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Fire service quality relies on fast response and cooperation of various types of responders to maintain efficient operations and reliable rescue services. This paper investigates a joint location and assignment optimization (JLAO) problem, where fire vehicles from different fire stations can be dispatched jointly as a cooperative unit in a fire rescue operation. We first propose a mixed integer non-linear program to optimize the station location and vehicle assignment decisions, aiming to minimize the total system cost including facility construction, operations cost, and fire damage losses. We proposed a Stingy-Interchange (SI) algorithm to efficiently solve this problem to a near-optimal solution. The JLAO model and the proposed solution method are then applied to hypothetical instances with different sizes and parameter settings to compare the performance of the SI algorithm with a commercial solver (Gurobi). An empirical case study on a major city is conducted to reveal insights on how cost measures are affected by key parameters.