Time windows. The model we are trying to develop must be capable of generating solutions that takes time windows into consideration. It is important that the vessels arrive within the opening hours at each customer locations. The sites and terminals are open day and night, however at almost all the customer locations the vessels can only be served at the ports from 07:00 to 16:00 hours. In contrast to soft time windows, opening hours are not interchangeable and therefore considered as hard time windows. Waiting time is a significant problem during the peaks, and needs to be taken care of by improving the routing scheduling. Vessels operated by Stema Shipping have first priority at all sites when they arrive at sites and they occupy the ports for about 15-20 hours during each loading. Therefore, in situations where the site is occupied, smaller vessels have to either wait for loading or call on other sites that can provide the customer needs. Moreover, the operators in NorStone is restricted to complete the customer orders within a predetermine time span of earliest and latest time of delivery.
Time windows. Time windows are an important aspect of our real-world problem and in order to solve the maritime distribution problem, it is important that the mathematical model include time window constraints. A process of constraint relaxation from hard into soft time windows could be an option to help obtain good solutions to the problem, in a shorter amount of time. However, relaxations of these time windows cannot be performed without significantly changing the solutions. An optimization model to the maritime distribution problem without considering time windows will not generate satisfactory results, since this is a scheduling problem where customer nodes are visited and there are working hours to consider at all nodes (production sites, terminals and customers). In our model, opening hours at shipping facilities at the production sites are assumed to be open 24 hours, seven days a week. There are also other time limitations like the potential to build waiting time for vessels, at the unloading locations, into the model and this is an area we have chosen to disregard in the current model. However, this can be an area of imminent potential for further research.
Time windows. If the retailers have certain time windows when they must be served, constraints for this must be added. Such constraints can be either hard or soft, depending on the real world problem. When time windows are implemented as hard constraints, no violation of time windows are allowed in a feasible solution. Soft constraints usually adds a penalty to the solution if there is a constraint violation, meaning that the solution still is feasible. • Distance or duration constraints. Typically maximum distance per route, or maximum time consumption per route. This will of course have an influence on the number of routes and the total cost for the whole set of routes. • Heterogeneous vehicle fleet. In many real world situations, a company have many types of vehicles. These vehicles can range from small to large, have different purposes and varying cost efficiency. • Split delivery When split delivery is allowed, a customer can be visited by more than one vehicle each period. The customer’s demand then gets fulfilled by one or more deliveries. In real life this can often occur because of capacity limits on the vehicles. • Multiple depot. There might be more than one depot, which introduces the choice of which depot that should supply which customer.
