Marielle Christiansen

A maritime inventory routing problem with stochastic sailing and port times

This paper describes a stochastic short sea shipping problem where a company is responsible for both the distribution of oil products between islands and the inventory management of those products at consumption storage tanks located at ports. In general, ship routing and scheduling is associated with uncertainty in weather conditions and unpredictable waiting times at ports. In this work, both sailing times and port times are considered to be stochastic parameters. A two-stage stochastic programming model with recourse is presented where the first stage consists of routing, loading and unloading decisions, and the second stage consists of scheduling and inventory decisions. The model is solved using a decomposition approach similar to an L-shaped algorithm where optimality cuts are added dynamically, and this solution process is embedded within the sample average approximation method. A computational study based on real-world instances is presented.

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.

A new decomposition algorithm for a liquefied natural gas inventory routing problem

We consider an inventory routing problem (IRP) in the liquefied natural gas (LNG) supply chain, called the LNG-IRP. Here, an actor is responsible for the LNG production and inventory management at the liquefaction plants, the routing and scheduling of a heterogeneous fleet of LNG ships, as well as the inventories and sales at the regasification terminals. Furthermore, all ports have a limited number of berths available for loading and unloading. The LNG-IRP is more complicated than many other maritime inventory routing problems because a constant rate of the cargo evaporates in the tanks each day and is used as fuel during transportation. In addition, a variable number of tanks are unloaded at the regasification terminals. We introduce a new path flow formulation for this problem arising from a novel decomposition scheme based on parts of a ship schedule, called duties. A ship schedule for the entire planning horizon can be divided into duties consisting of a visit to a liquefaction plant, then one or two visits to a regasification terminal before ending in a liquefaction plant. The solution method suggested is based on a priori generation of duties, and the formulation is strengthened by valid inequalities. The same problem was previously solved by a branch-price-and-cut algorithm for a schedule-based formulation. Computational results show that the new formulation provides tighter bounds than the previous schedule-based formulation. Furthermore, on a set of 27 benchmark instances, the proposed algorithm clearly outperforms the previous branch-price-and-cut algorithm both with regard to computational time and the number of problems solved within a 10-h time limit.

An iterative two-phase hybrid matheuristic for a multi-product short sea inventory-routing problem

This paper considers a multi-product short sea inventory-routing problem in which a heterogeneous fleet of ships transports multiple products from production sites to consumption sites in a continuous time framework. A many-to-many distribution structure is taken into account, which makes it extremely hard to even compute feasible solutions. We propose an iterative two-phase hybrid matheuristic called Hybrid Cargo Generating and Routing (HCGR) to solve the problem. In the first phase the inventory-routing problem is converted into a ship routing and scheduling problem by generating cargoes subject to inventory limits through the use of mathematical programming. In the second phase, an adaptive large neighborhood search solves the resulting ship routing and scheduling problem. The HCGR heuristic iteratively modifies the generated cargoes based on information obtained during the process. The proposed heuristic is compared with an exact algorithm on small size instances; computational results are also presented on larger and more realistic instances.

Inventory routing with pickups and deliveries

Abstract This paper introduces a class of problems which integrate pickup and delivery vehicle routing problems (PDPs) and inventory management, and we call them inventory routing problems with pickups and deliveries (IRP-PD). We consider a specific problem of this class, where a commodity is made available at several origins and demanded by several destinations. Time is discretized and transportation is performed by a single vehicle. A mathematical programming model is proposed together with several classes of valid inequalities. The models are solved with a branch-and-cut method. Computational tests are performed to show the effectiveness of the valid inequalities on instances generated from benchmark instances for the inventory routing problem. Results show that the branch-and-cut algorithm is able to solve to optimality 345 over 400 instances with up to 50 customers over 3 periods of time, and 142 over 240 instances with up to 30 customers and 6 periods. From a management perspective, results show that the average cost of a non integrated policy is more than 35% higher than the cost of an integrated policy.

A New Formulation for the Combined Maritime Fleet Deployment and Inventory Management Problem

This paper addresses the fleet deployment problem and in particular the treatment of inventory in the maritime case. A new model based on time-continuous formulation for the combined maritime fleet deployment and inventory management problem in Roll-on Roll-off shipping is presented. Tests based on realistic data from the Ro-Ro business show that the model yields good solutions to the combined problem within reasonable time.

The Vehicle Routing Problem with Dynamic Occasional Drivers

Technological advances, such as smart phones and mobile internet, allow for new and innovative solutions for transportation of goods to customers. We consider a setting where a company not only uses its own fleet of vehicles to deliver products, but may also make use of ordinary people who are already on the road. This may include people who visit the store, who are willing to take a detour on their way home for a small compensation. The availability of these occasional drivers is naturally highly uncertain, and we assume that some stochastic information is known about their appearance. This leads to a stochastic vehicle routing problem, with dynamic appearance of vehicles. The contribution of this paper is a mixed integer programming formulation, and insights into how routes for the company vehicles could be planned in such a setting. The results of the stochastic model are compared with deterministic strategies with reoptimization.

A Multi-product Maritime Inventory Routing Problem with Undedicated Compartments

This paper considers the problem of routing bulk tankers to minimize cost while managing the inventory in ports. Multiple non-mixable products are transported and the allocation of products to undedicated compartments onboard the ships is an important aspect of the problem. A mixed integer programming formulation of the problem is proposed, and the model is strengthened by including several valid inequalities. Computational results are reported for an evaluation of the model and the valid inequalities. Results are also reported for two simplified models where either the compartments are dedicated or the products are mixable.