE model asa basis and dynamically incorporating events as they unfold. TheSAVE model could be re-solved each time new information perti-nent to the model is gathered, updating the recommendations forevacuation decisions. For example, if the travel time for an ambu-lance is longer than anticipated, this information could be foldedinto the model and it could be solved again. This implementationstrategy requires more coordination among the disparate informa-tion sources. Such an implementation could be integrated within adecision support system that utilizes information from sourcessuch as the hospitals (for capacity information), emergency medi-cal technicians in the field responding to the disaster (for victiminformation), and ambulances (for transport availability informa-tion). Collecting and combining all of this data is technically possi-ble, but new systems (hardware, software, processes, procedures,etc.) would have to be developed and agreed upon by the variousinvolved parties. This rolling solving of an information-aware SAVEmodel would provide one way to handle unforeseen disruptions.The authors are currently working in collaboration with an airporton a proof-of-concept system to help them with their MCI trainingsessions. It should be noted that this approach is a viable optionbecause the underlying MIP can be solved quickly and efficientlyusing a commercial solver. In the experiments for this study, Guro-bi (Gurobi Optimization & Gurobi optimizer reference manual,2013) was used to solve the MIPs consisting of 3067 constraints
Fig. 7. An example of an evacuation guideline that could be used as ‘‘cheat sheet’’ by an ihospital, and the size of the circle shows the number of victims (one or two) to be sent
and 3869 variables in an average of less than three seconds on a2 GHz Windows machine with 4.00 GB of RAM.
A secondary challenge facing implementation of the SAVE modelis the perception that using the SAVE model may be too ‘‘involved’’for the incident commander. Remember, he is accustomed to usingthe ‘‘rule of thumb’’ heuristics discussed in the previous section.Generally, these simple rules are easy to implement. One strategyis to have the SAVE model produce beforehand ‘‘cheat sheets’’ thatprovide similar guidelines for the incident commander to helphim make evacuation decisions. These graphical cheat sheets canbe generated for any number of different possible disaster responsescenarios for a particular geographic area in anticipation of an actualMCI. Fig. 7 below depicts one possible cheat sheet. Similar graphicalguidelines could be produced for any number of situations.
The situation considered in Fig. 7 is with blunt trauma victimsresulting in a left-skewed distribution (as shown in Fig. 3). Thereare initially five ambulances with the capacity of both the localand remote hospitals set at two victims per score level. The one-way travel distance to the local hospital is 5 min and it is 8 minto the remote hospital.
7. Managerial implications and conclusions
The most commonly used current triage methods of START andSALT do not provide specifics on how to ‘‘provide the most good to
ncident commander (numbers indicate the number of victims to be sent to the localto the remote hospital).
M.D. Dean, S.K. Nair / European Journal of Operational Research 238 (2014) 363–373 373
the most people’’. The STM model filled this gap by quantifyingsurvival probabilities of victims and suggesting the use of the over-all number of expected survivors as a quantifiable objective in or-der to capture the idea of ‘‘most good to most people’’. However,the STM model is a static macro model. The work presented heresuggests that the SAVE model provides four major enhancementsto the STM model. It was shown that the SAVE model is better sui-ted to recommending evacuation decisions when the hospitalcapacity is explicitly considered and multiple hospitals are avail-able to send victims to during an MCI. An experimental design set-ting is provided which allows testing of various in-use heuristics.In particular, it was shown that the effectiveness of using a low-score-first implementation of the closest-first heuristic dependsupon the underlying victim distribution and which RPM scorevalue was the lowest considered. Also investigated was how wellthe SAVE model performs in comparison to several heuristics thatare currently used in real life. The SAVE model was tested againstthe heuristics that used a high-score-first implementation.Although, most evacuation heuristics use a low-score-first ap-proach rather than a high-score-first approach, we compared theSAVE model to the high-score-first heuristics providing a moreconservative estimates of the improvement measures. The SAVEmodel outperforms all of the heuristics on the order of 10–30%on average. While this percentage of improvement may not seemsignificant on the surface, the objective function is measured in hu-man lives; even a minuscule improvement should be celebrated.
