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  • 1.
    Baltz, Andreas
    et al.
    Christian-Albrechts Universität Kiel.
    El Ouali, Mourad
    Christian-Albrechts Universität Kiel.
    Jäger, Gerold
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Sauerland, Volkmar
    Christian-Albrechts Universität Kiel.
    Srivastav, Anand
    Christian-Albrechts Universität Kiel.
    Exact and heuristic algorithms for the Travelling Salesman Problem with Multiple Time Windows and Hotel Selection2015In: Journal of the Operational Research Society, ISSN 0160-5682, E-ISSN 1476-9360, Vol. 66, no 4, p. 615-626Article in journal (Refereed)
    Abstract [en]

    We introduce and study the Travelling Salesman Problem with Multiple Time Windows and Hotel Selection (TSP-MTWHS), which generalises the well-known Travelling Salesman Problem with Time Windows and the recently introduced Travelling Salesman Problem with Hotel Selection. The TSP-MTWHS consists in determining a route for a salesman (eg, an employee of a services company) who visits various customers at different locations and different time windows. The salesman may require a several-day tour during which he may need to stay in hotels. The goal is to minimise the tour costs consisting of wage, hotel costs, travelling expenses and penalty fees for possibly omitted customers. We present a mixed integer linear programming (MILP) model for this practical problem and a heuristic combining cheapest insert, 2-OPT and randomised restarting. We show on random instances and on real world instances from industry that the MILP model can be solved to optimality in reasonable time with a standard MILP solver for several small instances. We also show that the heuristic gives the same solutions for most of the small instances, and is also fast, efficient and practical for large instances.

  • 2.
    Hartley, Roger
    et al.
    Economics Department, Keele University, Keele, UK.
    Lanot, Gauthier
    Economics Department, Keele University, Keele, England.
    On the design of lottery games2003In: Journal of the Operational Research Society, ISSN 0160-5682, E-ISSN 1476-9360, Vol. 54, no 1, p. 89-100Article in journal (Refereed)
    Abstract [en]

    We describe a model of participation in lottery games designed to address the optimisation of tax revenue in state-sponsored lotteries. The model treats participants dynamically and examines a long-run equilibrium. A novel high frequency approximation is used to turn the problem into a static, state-contingent deterministic programming problem. We demonstrate that the solution of this problem has qualitatively plausible properties and then calibrate the model against the United Kingdom National Lottery (UKNL). The results suggest that the current design of the UKNL may not be maximising tax revenue.

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