## 5 Case Study Applications  
Two case studies have been developed to analyze and evaluate the proposed H&S transportation system's effectiveness in regulating vessel routes and passenger flows moving from mainland Greece to the Aegean Islands. The first includes 17 ports, and the second includes 51 ones. The Aegean Islands cluster includes more than 150 inhabited islands, many of them being within the top tourist attraction destinations. Two central ports on the mainland (Piraeus and Rafina, next to Athens) connect to the Aegean Islands, serving more than 3 million visitors yearly. Piraeus Port (one of the busiest ports in the Mediterranean and Europe) is located 12 km southwest of Athens and constitutes the Aegean Islands central getaway. Rafina is located 50 km northeast of Athens, is the second gateway port for the Aegean Islands, and has presented significant growth in recent years. Figure 7 presents the location of the two central ports and the traveling flows to the Aegean Sea islands. Several cases and operational scenarios have been developed for model testing and evaluation based on the Network of Short Sea Shipping in the Aegean area. The island cluster that is considered in the case study consists of 15 islands, rather sparsely and unevenly located on the map to facilitate result justification. Table 1 illustrates the necessary data for the case study application. They include the distances between islands, the number of passengers by destination, and the vessel's average speed. The time for boarding and disembarkation is assumed to be ten minutes on every island. Figure 7: Traveler flows to the Aegean Islands. Vessels can depart from two central ports (Piraeus or Rafina), while three islands (Chios, Limnos, Ikaria) have been set as potential Hub nodes. Two vessel types with different characteristics (speed) are considered depending on their route origin. The following scenarios are examined to evaluate the model's capability to effectively and realistically assess optimal route planning:  
* C1: One vessel departs from a central port (Piraeus) and serves all islands without hub nodes. * C2: Two vessels depart from central ports (one from Piraeus and one from Rafina) and serve all islands without hub nodes. * C3: One vessel departs from a central port (Piraeus) with one hub connector. * C4: Two vessels depart from central ports (Piraeus and Rafina) with one hub connector to be assigned by the algorithm. The optimization is performed upon single or combined objectives referring to the total distance traveled (D) and the cumulative passenger hours (PH) while two more parameters are recorded and evaluated in each case, the total travel time (T) of all vessels and the maximum trip length (T\({}_{\text{max-trip}}\)) among all passengers. The simplest case, C1, where one vessel serves all islands, imitates the classic Travel Salesman Problem (TSP). Three alternatives are presented to emphasize the scope of the proposed methodology. C1a aims to minimize the traveling distance (and consequently the routing cost). C1b attempts to reduce the total passenger time spent on board. C1c provides a trade-off solution between the above (into some extent) competing goals. The results in Figure 8 indicate that C1a provides the shortest route but at a considerable expense of the total passenger time on board. InsteadC1b recommends a relatively lower total passenger time solution compared to C1a but with increased traveling distance. This happens because small islands with fewer passengers are left to be served last without special attention to proximity criteria. Further, several alternative solutions can be found following the trade-off between the two goals. An indicative such solution (C1c) achieves an almost minimum passenger-hour solution and a competitive traveling distance one. In Case 2, two vessels depart from central ports (one from Pireaus and one from Rafina) to serve the whole island cluster.