As the number of available ambulances varies but the hospitalcapacities remain constant, the improvement of the SAVE modelover the closest-first heuristic stayed relatively stable at approxi-mately 10%. Not surprisingly, as more ambulances are added, thecyclical heuristics performance improves. However, the SAVE mod-el still performs better but the improvement gap between modelsstarts to level off. Another investigation kept the number of avail-able ambulances and the remote hospital’s capacity constant,while increasing the capacity at the local hospital. This experimentshows the performance gap between the SAVE model and the heu-ristics as remaining steady after having reached a capacity of fourbeds at the local hospital.
Some related research that the authors are currently pursuingincludes a proof-of-concept decision support system for the roll-ing-horizon approach discussed in Section 6. This work is beingconducted in collaboration with an airport. The authors are alsodeveloping new models that build stochasticity directly into theSAVE model. Another interesting extension would be to includemodeling of the hospitals’ downstream resources. After a victimhas been stabilized, he will often be admitted to an inpatient unitof the hospital. How does the increase of inpatients stemming froman MCI affect the overall patient flow of a hospital? Yet anotheravenue for future research is to investigate the option of usingsome ambulances to transfer existing inpatients to a ‘‘farther’’ hos-pital in order to ‘‘make room’’ for the incoming victims of the MCI.Exploring such an option does have interesting legal aspects to it.
References
Altay, N., & Green, W. G. III, (2006). OR/MS research in disaster operationsmanagement. European Journal of Operational Research, 175(3), 475–493.
Baker, K. R., & Trietsch, D. (2009). Principles of sequencing and scheduling (1st ed.).Hoboken, New Jersey: John Wiley & Sons, Inc..
Barbarosoglu, G., & Arda, Y. (2004). A two-stage stochastic programming frameworkfor transportation planning in disaster response. Journal of the OperationalResearch Society, 55(1), 43–53. 122.
Barbarosoglu, G., Özdamar, L., & Çevik, A. (2002). An interactive approach forhierarchical analysis of helicopter logisitics in disaster relief operations.European Journal of Operational Research, 140(1), 118–133.
Brown, G. G., & Vassiliou, A. L. (1993). Optmizing disaster relief–real-timeoperational and tactical decision support. Naval Research Logistics, 40(1), 1–23.
Caunhye, A. M., Nie, X., & Pokharel, S. (2012). Optimization models in emergencylogistics: A literature review. Socio-Economic Planning Sciences, 46(1), 4–13.
Christie, P. M. J., & Levary, R. R. (1998). The use of simulation in planning thetransportation of patients to hospitals following a disaster. Journal of MedicalSystems, 22(5), 289–300.
Cone, D. C., Sera, J., Burnes, K., MacMillan, D. S., Kurland, L., & Van Gelder, C. (2009).Pilot test of the SALT mass casualty triage system. Pediatric Emergency Care,13(4), 536–540.
de Silva, F. N., & Eglese, R. W. (2000). Integrating simulation modelling and GIS:Spatial decision support for evacuation planning. Journal of the OperationalResearch Society, 51(4), 423–430.
Fiedrich, F., Gehbauer, F., & Rickers, U. (2000). Optimized resource allocation foremergency response after earthquake disasters. Safety Science, 35(1–3), 41–57.
French, S. (1996). Multi-attribute decision support in the event of a nuclearaccident. Journal of Multi-Criteria Decision Analysis, 5(1), 39–57.
Frykberg, E. R. (2002). Medical management of disasters and mass casualties fromterrorist bombings: How can we cope? The Journal of Trauma Injury, Infection,and Critical Care, 53(2), 201–212.
Frykberg, E. R. (2005). Triage: Principles and practice. Scandinavian Journal ofSurgery, 94, 272–278.
Gurobi Optimization, Inc., Gurobi optimizer reference manual, 2013. <http://www.gurobi.com>.
