VRP Contiguous to Multimodal Transportation Problem: An Integrated Approach

What has initiated the idea of this research is the situation of marine, rail and road transportations in the south region of Iran, the Persian Gulf and Oman see. There are a few large Iranian ports in the region (e.g. Imam Khomeini and Shahid Rajaee) that have been equipped to serve large containerships while, most of the other ports either have not been developed or their geographical and topological restrictions do not let them to serve large ships. For instance, Abadan and Khorramshahr were two active ports and main Iranian Import/Export terminals until the Iraqi army attacked them in 1981. Although, the war finished in 1989, nowadays these are unable to serve current fleet of large container ships due to the limitation of their water way, the Arvand-River. Therefore, their rail and road transportation system's capacity are mostly unused. On the other hand, due to the national economic development programs and the especial attention to the Iranian 20 year's economic vision, Iran needs to develop continuously new transportation capacities as well as better utilization of the existing capacities. To develop the transportation capacity, one way is to invest on the existing ports in order to serve larger ships. However, in one hand, the investment should continuously grow because, as the literature shows, mega-ships and rapid-ships are going to emerge until the year 2020. On the other hand, some of the ports, due to their geographical situation, are not able to catch any share of those investments. Therefore, we need to find a way to activate the small ports to use their capacities.A way that could be theoretically investigated is that the large ports could be used as hobs (intermediate centers) to feed the transportation network (include small ports and ships). In this case, it might be possible to plan a rout for a mega-ship which comes from a depot (outside the region, such as the sought east of Asia) so that it discharges goods at some ports in the region (the Iranian and other nation ports in the Persian Gulf, Oman Sea and the Mouth of Indian Ocean), and then set back to the depot. Consequently, the discharged goods are handled to some consumer centers (the centers in Iran as well as the transit destinations like: Afghanistan, Iraq, Turkey, Russia, and the new independent countries in north of Iran) by a multimodal network (with road, rail and marine modes). Applying this idea could brisk up the utilization of the Iranian private fleets and ports in the region. That is because in one hand, there are plenty of small and medium size ships (that are mostly private ones), which could provide us with a large amount of marine capacity among Iranian and other nations ports in the region. On the other hand, most of the Iranian ports are not able to serve large ships. Moreover, some of the countries in the region (e.g. Pakistan and the Arab Emirates) have extensively invested on some of their ports, so those ports could be used to brisk up utilization of the Iranian fleets and ports and to increase the transit of goods through Iran. In this case, an opportunity rises to get advantage of other nations capitals in order to speed up the flow of goods to/from Iran. However, in order to get advantage of this opportunity, its feasibility, conditions, benefits and other political and social aspects should be studied. This paper concerns with studying the network aspects of the idea in order to evaluate its costs and possibly optimize them. From the network design point of view, the network among the depot and the intermediate ports of the marine transportation network could be considered as a Split Delivery VRP (SDVRP) except than that the demands of the customers (the intermediate centers) are not known in advance, and they are variables to be decided. In the split delivery vehicle routing problem (SDVRP), a fleet of homogeneous vehicles should serve a set of customers, while each customer can be visited more than once, contrary to the assumption in the VRP. So, the demand of each customer can be greater than the capacity of the vehicles. No constraint on the number of available vehicles is considered. Moreover, the network among the intermediate and the consumer centers is a multimodal transportation one in which the goods supplies at the intermediate centers are not known in advance and they are variables to be decided. In this network, it is possible to change the mode of transportation at some of the intermediate or consumer centers with some charges. In this paper the idea has been introduced and, a general transportation system based on it has been originally designed and modeled. The system consists of a Split Delivery Vehicle Routing contiguous to a Multimodal Transportation. The system has originally been modeled and solved in this paper using exact and heuristic methods. The branch-and-bound technique has been used to solve small size test problems. Moreover, in order to solve larger size instances, a heuristic method, called SB-RAB, has been developed which works based on limited entry Simplex method. SB-RAB has been applied to solve two series of test problems which have been barrowed from the VRP literature. Both exact and SB-RAB algorithms are then applied to solve a series of problems which has been adapted in this paper from a set of VRP benchmark problems. Finally the results have been compared and show that the SB-RAB is able to produce good quality solutions in an acceptable time.