Jørgen Glomvik Rakke

A construction and improvement heuristic for a liquefied natural gas inventory routing problem

We present a large scale ship routing and inventory management problem for a producer and distributor of liquefied natural gas (LNG). The problem contains multiple products, inventory and berth capacity at the loading port and a heterogeneous fleet of ships. The goal is to create an annual delivery program to fulfill the producers long-term contracts at minimum cost, while maximizing the revenue from selling LNG in the spot market. To solve this problem we have developed a construction and improvement heuristic (CIH). The CIH is a multi-start local search heuristic that constructs a set of solutions using a greedy insertion procedure. The solutions are then improved using either a first-descent neighborhood search, branch-and-bound on a mathematical formulation, or both. Tests on real-life instances show that the CIH provides good solutions in a short amount of time.

A Branch-Price-and-Cut Algorithm for the Inventory-Routing Problem

The inventory-routing problem IRP integrates two well-studied problems, namely, inventory management and vehicle routing. Given a set of customers to service over a multiperiod horizon, the IRP consists of determining when to visit each customer, which quantity to deliver in each visit, and how to combine the visits in each period into feasible routes such that the total routing and inventory costs are minimized. In this paper, we propose an innovative mathematical formulation for the IRP and develop a state-of-the-art branch-price-and-cut algorithm for solving it. This algorithm incorporates known and new families of valid inequalities, including an adaptation of the well-known capacity inequalities, as well as an ad hoc labeling algorithm for solving the column generation subproblems. Through extensive computational experiments on a widely used set of 640 benchmark instances involving between two and five vehicles, we show that our branch-price-and-cut algorithm clearly outperforms a state-of-the-art branch-and-cut algorithm on the instances with four and five vehicles. In this instance set, 238 were still open before this work and we proved optimality for 54 of them.

The Traveling Salesman Problem with Draft Limits

In maritime transportation, routing decisions are sometimes affected by draft limits in ports. The draft of a ship is the distance between the waterline and the bottom of the ship and is a function of the load onboard. Draft limits in ports can thus prevent ships to enter these ports fully loaded and may impose a constraint on the sequence of visits made by a ship. This paper introduces the Traveling Salesman Problem with Draft Limits (TSPDL), which is to determine an optimal sequence of port visits under draft limit constraints. We present two mathematical formulations for the TSPDL, and suggest valid inequalities and strengthened bounds. We also introduce a set of instances based on TSPLIB. A branch-and-cut algorithm is applied on both formulations for all these instances. Computational results show that introducing draft limits make the problem much harder to solve. They also indicate that the proposed valid inequalities and strengthened bounds significantly reduce both the number of branch-and-bound nodes and the solution times.

A New Formulation Based on Customer Delivery Patterns for a Maritime Inventory Routing Problem

In this paper we address a maritime inventory routing problem encountered by one of the worlds largest producers of liquefied natural gas LNG. The producer is responsible for the LNG inventories at the liquefaction plant, the loading port with a limited number of berths, and the routing and scheduling of a heterogeneous fleet of LNG ships. In addition, the producer has to fulfill a set of long-term contracts to customers all around the world. The producers goal is to create a minimum-cost long-term delivery program that respects the long-term contracts while maximizing revenue from selling LNG in the spot market. We introduce a new formulation for this problem arising from a novel decomposition scheme based on delivery patterns. To solve this formulation, we develop an exact branch-price-and-cut algorithm. Computational results show that this new formulation provides much tighter lower bounds than the only known mixed integer programming MIP formulation for this problem. Furthermore, on a set of 27 benchmark instances, the proposed branch-price-and-cut method clearly outperforms a commercial MIP solver applied to the existing MIP model.

2D-Packing with an Application to Stowage in Roll-On Roll-Off Liner Shipping

Roll-on/Roll-off (RoRo) ships represent the primary source for transporting vehicles and other types of rolling material over long distances. In this paper we focus on operational decisions related to stowage of cargoes for a RoRo ship voyage visiting a given set of loading and unloading ports. By focusing on stowage on one deck on board the ship, this can be viewed as a special version of a 2-dimensional packing problem with a number of additional considerations, such as one wants to place vehicles that belong to the same shipment close to each other to ease the loading and unloading. Another important aspect of this problem is shifting, which means temporarily moving some vehicles to make an entry/exit route for the vehicles that are to be loaded/unloaded at the given port. We present several versions of a new mixed integer programming (MIP) formulation for the problem. Computational results show that the model provides good solutions on small sized problem instances.