# University of Twente Student Theses

## EMS- & Hospital-Cluster determination with Linear Programming

Ploeg, M.
(2010)
*EMS- & Hospital-Cluster determination with Linear Programming.*

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Abstract: | During a medical surge, like a pandemic, a large percentage of the population is infected. During such a medical surge, a large group of people need medical care. In such a scenario it is important that the medical care is optimal to make sure the number of victims is minimized. A problem the emergency agencies have to face is how to allocate and locate the available resources to optimize the given medical aid. Furthermore, during such pandemic, the agencies itself are also infected making the resources even more limited. To make sure that the given medical aid is optimal during a medical surge, the authorities in the United States have assigned the University of Louisville to solve this problem. One of the problems of this big project is locating and allocating the EMS-vehicles (ambulances) during such a surge. Due to high demand of these ambulances, it is important to locate and allocate these vehicles to make sure the number of patients being transported is as high as possible. Assumed is that in a certain region, let’s say a county, a number of hospitals and a number of EMS-stations (where ambulances stay) exist. Each EMS-station takes care of a certain region within the county, forming an EMS-cluster. Each EMS-cluster can bring its patients to a certain hospital. Furthermore, each hospital takes care of certain number of EMS-clusters, forming the Hospital-cluster. To make sure the EMS-vehicles (ambulances) drive the shortest distance, linear programming (LP) will be used to optimize this problem. Due to the pandemic, one can imagine that the demand can be fluctuating in the different cluster. So it can happen that in one EMS- or Hospital-cluster a shortage of vehicles or hospital-capacity occurs. Therefore the LP-model has to work fast to make sure emergency agencies can generate new optimal clusters quickly. In this case the Jefferson County in Kentucky, USA is used as example. To solve this problem, the software program Lingo is used to find an answer. Although the program gives results as it gives EMS- and Hospital-clusters, the calculation time is too large (over sixteen hours). Therefore the search method Simulated Annealing (S.A.) will be used to reduce the calculation time to an acceptable level. The results the S.A.-model will give, is an approximation of the optimal solution generated by the LP-model. Therefore the parameters of the S.A.-model have to be chosen carefully. The results of the S.A.-model show a major time saving from over 16 hours of the LP-model to 20 minutes of the S.A-model. However, the total driving distance for the ambulances are increased with 15% compared the optimal solution of the LP-model, but this is acceptable. An extra improvement can be made by making the neighborhood/solution-area of the S.A.-model smaller. On this way the S.A.-model need to make less calculations resulting in a lower total calculation time. When applying this to the S.A-model, the calculation time dropped further to 13 minutes and the objective (total driving distance) decreased 2% making it 13% larger than the optimal solution of the LP-model. Another improvement was made by merging hospital into one hospital if these hospitals have a distance between them lower then a certain limit. On this way the model has less variables and the total calculation time will drop further. Also, by merging hospitals which are close together, more logical clusters will appear making it more useful. Overall, this report shows that simulated annealing is a good way to determine hospital and EMS-clusters which can be used for ambulance location and allocation. Although the best solution generated by the S.A.-model was 13% larger compared to the optimal solution given by the LP-model, the S.A.-model was able to generate the solution quickly which is crucial during a medical surge. The next step to be taken in this process is a dynamic model which actual allocates the ambulances during the medical surge. |

Item Type: | Internship Report (Master) |

Clients: | University of Louisville |

Faculty: | ET: Engineering Technology |

Subject: | 52 mechanical engineering |

Programme: | Mechanical Engineering MSc (60439) |

Link to this item: | http://purl.utwente.nl/essays/59616 |

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