Pricing routines for vehicle routing with time windows on road networks

Several very effective exact algorithms have been developed for vehicle routing problems with time windows. Unfortunately, most of these algorithms cannot be applied to instances that are defined on road networks, because they implicitly assume that the cheapest path between two customers is equal to the quickest path. Garaix and coauthors proposed to tackle this issue by first storing alternative paths in an auxiliary multi-graph, and then using that multi-graph within a branch-and-price algorithm. We show that, if one works with the original road network rather than the multi-graph, then one can solve the pricing subproblem more quickly, in both theory and practice

Pricing routines for vehicle routing with time windows on road networks

Several very effective exact algorithms have been developed for vehicle routing problems with time windows. Unfortunately, most of these algorithms cannot be applied to instances that are defined on road networks, because they implicitly assume that the cheapest path between two customers is equal to the quickest path. Garaix and coauthors proposed to tackle this issue by first storing alternative paths in an auxiliary multi-graph, and then using that multi-graph within a branch-and-price algorithm. We show that, if one works with the original road network rather than the multi-graph, then one can solve the pricing subproblem more quickly, in both theory and practice

Exenatide once weekly versus placebo in Parkinson's disease: a randomised, double-blind, placebo-controlled trial

BACKGROUND: Exenatide, a glucagon-like peptide-1 (GLP-1) receptor agonist, has neuroprotective effects in preclinical models of Parkinson's disease. We investigated whether these effects would be apparent in a clinical trial. METHODS: In this single-centre, randomised, double-blind, placebo-controlled trial, patients with moderate Parkinson's disease were randomly assigned (1:1) to receive subcutaneous injections of exenatide 2 mg or placebo once weekly for 48 weeks in addition to their regular medication, followed by a 12-week washout period. Eligible patients were aged 25-75 years, had idiopathic Parkinson's disease as measured by Queen Square Brain Bank criteria, were on dopaminergic treatment with wearing-off effects, and were at Hoehn and Yahr stage 2·5 or less when on treatment. Randomisation was by web-based randomisation with a two strata block design according to disease severity. Patients and investigators were masked to treatment allocation. The primary outcome was the adjusted difference in the Movement Disorders Society Unified Parkinson's Disease Rating Scale (MDS-UPDRS) motor subscale (part 3) in the practically defined off-medication state at 60 weeks. All efficacy analyses were based on a modified intention-to-treat principle, which included all patients who completed any post-randomisation follow-up assessments. The study is registered at ClinicalTrials.gov (NCT01971242) and is completed. FINDINGS: Between June 18, 2014, and March 13, 2015, 62 patients were enrolled and randomly assigned, 32 to exenatide and 30 to placebo. Our primary analysis included 31 patients in the exenatide group and 29 patients in the placebo group. At 60 weeks, off-medication scores on part 3 of the MDS-UPDRS had improved by 1·0 points (95% CI -2·6 to 0·7) in the exenatide group and worsened by 2·1 points (-0·6 to 4·8) in the placebo group, an adjusted mean difference of -3·5 points (-6·7 to -0·3; p=0·0318). Injection site reactions and gastrointestinal symptoms were common adverse events in both groups. Six serious adverse events occurred in the exenatide group and two in the placebo group, although none in either group were judged to be related to the study interventions. INTERPRETATION: Exenatide had positive effects on practically defined off-medication motor scores in Parkinson's disease, which were sustained beyond the period of exposure. Whether exenatide affects the underlying disease pathophysiology or simply induces long-lasting symptomatic effects is uncertain. Exenatide represents a major new avenue for investigation in Parkinson's disease, and effects on everyday symptoms should be examined in longer-term trials. FUNDING: Michael J Fox Foundation for Parkinson's Research