A multi-objective programming model for fire station location under incomplete information environment

Identifying the optimal locations of fire stations is a critical problem in urban planning and emergency management, which directly affects the efficiency of emergency services. However, fire station location decisions are often made under incomplete information environments. This incompleteness is primarily manifested in two aspects: one is human cognitive uncertainty due to a lack of historical data (referred to as human uncertainty), and the other is inherently ambiguous probability distributions of randomness itself. Therefore, during the location process, factors such as travel time, operating cost, and fixed cost often exhibit certain degrees of randomness with ambiguous probability distributions or human uncertainty. To address these challenges, this paper presents a multi-objective chance constrained programming model that simultaneously considers four factors: distance, travel time, annual operating cost, and fixed cost. It also introduces sublinear expectation theory and uncertainty theory to handle randomness with ambiguous probability distributions and human uncertainty, respectively. This paper offers significant theoretical insights and practical guidance for urban fire safety planning and emergency management under an incomplete information environment. One example is that fire station location plans in Changqing District of Jinan City are derived by applying a genetic algorithm (GA) to solve the model.