## 6 Conclusions  
In order to secure a competitive advantage in the current market, an efficient logistics service has been regarded as one of the most important strategies. In particular, the transportation, which accounts for the largest cost in logistics activities, is critical for enhancing the service level and saving the cost. However, the current transport management system (TMS) focuses on designing the optimal route, which minimizes the objective function consisting of different factors such as travelling distance, required vehicles, and drivers, while meeting several different constraints, like maximum capacities, time windows to visit, and demand for delivery and pick-up. Many previous studies have presented very advanced models, methods, and algorithms to solve the mathematical problems related to VRP. Still, it is not easy to find previous research which considers the valuable assets for transportation services, like containers and trays, except vehicles and drivers, even though these assets are very critical to enhancing the service level and may cause additional operating costs. In this work, we devised a novel mathematical problem, VRPSDP-TW-LO, which considers the cost from the left-over trays, travelling distance, and time-window penalty at the same time. This model may reflect the practical circumstances of daily distribution services by relaxing some constraints of traditional VRPSDP or VRPSDP-TW and adding more factors. With small and simple numerical experiments and statistical tests, we verified the practical applicability of the proposed model by comparing the various performance metrics, such as travelling distance, number of time-window penalties, and number of left-over trays, not only the total cost. The results show that the proposed model can save 2.9% of the average total cost for every day when compared to the VRPSDP-TW model in the simple numerical example. In addition, we evaluated the performance based on a practical business environment for 30 days, to check the cumulative effect of daily operations. As could be seen in the examples, a trade-off exists between the time window penalty and left-over trays. However, the proposed model, VRPSDP-TW-LO, can reduce the number of left-over trays with a very small difference in time window violations. Therefore, it could be concluded that the proposed model may guarantee a better service level, as well as reducing the cost. In addition, it seems possible to apply the proposed model to the various industries and services in which reusable assets are regarded as very important, such as unit containers and trays. Still, this research has some limitations to being applied to a real practical business environment. External environmental factors like the traffic conditions, which have great impacts on the arrival time to the customer and transportation costs, have not been considered. Also, the number of left-over trays could not be deterministic, because the trays may be missed or damaged. Therefore, in future research, the constraints of external environmental factors and stochastic variables and parameters, which are out of scope of this research, should be considered. In addition, even though the two penalty costs, time window violations, and left-over trays have been acquired from an actual logistics company, it may be helpful to evaluate the sensitivity and robustness of the solution by changing the value of penalty costs. In addition, in this research, the proposed model was only verified with small numerical experiments. Thus, to apply the proposed model to a real business environment and find the optimal solution, it is required to design heuristic algorithms like Tabu search, genetic algorithms, or swarm optimization approaches to solve the bigger problem with the larger number of delivery points. Conceptualization, I.G., K.L. and K.S. ; methodology, J.K., and Y.M. ; software, I.G., K.S. ; validation, I.G., Y.M. and K.S. ; formal analysis, I.G, and K.S. ; resources, K.L. ; data curation, K.L. and I.G.