Tramp shipment routing and scheduling with inventory and stowage constraints

Maritime transport has been a fundamental mode of transportation for centuries, enabling the transportation of heavy and bulky items in large quantities across oceans and seas. The use of ships has allowed for the efficient movement of goods and commodities and has been vital in facilitating global trade and commerce. In modern times, maritime transport has become even more critical with the exponential growth in global trade and the movement of goods, making it an essential component of the global economy. There are various types of operations involved in maritime transport, with liner, tramp, and industrial shipping being the three most commonly used. Liner shipping refers to the use of regularly scheduled services between designated ports, where ships follow a fixed timetable and transport a specific type of cargo. In contrast, tramp shipping operates on an ad hoc basis, with ships not following a fixed schedule but instead sailing according to the requirements of customers, and the ships are usually rented or leased. Industrial shipping, on the other hand, refers to the transportation of goods using ships that are owned by the supplier or customer. Tramp shipping alongside with the liner shipping is widely used in maritime transport, particularly for the transportation of bulk cargoes such as coal, iron, and grain. In this type of shipping, ships are chartered on a single voyage basis, and the cargo is loaded and transported according to the specific requirements of the customer. The ships used in tramp shipping are usually equipped with cranes to load and unload the cargo. In the tramp shipping problem considered in this study, the objective is to transport a set of cargoes from their origin ports to their respective destination ports using a homogeneous fleet of ships. The origin and destination ports of both the cargoes and the ships are predetermined. All of the cargoes are mandatory and have to be sent to their destination point within their respective deadline. If a cargo arrives at its destination point before the deadline, there will be a deduction from the cost as a reward. To minimize the sailing cost, inventory cost, and stowage cost, the problem is modeled as a mixed integer linear program, taking into account the stowage and inventory constraints that arise in real life applications. Stowage constraints are used to ensure the stability of the ship and to eliminate the loss of time when loading and unloading the cargoes. The ports have initial inventories of the cargoes, and their inventory value changes according to the amount shipped. Inventory constraints are developed to control the changes in inventory levels. Decisions must be made based on the routes and schedules of the ships, as well as the stowage and inventory constraints. The computational results obtained from 153 instances provides valuable insights for solving the tramp-shipping problem. The results show that while small-sized instances can be solved optimally, medium-sized and large-sized instances achieve gaps between 5-30% and 30-70%, respectively, depending on different problem characteristics. This gap is found by comparing the current solution to the best bound found in the problem. This study of the tramp shipping problem is designed to provide significant practical applications in the maritime transportation industry, as it can help shipping companies optimize their fleet utilization and reduce their transportation costs, leading to increased efficiency and profitability. Previous literature concerning the combination of these three maritime problems was limited, this study is designed to fill a significant gap in the literature and bring valuable insights for further research.