Berit Dangaard Brouer

The Vessel Schedule Recovery Problem (VSRP) – A MIP model for handling disruptions in liner shipping

Containerized transport by liner shipping companies is a multi billion dollar industry carrying a major part of the world trade between suppliers and customers. The liner shipping industry has come under stress in the last few years due to the economic crisis, increasing fuel costs, and capacity outgrowing demand. The push to reduce CO2 emissions and costs have increasingly committed liner shipping to slow-steaming policies. This increased focus on fuel consumption, has illuminated the huge impacts of operational disruptions in liner shipping on both costs and delayed cargo. Disruptions can occur due to adverse weather conditions, port contingencies, and many other issues. A common scenario for recovering a schedule is to either increase the speed at the cost of a significant increase in the fuel consumption or delaying cargo. Advanced recovery options might exist by swapping two port calls or even omitting one. We present the Vessel Schedule Recovery Problem (VSRP) to evaluate a given disruption scenario and to select a recovery action balancing the trade off between increased bunker consumption and the impact on cargo in the remaining network and the customer service level. It is proven that the VSRP is NP-hard. The model is applied to four real life cases from Maersk Line and results are achieved in less than 5seconds with solutions comparable or superior to those chosen by operations managers in real life. Cost savings of up to 58% may be achieved by the suggested solutions compared to realized recoveries of the real life cases.

Liner Shipping Cargo Allocation with Repositioning of Empty Containers

Abstract This paper is concerned with the cargo allocation problem considering empty repositioning of containers for a liner shipping company. The aim is to maximize the profit of transported cargo in a network, subject to the cost and availability of empty containers. The formulation is a multi-commodity flow problem with additional inter-balancing constraints to control repositioning of empty containers. In a study of the cost efficiency of the global container-shipping network, Song et al. (2005) estimate that empty repositioning cost constitutes 27% of the total world fleet running cost. An arc-flow formulation is decomposed using the Dantzig-Wolfe principle to a path-flow formulation. A linear relaxation is solved with a delayed column generation algorithm. A feasible integer solution is found by rounding the fractional solution and adjusting flow balance constraints with leased containers. Computational results are reported for seven instances based on real-life shipping networks. Solving the relaxed linear path-flow model with a column generation algorithm outperforms solving the relaxed linear arc-flow model with the CPLEX barrier solver even for very small instances. The proposed algorithm is able to solve instances with 234 ports, 16,278 demands over 9 time periods in 34 min. The integer solutions found by rounding down are computed in less than 5 s and the gap is within 0.01% from the upper bound of the linear relaxation. The solved instances are quite large compared to those tested in the reviewed literature.

Competitive Liner Shipping Network Design

Abstract We present a solution method for the liner shipping network design problem which is a core strategic planning problem faced by container carriers. We propose the first practical algorithm which explicitly handles transshipment time limits for all demands. Individual sailing speeds at each service leg are used to balance sailing speed against operational costs, hence ensuring that the found network is competitive on both transit time and cost. We present a matheuristic for the problem where a MIP is used to select which ports should be inserted or removed on a route. Computational results are presented showing very promising results for realistic global liner shipping networks. Due to a number of algorithmic enhancements, the obtained solutions can be found within the same time frame as used by previous algorithms not handling time constraints. Furthermore, we present a sensitivity analysis on fluctuations in bunker price which confirms the applicability of the algorithm.

A Matheuristic for the Liner Shipping Network Design Problem with Transit Time Restrictions

We present a mathematical model for the liner shipping network design problem with transit time restrictions on the cargo flow. We extend an existing matheuristic for the liner shipping network design problem to consider transit time restrictions. The matheuristic is an improvement heuristic, where an integer program is solved iteratively as a move operator in a large-scale neighborhood search. To assess the effects of insertions/removals of port calls, flow and revenue changes are estimated for relevant commodities along with an estimation of the change in the vessel cost. Computational results on the benchmark suite LINER-LIB are reported, showing profitable networks for most instances. We provide insights on causes for rejecting demand and the average speed per vessel class in the solutions obtained.

Big Data Optimization in Maritime Logistics

Seaborne trade constitutes nearly 80 % of the world trade by volume and is linked into almost every international supply chain. Efficient and competitive logistic solutions obtained through advanced planning will not only benefit the shipping companies, but will trickle down the supply chain to producers and consumers alike. Large scale maritime problems are found particularly within liner shipping due to the vast size of the network that global carriers operate. This chapter will introduce a selection of large scale planning problems within the liner shipping industry. We will focus on the solution techniques applied and show how strategic, tactical and operational problems can be addressed. We will discuss how large scale optimization methods can utilize special problem structures such as separable/independent subproblems and give examples of advanced heuristics using divide-and-conquer paradigms, decomposition and mathematical programming within a large scale search framework. We conclude the chapter by discussing future challenges of large scale optimization within maritime shipping and the integration of predictive big data analysis combined with prescriptive optimization techniques.

Optimization in liner shipping

Seaborne trade is the lynchpin in almost every international supply chain, and about 90% of non-bulk cargo worldwide is transported by container. In this survey we give an overview of data-driven optimization problems in liner shipping. Research in liner shipping is motivated by a need for handling still more complex decision problems, based on big data sets and going across several organizational entities. Moreover, liner shipping optimization problems are pushing the limits of optimization methods, creating a new breeding ground for advanced modelling and solution methods. Starting from liner shipping network design, we consider the problem of container routing and speed optimization. Next, we consider empty container repositioning and stowage planning as well as disruption management. In addition, the problem of bunker purchasing is considered in depth. In each section we give a clear problem description, bring an overview of the existing literature, and go in depth with a specific model that somehow is essential for the problem. We conclude the survey by giving an introduction to the public benchmark instances LINER-LIB. Finally, we discuss future challenges and give directions for further research.