Stochastic demand facility location and vehicle routing problem: A case study of a pharmaceutical warehouse

The logistics sector is increasingly challenged by uncertain demand dynamics, changing customer expectations, and frequent operational problems. Therefore, effectively managing logistics operations and utilizing resources in the most efficient manner is crucial for companies in the sector to gain a competitive advantage. Facility location and vehicle routing decisions have significant impacts on logistics costs. In real-world problems, the variability of demands makes these decisions more complex. The purpose of this study is to develop a cost-optimizing model that addresses uncertainties caused by fluctuating customer demands in logistics operations and to provide a practical solution. In the literature, studies that jointly address stochastic demand facility location and vehicle routing problems are limited. Additionally, the introduction of the approach to meet stochastic demands by calculating customer service levels makes this research unique. In this study, stochastic demand facility location and vehicle routing problems were jointly addressed. For an existing pharmaceutical warehouse operating in İzmir, the location of a new facility and vehicle routing decisions were determined to meet customer demands at the optimal cost. In this context, customer demands were analyzed using the Arena Simulation Software 16, and the suitability of demand distributions was evaluated. Subsequently, a mixed-integer mathematical model was developed for the stochastic demand facility location and vehicle routing problem and solved using GAMS 24.9.1 software. The proposed models were compared based on the expected value of the demand and a 90% customer service level, with the minimum costs found to be 317,184,890 and 316,645,050, respectively. Due to the presence of penalty costs, a 90% customer service level was found to yield the most appropriate result for this case study. The aim is to develop a model that ensures optimization and offers a practical solution.