Bjørn Nygreen

Ship routing and scheduling in the new millennium

We review research on ship routing and scheduling and related problems during the new millennium and provide four basic models in this domain. The volume of research in this area about doubles every decade as does the number of research outlets. We have found over a hundred new refereed papers on this topic during the last decade. Problems of wider scope have been addressed as well as more specialized ones. However, complex critical problems remain wide open and provide challenging opportunities for future research.

Chapter 4 Maritime Transportation

Publisher Summary This chapter discusses various aspects of maritime transportation operations and presents associated decision-making problems and models with an emphasis on ship routing and scheduling models. The chapter describes prescriptive operations research (OR) models and associated methodologies, rather than descriptive models that are usually of interest to economists and public policy makers. The ocean shipping industry has a monopoly on transportation of large volumes of cargo among continents. Pipeline is the only transportation mode that is cheaper than ships for moving large volumes of cargo over long distances. Maritime transportation is the backbone of international trade. The volume of maritime transportation has been growing for many years and is expected to continue growing in the foreseeable future. Maritime transportation is a unique transportation mode possessing characteristics that differ from other modes of transportation and requires decision support models that fit the specific problem characteristics. Maritime transportation poses a wide variety of challenging research problems, the solutions to which have high potential to improve economic performance and increase profitability in the highly competitive arena.

A method for solving ship routing problemswith inventory constraints

We present an optimisation-based solution approach for a real ship planning problem,which is a combination of a variant of the multi-vehicle pickup and delivery problemwith time windows (m-PDPTW), and a multi-inventory model. This problem involves thedesign of a set of minimum cost routes for a fleet of heterogeneous ships servicing a set ofproduction and consumption harbours with a single product (ammonia). The production andinventory information at each harbour, together with the ship capacities and the location ofthe harbours, determine the number of possible arrivals at each harbour during the planningperiod, the time windows for start of service and the load quantity intervals at each arrival.We call this problem the inventory pickup and delivery problem with time windows -IPDPTW. In the mathematical programming model, we duplicate some of the variables anduse a Dantzig - Wolfe decomposition approach. Then the IPDPTW decomposes into a sub-problemfor each harbour and each ship. By synchronising the solutions from both types ofsubproblems, we get extra constraints in the master problem as compared to the masterproblem for the m-PDPTW discussed in the literature. The LP-relaxation of the masterproblem is solved by column generation, where the columns represent ship routes or harbourvisit sequences. Finally, this iterative solution process is embedded in a branch-and-boundsearch to make the solution integer optimal. Our computational results indicate that theproposed method works for the real planning problem.

A multi-start local search heuristic for ship scheduling— a computational study

We present a multi-start local search heuristic for a typical ship scheduling problem. A large number of initial solutions are generated by an insertion heuristic with random elements. The best initial solutions are improved by a local search heuristic that is split into a quick and an extended version. The quick local search is used to improve a given number of the best initial solutions. The extended local search heuristic is then used to further improve some of the best solutions found. The multi-start local search heuristic is compared with an optimization-based solution approach with respect to computation time and solution quality. The computational study shows that the multi-start local search method consistently returns optimal or near-optimal solutions to real-life instances of the ship scheduling problem within a reasonable amount of computation time.

Modelling path flows for a combined ship routingand inventory management problem

We consider a combined time constrained ship routing and inventory managementproblem. A fleet of ships transports a single product between production and consumptionharbours. The transporter has the responsibility for keeping the stock level within its limitsat all actual harbours, and there should be no need to stop the production at any harboursdue to missing transportation possibilities. The number of arrivals to each harbour and thequantities loaded and discharged at each arrival are determined by the continuous productionrates at the harbours, the stock limits and the actual ships visiting the harbours. We use apath flow formulation for this planning problem, and generate paths for each ship includinginformation about the geographical route, the load quantity and start time at each harbourarrival. In addition, we generate paths for each harbour including information about thenumber of arrivals to the harbour, the load quantity and start time at each harbour arrival.We emphasise the formulation of the path generation problems which are subproblems inthe total planning problem. The generated paths appear as columns in a path flow problemwhich corresponds to a master problem. We use a column generation approach to solve thecontinuous problem. The solution is made integer optimal by branch-and-bound. Computationalresults indicate that a path flow formulation and an optimisation based solutionapproach work for real instances of the planning problem.

Column generation approaches to ship scheduling with flexible cargo sizes

We present a Dantzig-Wolfe procedure for the ship scheduling problem with flexible cargo sizes. This problem is similar to the well-known pickup and delivery problem with time windows, but the cargo sizes are defined by intervals instead of by fixed values. The flexible cargo sizes have consequences for the times used in the ports because both the loading and unloading times depend on the cargo sizes. We found it computationally hard to find exact solutions to the subproblems, so our method does not guarantee to find the optimum over all solutions. To be able to say something about how good our solution is, we generate a bound on the difference between the true optimal objective and the objective in our solution. We have compared our method with an a priori column generation approach, and our computational experiments on real world cases show that our Dantzig-Wolfe approach is faster than the a priori generation of columns, and we are able to deal with larger or more loosely constrained instances. By using the techniques introduced in this paper, a more extensive set of real world cases can be solved either to optimality or within a small deviation from optimality.

Tactical planning of offshore petroleum production

This paper describes a model for tactical planning of Norwegian petroleum production. The problem involves regulation of production levels from wells, splitting of production flows into oil and gas products, further processing of gas and transportation in a pipeline network. Blending and processing of gas is necessary to satisfy quality requirements in the markets. The problem is formulated with multi-component flows, regulation alternatives in production, non-linear splitting for chemical processing and linear quality constraints on composite products. Production and splitting are modelled with integer requirements. The model is implemented in XpressMP with a Visual Basic supported user interface in Excel. It is constructed in cooperation with the major Norwegian oil company, Statoil and can identify optimal production patterns and assist in planning of possible shut-downs, demonstrate system robustness to customers and aid in contract negotiations.

Ship routing and scheduling with flexible cargo sizes

Here, we describe a real planning problem in the tramp shipping industry. A tramp shipping company may have a certain amount of contract cargoes that it is committed to carry, and tries to maximize the profit from optional cargoes. For real long-term contracts, the sizes of the cargoes are flexible. However, in previous research within tramp ship routing, the cargo quantities are regarded as fixed. We present an MP-model of the problem and a set partitioning approach to solve the multi-ship pickup and delivery problem with time windows and flexible cargo sizes. The columns are generated a priori and the most profitable ship schedule for each cargo set–ship combination is included in the set partitioning problem. We have tested the method on several real-life cases, and the results show the potential economical effects for the tramp shipping companies by utilizing flexible cargo sizes when generating the schedules.

Robust Inventory Ship Routing by Column Generation

We consider a real integrated ship scheduling and inventory management problem. A fleet of ships transports a single product between production and consumption plants. The transporter has the responsibility for keeping the inventory level within its limits at all actual plants, and there should be no need to stop the production at any plants caused by missing transportation possibilities.

Modeling Norwegian petroleum productionand transportation

In the continental shelf off the coast of Norway, there are several petroleum fields containinga mixture of oil and gas. A multiperiod mixed integer programming model for investmentplanning for these fields has been used by The Norwegian Petroleum Directorate for morethan fifteen years. In practical use, the production from each field has mostly been declaredto follow profiles given by the user, but the user may also declare that the production canvary from the given profile. This paper describes the model and comments on some of thereal problems the model has been used to analyze and the modeling process involved.