Linear upper-bound unavailability set covering models for locating ambulances: Application to Tehran rural roads

This paper presents a linear reliability-based model as an extension of the well-known linear location set covering problem (LSCP) for emergency service vehicles such as ambulances. Linear programming models have a practical advantage over other nonlinear or queuing-based models. They can be simply coded by practitioners and can be solved routinely using existing commercial software to achieve exact solutions especially for large problem instances.The proposed model provides a pre-specified minimum reliability level for each demand point based on the busy fraction of ambulances located within a specified coverage time threshold while minimizing the number of required ambulances. A set of linear constraints are sought to ensure that the obtained busy fractions for all deployed ambulances are less than a pre-specified upper-bound. This approach allows the busy fractions and locations of ambulances to be determined through the model simultaneously avoiding dealing with the busy fractions as inputs before determining the locations of the ambulances. As a result, a maximum workload will be guaranteed for the deployed ambulances. A second model is presented to relocate the number of ambulances prescribed by the first model to minimize the total response time. Finally, computational results are provided for the EMS system of a rural outskirt area of Tehran to show the capability of the proposed models to minimize both the number of ambulances and the total response time.

► We present two reliability-based linear models for optimal location of ambulances.
► Here, the ambulances’ busy fraction is not an a priori input.
► Our simultaneous approach can significantly reduce the previous overestimations.
► Real-world application issues are demonstrated for the rural roads of Tehran County.