Mathematical Modeling of the Vehicle Routing Problem with Relaxed Time Windows and Delay Penalties

The Vehicle Routing Problem with Relaxed Time Windows (VRP-RTW) is an extension of the classic Vehicle Routing Problem (VRP) that incorporates flexibility in service time windows. In VRP-RTW, vehicles are allowed to arrive later than the specified time window. However, a violation will be imposed for exceeding the specified time limit. in the form of fines or similar penalties. This research aims to design a mathematical model for VRP-RTW to minimize total travel costs and delay penalties, while ensuring that all customers are served within the capacity limits of the available vehicles. This research uses literature review methods and mathematical formulation approaches to describe the logistics distribution problem. The developed model considers several constraints, such as vehicle capacity, route balance, and service time limitations. The results of this research are expected to contribute to more efficient and flexible logistics distribution decision-making and serve as a basis for the development of vehicle route optimization models that can be applied in real-world scenarios.