The selective travelling salesman problem
Discrete Applied Mathematics - Southampton conference on combinatorial optimization, April 1987
A heuristic for the multiple tour maximum collection problem
Computers and Operations Research
Resource-constrained geometric network optimization
Proceedings of the fourteenth annual symposium on Computational geometry
Computers and Operations Research
A branch and bound method for stochastic global optimization
Mathematical Programming: Series A and B
The Sample Average Approximation Method for Stochastic Discrete Optimization
SIAM Journal on Optimization
Solving the Orienteering Problem Through Branch-And-Cut
INFORMS Journal on Computing
A Personalized Tourist Trip Design Algorithm For Mobile Tourist Guides
Applied Artificial Intelligence
Variable neighborhood search for the orienteering problem
ISCIS'06 Proceedings of the 21st international conference on Computer and Information Sciences
Monte Carlo bounding techniques for determining solution quality in stochastic programs
Operations Research Letters
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The Orienteering Problem (OP) is a routing problem which has many interesting applications in logistics, tourism and defense. The aim of the OP is to find a maximum profit path or tour, which is feasible with respect to a capacity constraint on the total weight of the selected arcs. In this paper we consider the Orienteering Problem with Stochastic Weights (OPSWs) to reflect uncertainty in real-life applications. We approach this problem by formulating a two-stage stochastic model with recourse for the OPSW where the capacity constraint is hard. The model takes into account the effect that stochastic weights have on the expected total profit value to be obtained, already in the modeling stage. Since the expected profit is in general non-linear, we introduce a linearization that models the total profit that can be obtained for a given tour and a given scenario of weight realizations. This linearization allows for the application of Sample Average Approximation (SAA). The SAA solution asymptotically converges to the optimal solution of the two-stage model, but is computationally expensive. Therefore, to solve large instances, we developed a heuristic that exploits the problem structure of the OPSW and explicitly takes the associated uncertainty into account. In our computational experiments, we evaluate the benefits of our approach to the OPSW, compared to both a standard deterministic approach, and a deterministic approach that is extended with utilization of real-time information.