Savings Algorithm with Time Windows

In vehicle routing problems, the Savings Algorithm with Time Windows serves as a crucial functional approach that significantly enhances vehicle route optimization. This algorithm effectively reduces total travel distance by incorporating time window constraints, thereby saving both time and operational costs. The implementation typically involves calculating savings values between customer pairs while verifying time feasibility through forward/backward scheduling checks. Due to its exceptional performance in real-world applications, this algorithm has been widely adopted in logistics and distribution industries, becoming an indispensable component in modern supply chain management systems. The core function usually includes: 1) Initializing individual routes for each customer, 2) Computing savings matrix considering travel time and time windows, 3) Merging routes based on maximum savings while maintaining time feasibility, and 4) Iterating until no further improvements can be made.