Discrete time and continuous time formulations for a short sea inventory routing problem

We consider a fuel oil distribution problem where an oil company is responsible for the routing and scheduling of ships between ports such that the demand for various fuel oil products is satisfied during the planning horizon. The production/consumption rates are given and assumed to be constant. We provide two alternative mixed integer formulations: a discrete time model adapted from the case where the production/consumption rates are varying and a classical continuous time formulation. We discuss different extended formulations and valid inequalities that allow us to reduce the linear gap of the two initial formulations. A computational study comparing the various models accordingly to their size, linear gap and running time, was conducted based on real small-size instances, using a commercial software

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

Comparing techniques for modelling uncertainty in a maritime inventory routing problem

Uncertainty is inherent in many planning situations. One example is in maritime transportation, where weather conditions and port occupancy are typically characterized by high levels of uncertainty. This paper considers a maritime inventory routing problem where travel times are uncertain. Taking into account possible delays in the travel times is of main importance to avoid inventory surplus or shortages at the storages located at ports. Several techniques to deal with uncertainty, namely deterministic models with inventory buffers; robust optimization; stochastic programming and models incorporating conditional value-at-risk measures, are considered. The different techniques are tested for their ability to deal with uncertain travel times for a single product maritime inventory routing problem with constant production and consumption rates, a fleet of heterogeneous vessels and multiple ports. At the ports, the product is either produced or consumed and stored in storages with limited capacity. We assume two-stages of decisions, where the routing, the visit order of the ports and the quantities to load/unload are first-stage decisions (fixed before the uncertainty is revealed), while the visit time and the inventory levels at ports are second-stage decisions (adjusted to the observed travel times). Several solution approaches resulting from the proposed techniques are considered. A computational comparison of the resulting solution approaches is performed to compare the routing costs, the amount of inventory bounds deviation, the total quantities loaded and unloaded, and the running times. This computational experiment is reported for a set of maritime instances having up to six ports and five ships.publishe

Stochastic master surgery scheduling

The aim of the Master Surgery Scheduling Problem (MSSP) is to schedule the medical specialties to the different operating rooms available, such that surgeries may be performed efficiently. We consider a MSSP where elective and emergency patients can be treated in the same operating rooms. In addition to elective-dedicated operating room slots, flexible operating room slots are introduced to handle the fluctuating demand of emergency patients. To solve the MSSP, we propose a simulation-optimization approach consisting of a two-stage stochastic optimization model and a discrete-event simulation model. For the two-stage stochastic optimization model, uncertain arrivals of emergency patients are represented by discrete scenarios. The discrete-event simulation model is developed to address uncertainty related to the surgery duration and the length of stay at the hospital, and to test the Master Surgery Schedule (MSS) developed by the optimization model in a stochastic operational-level environment. In addition, the simulation model is used to generate scenarios for the optimization model. We present some general advice for surgery scheduling based on testing the optimization model in a numerical study. The simulation-optimization approach is applied to a case study from a hospital department that treats both elective and emergency patients. The optimized MSS outperforms the manually generated MSS, both in terms of emergency waiting time for surgery, and emergency interruptions to the flow of electives.acceptedVersio

Discrete time and continuous time formulations for a short sea inventory routing problem

We consider a fuel oil distribution problem where an oil company is responsible for the routing and scheduling of ships between ports such that the demand for various fuel oil products is satisfied during the planning horizon. Inventory management considerations are taken into account at the demand side only, and consumption rates are given and assumed to be constant. We provide two alternative mixed integer formulations: a discrete time model adapted from the case where the consumption rates are varying and a classical continuous time formulation. We discuss different extended formulations and valid inequalities that allow us to reduce the linear gap of the two initial formulations. A computational study comparing the various models accordingly to their size, linear gap and running time, was conducted based on real small-size instances, using a commercial software

Combined maritime fleet deployment and inventory management with port visit flexibility in roll-on roll-off shipping

We consider a combined fleet deployment and inventory management problem in Roll-on Roll-off shipping. Along given trade routes there are ports with inventories that should be kept within their limits. Current planning practice is to visit all ports every time a trade route is serviced. We instead aim at determining the sailing routes of each voyage along the trade route, where some ports can be skipped on certain voyages. A novel mixed integer programming model is proposed and tested on realistic instances. The results indicate that substantial gains can be achieved from this more flexible way of planning

Robust optimization for a maritime inventory routing problem

We consider a single product maritime inventory routing problem in which the production and consumption rates are constant over the planning horizon. The problem involves a heterogeneous fleet and multiple production and consumption ports with limited storage capacity. Maritime transportation is characterized by high levels of uncertainty, and sailing times can be severely influenced by varying and unpredictable weather conditions. To deal with the uncertainty, this paper investigates the use of adaptable robust optimization where the sailing times are assumed to belong to the well-known budget polytope uncertainty set. In the recourse model, the routing, the order of port visits, and the quantities to load and unload are fixed before the uncertainty is revealed, while the visit time to ports and the stock levels can be adjusted to the scenario. We propose a decomposition algorithm that iterates between a master problem that considers a subset of scenarios and an adversarial separation problem that searches for scenarios that make the solution from the master problem infeasible. Several improvement strategies are proposed aiming at reducing the running time of the master problem and reducing the number of iterations of the decomposition algorithm. An iterated local search heuristic is also introduced to improve the decomposition algorithm. A computational study is reported based on a set of real instances.publishe

Hybrid heuristics for a maritime short sea inventory routing problem

We consider a short sea fuel oil distribution problem where an oil company is responsible for the routing and scheduling of ships between ports such that the demand for various fuel oil products is satisfied during the planning horizon. The inventory management has to be considered at the demand side only, and the consumption rates are given and assumed to be constant within the planning horizon. The objective is to determine distribution policies that minimize the routing and operating costs, while the inventory levels are maintained within their limits. We propose an arc-load flow formulation for the problem which is tightened with valid inequalities. In order to obtain good feasible solutions for planning horizons of several months, we compare different hybridization strategies. Computational results are reported for real small-size instances

A decision support methodology for strategic planning in maritime transportation

a b s t r a c t This paper presents a decision support methodology for strategic planning in tramp and industrial shipping. The proposed methodology combines simulation and optimization, where a Monte Carlo simulation framework is built around an optimization-based decision support system for short-term routing and scheduling. The simulation proceeds by considering a series of short-term routing and scheduling problems using a rolling horizon principle where information is revealed as time goes by. The approach is flexible in the sense that it can easily be configured to provide decision support for a wide range of strategic planning problems, such as fleet size and mix problems, analysis of long-term contracts and contract terms. The methodology is tested on a real case for a major Norwegian shipping company. The methodology provided valuable decision support on important strategic planning problems for the shipping company

Combined ship routing and inventory management in the salmon farming industry

We consider a maritime inventory routing problem for Norway's largest salmon farmer both producing the feed at a production factory and being responsible for fish farms located along the Norwegian coast. The company has bought two new ships to transport the feed from the factory to the fish farms and is responsible for the routing and scheduling of the ships. In addition, the company has to ensure that the feed at the production factory as well as at the fish farms is within the inventory limits. A mathematical model of the problem is presented, and this model is reformulated to improve the efficiency of the branch-and-bound algorithm and tightened with valid inequalities. To derive good solutions quickly, several practical aspects of the problem are utilized and two matheuristics developed. Computational results are reported for instances based on the real problem of the salmon farmer