Logistic systems manage the flow of materials and information of companies and they are a relevant component in every sector. For this reason, the efficient design and the optimization of these systems is a necessary, but non-trivial, activity especially in the sectors most affected by the COVID-19 pandemic, like healthcare and e-commerce. These two are also characterised by a significant social sustainability impact. In particular, the healthcare sector focuses on the improvement of its service quality to enhance the patients satisfaction while e-commerce platforms must consider the drivers condition in their business to deliver goods in an ethical way. For this reason, the activities of this PhD aim at designing and optimizing the logistic systems of different real-world companies taking into account simultaneously multiple conflicting aspects. In the first PhD project, the research activity consists in the design of efficient systems for massive healthcare processes, such as the vaccination against COVID-19, in South Tyrol region. To reach this goal, a digital twin of the vaccination centre is developed through a NFC-based technology composed by common smartphones and card-size badges. This digital twin is based on a software architecture composed by a developed mobile application, which records time information of each process phase and sends this data to a central database, as well as a developed website which elaborates this data and reports dynamically the performance of the healthcare structure and the possible issues. This continuous exchange of information between the physical and the digital system supports practitioners in improving the quality of this healthcare service and increasing the patients satisfaction. In the second addressed PhD project, the focus moves to an outdoor logistic process, i.e. the distribution of goods in a real-world local e-commerce platform. To solve this problem, its mathematical model is defined and a multi-objective metaheuristic algorithm is developed since all the three aspects of sustainability (costs, environment and fairness) must be optimized simultaneously. This algorithm is tested in a real-world e-commerce platform, providing managers with a helpful decision-support system called Pareto frontier which includes all the optimal solutions of the targeted problem. Finally, the last PhD research activity carried out integrates different features of both the previous ones since it regards the optimization of the logistic system of a healthcare service, i.e. the transportation of dependent patients. Therefore, the mathematical model is formulated and an Adaptive Large Neighbourhood Search (ALNS) algorithm is developed to solve the problem efficiently. Also this project is validated with a real-world case study, provided by the Austrian Red Cross, and the results compare different configuration to support managers in finding the best one. In particular, different degree of time window violation, type of shifts and mix of vehicles are tested to define the most convenient situation both for patients, in terms of service quality, and for healthcare department, in terms of costs. In conclusion, through the development and implementation of different mathematical methods, multiple logistic systems have been efficiently designed or improved during this PhD. In addition, all the developed models and the results obtained have been applied and validated in real-world case studies provided by different companies, demonstrating the practical implication of the work carried out.