This study addresses the Long-Term Care Facility Location Problem (LTCFLP), focusing on the optimal location of long-term care facilities in İzmir, Turkiye. Long-term care facilities, often referred to as nursing homes, provide medical services and daily assistance to individuals, primarily the elderly, over extended periods. As the aging population increasing globally, the demand for such facilities has grown, prompting governments to invest in their development. This research aims to determine the best locations for these facilities, balance the load across facilities and o minimize both the establishment and patient assignment costs. The problem is formulated as a multi-objective optimization model, considering facility capacity, overcapacity allowance, and facility utilization. A mixed-integer programming model is developed to achieve these objectives. Additionally, a novel contribution is made by applying a constraint programming (CP) approach, which has not been used for LTCFLP before. The study compares the results from both mixed-integer programming (MIP) and constraint programming models to evaluate their efficiency and effectiveness in solving this complex, real-world problem. The results highlight the trade-offs between different models and propose future research directions for enhancing facility location planning.