First Advisor

Avinash Unnikrishnan

Term of Graduation

Spring 2021

Date of Publication


Document Type


Degree Name

Master of Science (M.S.) in Civil & Environmental Engineering


Civil and Environmental Engineering




Ambulance service -- Location -- Mathematical models, Conditional expectations (Mathematics), Emergency medical services



Physical Description

1 online resource (xi, 109 pages)


A classical maximum coverage facility location problem (MCLP) tries to maximize the coverage by serving all possible demands within the specified coverage radius. Depending on the applications, several families of MCLP variants have been developed - each with its unique set of additional constraints. One specific application is locating Emergency medical service (EMS) units. EMS units such as ambulances or drones with emergency supplies are located using models such as the maximum expected survival location problem (MEXSLP). However, a classical MEXSLP model tends to locate EMS units near densely populated regions, resulting in increased response times for lowly populated regions. If equity is to be taken into consideration, the EMS units would be placed more uniformly across the region which might result in reduced overall coverage.

In this thesis, a conditional expectation measure called the conditional ß-mean (CBM) is considered and integrated into the facility location models. First, the CBM measure is integrated into the MCLP, resulting in the development of a new MCLP model. Using an alternative and more intuitive definition for CBM, another modified MCLP model incorporated with CBM is developed. These new MCLP models incorporated with CBM are single objective facility location models with flexible coverage radius constraints. Two standard test cases and a Portland Metropolitan region dataset are used to test the MCLP models. A simple greedy based heuristic is developed, and its performance is compared to a state-of-the-art Mixed Integer Programming solver Gurobi. The integration of CBM into the MCLP model has improved its coverage. The proposed heuristic provides reliable solutions and saves considerable computational time.

Using the same CBM measure, equity is incorporated into the MEXSLP model. We propose two different approaches to estimate CBM and develop two modified MEXSLP models improving the quality of service provided to outlying and lowly populated areas. The two MEXSLP models modified with CBM are linear, and the decision maker has the leverage to chose the level of equity in the solution using the parameter ß. The same Portland dataset is used for testing the MEXSLP models. Integration of CBM into the MEXSLP has improved the service in Portland suburbs by locating few EMS units closer to them.


© 2021 Rohan Sirupa

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This research is a product of NSF grants awarded to Prof. Unnikrishnan (Grant numbers: 1562109 and 1826337).

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