Sustainable planning of penal facilities through multi-objective location-allocation modelling and data envelopment analysis

The escalating population of inmates necessitates a substantial increase in penal facilities. Consequently, there arises a pressing need for strategic planning to identify the location and capacities of new penal facilities, along with the appropriate allocation of prisoners therein. This study proposes a solution methodology to address this imperative by considering multiple future periods and objectives. Specifically, the study examines three objective functions simultaneously based on the three dimensions of sustainability, delineated along economy, society, and environment. To operationalize this framework, a multi-objective mixed integer linear programming model is developed, and an iterative solution methodology is proposed to generate alternative solutions. The alternative solutions are created for two scenarios: exact and fractional assignment of prisons in cities. Subsequently, the efficacy of these alternatives is assessed through the application of super-efficiency and cross-efficiency data envelopment analysis techniques. In each of these scenarios, the most efficient solution among alternatives is identified as the final solution. The empirical data utilized in the study is sourced from real-world cases in Turkey. Comparative analyses of the solutions under each scenario offer valuable insights into their respective advantages and disadvantages, thereby contributing to a comprehensive understanding of the problem.