Hobeika, A. G., Kim, S., & Beckwith, R. E. (1994). A decision support system fordeveloping evacuation plans around nuclear power stations. Interfaces, 24(5),22–35.
Jacobs, L. M., Jr., Goody, M. M., & Sinclair, A. (1983). The role of the trauma center indisaster management. The Journal of Trauma Injury, Infection, and Critical Care,23(8), 697–701.
Jianshe, D., Shuning, W., & Xiaoyin, Y. (1994). Computerized support systems foremergency decision making. Annals of Operations Research, 51(7), 315–325.
Jotshi, A., Gong, Q., & Batta, R. (2009). Dispatching and routing of emergencyvehicles in disaster mitigation using data fusion. Soci-Economic PlanningSciences, 43, 1–24.
Kahn, C. A., Schultz, C. H., Miller, K. T., & Anderson, C. L. (2009). Does START triagework? An outcomes assessment after a disaster. Annals of Emergency Medicine,54(3), 424–430.
Kourniotis, S. P., Kiranoudis, C. T., & Markatos, N. C. (2001). A systematic approach toeffective chemical emergency management. Safety Science, 38(1), 49–61.
Lee, E. K., Maheshwary, S., Mason, J., & Glisson, W. (2006a). Large-scale dispensingfor emergency response to bioterrorism and infectious-disease outbreak.Interfaces, 36(6), 591–607.
Lee, E. K., Maheshwary, S., Mason, J., & Glisson, W. (2006b). Decision support systemfor mass dispensing of medications for infectious disease outbreaks andbioterrorist attacks. Annals of Operations Research, 148, 25–53.
Lerner, E. B., Schwartz, R. B., Coule, P. L., Weinstein, E. S., Cone, D. C., Hunt, R. C., et al.(2008). Mass casualty triage: An evaluation of the data and development of aproposed national guideline. Disaster Medicine and Public Health Preparedness,2(Supplement 1):S25–S34.
Leung, J.Y.-T. (Ed.) (2004). Handbook of scheduling: Algorithms, models, andperformance analysis (1st ed.). Chapman and Hall/CRC.
Mould, G. I. (2001). Assessing systems for offshore emergency evacuation. Journal ofthe Operational Research Society, 52(4), 401–408.
Özdamar, L., Ekinci, E., & Küçükyazici, B. (2004). Emergency logisitics planning innatural disasters. Annals of Operations Research, 129(1–4), 217–245.
Papamichail, K. N., & French, S. (1999). Generating feasible strategies in nuclearemergencies – A constraint satisfaction problem. Journal of the OperationalResearch Society, 50(6), 617–626.
Pinedo, M. L. (2009). Planning and scheduling in manufacturing and services (2nd ed.).New York, NY: Springer.
Reshetin, V. P., & Regens, J. L. (2003). Simulation modeling of anthrax sporedispersion in a bioterrorism incident. Risk Analysis, 23(6), 1135–1145.
Sacco, W. J., Champion, H. (1983). Field testing of the trauma score. Honolulu, HI:Proceedings of the Sixteenth Hawaii International Conference on System Sciences.
Sacco, W. J., Michael Navin, D., Fiedler, K. E., Waddell, R. K., II, Long, W. B., &Buckman, R. F. Jr., (2005). Precise formulation, evidence-based application ofresource-constrained, triage. Academic Emergency Medicine, 12(8), 759–770.
Shim, K.-C., Fontane, D. G., & Labadie, J. W. (2002). Spatial decision support systemfor integrated river basin flood control. Journal of Water Resources Planning andManagement, 128(3), 190–201.
World Health Organization (WHO). (2007). Mass casualty systems: Strategies andguidelines for building health sector capacity. April. <http://www.who.int/hac/techguidance/tools/mcm_guidelines_en.pdf>. Last accessed on March 30, 2010.
Wright, P. D., Liberatore, M. J., & Nydick, R. L. (2006). A survey of operations researchmodels and applications in homeland security. Interfaces, 36(6), 514–529.
