Purpose: Ambulance response time is an important factor in saving lives and is highly linked with the ambulance location problem. The Maximum Expected Covering Location Problem (MEXCLP), introduced by Daskin (1983), is one of the most used ambulance location models that maximize the probability of stratifying demands for emergency medical service (EMS) centers. Due to huge increase in the operational costs of EMS centers, ambulance location models must consider the cost of coverage and the opportunity to use other companies’ private ambulances to answer emergency calls. The paper aims to discuss these issues. Design/methodology/approach: In this paper, the authors propose to extend the MEXCLP to a bi-objective optimization problem where the cost of satisfying emergency calls is minimized. Findings: The proposed model is tested using data retrieved from the Lebanese Red Cross (LRC) in Beirut capital of Lebanon. The reported findings show significant enhancements in the results where the LRC can fully satisfy the perceived demands from all areas in Beirut within 9 min with an affordable cost. Originality/value: The model is a first attempt to reduce operational costs of EMS centers while constraining the response time to satisfy emergency calls at an acceptable rate. © 2018, Emerald Publishing Limited.