A Robust Approach to the Capacitated Vehicle Routing Problem with Uncertain Costs

Eufinger, Lars; Kurtz, Jannis; Buchheim, Christoph; Clausen, Uwe

doi:10.1287/ijoo.2019.0021

Cited by 16 publications

(15 citation statements)

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“…Nevertheless the run-time increases with the dimension and with which is mainly due to the increasing run-time of Algorithm 1. Here with higher dimension the calculation time of the deterministic problem increases, while with increasing the number of iterations of Algorithm 1 increases which was already observed in [30,42]. Another positive observation is that the root gap is very small in general, mostly 0 and never larger than 34% .…”

supporting

confidence: 60%

“…We only require an arbitrary procedure which returns an optimal solution for the given scenario. In [42] the authors applied the latter algorithm to the min-max-min robust capacitated vehicle routing problem and showed that on classical benchmark instances the number of iterations of Algorithm 1 is significantly smaller than the dimension of Z in general.…”

Section: Proposition 1 If All First-stage Variables Are Fixed Then (Lb) Is Equal To the Exact Objective Value Of The Fixed First-stage Somentioning

confidence: 99%

“…In [46] it is shown that the k-adaptability problem is exact if k is chosen larger than the dimension of the problem. The authors in [30,31,42] apply the k-adaptability concept to one-stage combinatorial problems to calculate a set of solutions which is worst-case optimal if for each scenario the best of these solutions can be chosen. They furthermore show that solving this problem can be done in polynomial time if an oracle for the deterministic problem exists and if the number of calculated solutions is larger or equal to the dimension of the problem.…”

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confidence: 99%

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Oracle-based algorithms for binary two-stage robust optimization

Kämmerling

Kurtz

2020

Comput Optim Appl

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In this work we study binary two-stage robust optimization problems with objective uncertainty. We present an algorithm to calculate efficiently lower bounds for the binary two-stage robust problem by solving alternately the underlying deterministic problem and an adversarial problem. For the deterministic problem any oracle can be used which returns an optimal solution for every possible scenario. We show that the latter lower bound can be implemented in a branch and bound procedure, where the branching is performed only over the first-stage decision variables. All results even hold for non-linear objective functions which are concave in the uncertain parameters. As an alternative solution method we apply a column-and-constraint generation algorithm to the binary two-stage robust problem with objective uncertainty. We test both algorithms on benchmark instances of the uncapacitated single-allocation hub-location problem and of the capital budgeting problem. Our results show that the branch and bound procedure outperforms the column-and-constraint generation algorithm.

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confidence: 60%

Section: Proposition 1 If All First-stage Variables Are Fixed Then (Lb) Is Equal To the Exact Objective Value Of The Fixed First-stage Somentioning

confidence: 99%

mentioning

confidence: 99%

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Oracle-based algorithms for binary two-stage robust optimization

Kämmerling

Kurtz

2020

Comput Optim Appl

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“…Using the min-max-min approach a small number of transportation-plans can be calculated in advance to decide which long-term decision have to be made and to prepare all employees. Another example, taken from Eufinger et al (2018); Subramanyam et al (2017), considers a parcel service delivering to the same customers every day, i.e. X is the set of feasible solutions of the vehicle routing problem.…”

Section: Introductionmentioning

confidence: 99%

Faster algorithms for min-max-min robustness for combinatorial problems with budgeted uncertainty

Chassein

Goerigk

Kurtz

et al. 2019

European Journal of Operational Research

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We consider robust combinatorial optimization problems where the decision maker can react to a scenario by choosing from a finite set of k solutions. This approach is appropriate for decision problems under uncertainty where the implementation of decisions requires preparing the ground. We focus on the case that the set of possible scenarios is described through a budgeted uncertainty set and provide three algorithms for the problem. The first algorithm solves heuristically the dualized problem, a nonconvex mixed-integer non-linear program (MINLP), via an alternating optimization approach. The second algorithm solves the MINLP exactly for k = 2 through a dedicated spatial branch-and-bound algorithm. The third approach enumerates k-tuples, relying on strong bounds to avoid a complete enumeration. We test our methods on shortest path instances that were used in the previous literature and on randomly generated knapsack instances, and find that our methods considerably outperform previous approaches. Many instances that were previously not solved within hours can now be solved within few minutes, often even faster.

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“…Besides,[59][60][61] investigated the Cumulative CVRP in which the objective is to minimize the sum of arrival times at customers rather than total routing cost or distance.The authors concluded that this problem constitutes a good way to model situations where arrival time at customers is very important such as after natural disasters.Moreover, Lei et al[62] and Eufinger et al[63] incorporated some uncertainty in their studies; the former authors developed a neighborhood search heuristic to solve the problem with stochastic demands while the latter authors came up with a robust approach that takes travel times uncertainty into account. Results confirmed the superiority of the proposed heuristics over an alternative solution approaches.…”

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confidence: 99%