The number of cargos transported by the logistics industry is increasing every year due to the growth of sales on the internet. It is thus crucial to address issues such as long working hours for employees, fewer personnel, and increasing CO2 emissions for an effective transportation system. However, it is possible to create a productive delivery plan by considering uncertainties in time fluctuations, such as delays in work and delays in transportation due to the traffic congestion. Previous studies have defined mathematical programming models to build delivery plans that satisfy customer demand. However, few studies consider time fluctuations with multiple vehicles. Therefore, this study proposes an effective solution for the stochastic vehicle routing problem (VRP) using the L-shaped method, demonstrating the effectiveness of the proposed model by evaluating the value of stochastic solution (VSS). Specifically, we develop a model for VRP using multiple vehicles, taking into consideration the fluctuations in service and travel time between customers.