Featured Story November-December 2015
Optimizing Emergency Preparedness and Resource Utilization in Mass-Casualty Incidents

by Dr. Panagiotis Repoussis, Lecturer at Athens University of Economics and Business and Visiting Assistant Professor at Stevens Institute of Technology


Mass-Casualty Incidents (MCIs) are major events that acutely overwhelm local emergency medical and hospital resources. This work is concerned with the development of a full response model in the aftermath of a MCI that can be used to provide operational guidance for regional emergency planning as well as to evaluate strategic preparedness plans.
  • Where do we send the patients in order to minimize the amount of time it takes to treat them all?
  • Which hospitals should be included in the response?
  • Where should ambulances transport each patient?
  • How many patients should be transported to each hospital?

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"…during 9/11, uptown hospitals had an abundance of staff on call and available space, while downtown hospitals were overwhelmed"
The combined ambulance dispatching, patient-to-hospital assignment, and treatment ordering problem is a hard to solve complex combinatorial optimization. Below the characteristics of the problem are summarized and Figure 1 shows the sequence of events.

Operational Realities

  • Limited availability of responders (ambulances):
       - Different bounds on the maximum number of trips per ambulance
       - Traveling times proportional to the geographical distances between hospitals and the disaster site
  • Patient prioritization based the Simple Triage and Rapid Treatment (START) triage protocol:
       - First priority is given on intermediate and delayed patients with time-critical injuries
  • Restrictions on the patient-to-hospital assignments:
       - Pairing of injury types with specific subsets of hospitals
       - High priority patients can only be send to trauma level I and II hospitals
  • Limited number of hospitals/medical facilities - different trauma levels, capacities & patient throughputs
  • Treatment times are different for every patient & hospital:
       - Treatment capability is measured based on the number of emergency department (ED) trauma bays and the associated operating rooms (OR)
  • The number of available beds limits the number of patients that can be assigned to a hospital
  • Sequential processing of the patients:
       - Hospital resources (EDs & ORs) are recycled after each use
       - Treatment ordering is dictated by the patient arrival times

Objectives

  • Makespan (Cmax): Long delays w.r.t. the completion of treatment for each patient leads to a higher mortality rate
  • Weighted total flow time (WTFT): The weight given at each patient reflects their prioritization as defined by their triage level.
Figure 1. Sequence and timeline of events

A mixed integer mathematical programming (MIP) formulation is proposed. The goal is to allocate effectively the limited resources during the response effort so as to improve patient outcomes, while the objectives are to minimize the overall response time and the total flow time required to treat all patients, in a hierarchical fashion.

The model is solved via exact for small scale problem instances and MIP-based matheuristic solution methods for large scale problems. The novel matheuristic works as follows: Initially, a greedy randomized scheme is employed to find and fix part of the patient-to-hospital and patient-to-ambulance assignments. Next, the resulting partially reduced problem is solved to optimality (using IBM ILOG CPLEX solver 12.6), and a complete solution is produced by determining the patient dispatching sequence and treatment order. This MIP-based construction heuristic scheme generates quickly high quality feasible starting upper bounds. On return, these initial heuristic solutions serve as the starting points for an Iterated Tabu Search metaheuristic algorithm, which is mainly applied for further improvement. The oscillations between the MIP-based construction heuristic and the local search algorithm are repeated for a number of iterations.

The applicability of the model and the performance of the new optimization methods are challenged on realistic MCI scenarios. Table 1 provides some computational experiments conducted on simulated problem instances.

Table 1: Computational results on simulated problem instances with up to 120 patients
The hypothetical case of a terror attack at the New York Stock Exchange in the Lower Manhattan metropolitan area is also simulated with up to 150 trauma patients and treatment times (~normal(60,15) minutes / hospital throughput), 40 ambulances (single patient capacity), ambulances arrive 8 minutes after the attack and 10 hospitals. Figure 2 demonstrates graphically the actual location of the MCI site and the locations of the hospitals included in the response effort.
Figure 2. MCI site and hospital locations

The bottlenecks for various capacity settings are identified in terms of the number of ambulances and available hospital beds (see Figures 3a and 3b). The effect of considering remote hospitals as opposed to reduced ambulance transportation times is also examined, aiming at evenly spreading the demand across hospitals. Lastly, Figure 4 presents the Gantt chart of an indicative schedule for an MCI scenario with 150 patients.
Figure 3a. Makespan vs number of ambulances for different hospital capacity scenarios
Figure 3b. Total flow time vs number of ambulances for different hospital capacity scenarios
Figure 4. Indicative schedule for an MCI scenario with 150 patients

The above model and solution approach can be used to guide strategic and operations decisions for disaster preparedness and response by local and governmental authorities. In future it will be of great value to study the overtriage and the effect on the hospital's capacity of self-presenting patients.

References

Repoussis P.P., Paraskevopoulos D.C. Vazacopoulos A. Hupert N. (2015). Optimizing Emergency Preparedness and Resource Utilization in Mass-Casualty Incidents. EURO 2015 - 27th European Conference on Operational Research, July 12-15, Glasgow, UK.

Repoussis P.P., Paraskevopoulos D.C. Vazacopoulos A. Hupert N. (2015). Optimizing Emergency Preparedness and Resource Utilization in Mass-Casualty Incidents. INFROMS Business Analytics and Operations Research Conference, April 14-18, Los Angeles, California, USA.