A heterogeneous fleet liner ship scheduling problem with port time uncertainty

We deal with a schedule design problem for a heterogeneous fleet liner shipping service under uncertain waiting and handling times at ports. In a liner shipping service, longer than expected waiting and handling times at a port may cause a delay from scheduled departure time. We consider the problem to find the departure times at ports and sailing times of ships between ports so that the total fuel burn is minimized while targeted overall service level (a performance measure based on on-time departure probabilities) is achieved. We consider two new aspects of the problem. The first one is the heterogeneous fleet where each ship type may have different fuel efficiency, i.e. a different fuel burn function. The second one is considering critical ports on the route, i.e. considering the fact that on-time performance at some critical ports might be more important for the shipping company. We propose a model which finds different service levels for different ship type-port pairs by considering importance of ports and fuel efficiencies of ships. We also give a new overall service level measure for the entire route by combining service levels for different ship type-ports pairs. We propose a chance constrained nonlinear mixed integer programming formulation for the problem. Finally, we give computational results that show the effects of several experimental factors on fuel consumption, speed and service level

External validation and recalibration of an incidental meningioma prognostic model - IMPACT: protocol for an international multicentre retrospective cohort study

Introduction: Due to the increased use of CT and MRI, the prevalence of incidental findings on brain scans is increasing. Meningioma, the most common primary brain tumour, is a frequently encountered incidental finding, with an estimated prevalence of 3/1000. The management of incidental meningioma varies widely with active clinical-radiological monitoring being the most accepted method by clinicians. Duration of monitoring and time intervals for assessment, however, are not well defined. To this end, we have recently developed a statistical model of progression risk based on single-centre retrospective data. The model Incidental Meningioma: Prognostic Analysis Using Patient Comorbidity and MRI Tests (IMPACT) employs baseline clinical and imaging features to categorise the patient with an incidental meningioma into one of three risk groups: low, medium and high risk with a proposed active monitoring strategy based on the risk and temporal trajectory of progression, accounting for actuarial life expectancy. The primary aim of this study is to assess the external validity of this model. Methods and analysis: IMPACT is a retrospective multicentre study which will aim to include 1500 patients with an incidental intracranial meningioma, powered to detect a 10% progression risk. Adult patients ≥16 years diagnosed with an incidental meningioma between 1 January 2009 and 31 December 2010 will be included. Clinical and radiological data will be collected longitudinally until the patient reaches one of the study endpoints: intervention (surgery, stereotactic radiosurgery or fractionated radiotherapy), mortality or last date of follow-up. Data will be uploaded to an online Research Electronic Data Capture database with no unique identifiers. External validity of IMPACT will be tested using established statistical methods. Ethics and dissemination: Local institutional approval at each participating centre will be required. Results of the study will be reported through peer-reviewed articles and conferences and disseminated to participating centres, patients and the public using social media