Layered Formulation for the Robust Vehicle Routing Problem with Time Windows

Agra, Agostinho; Christiansen, Marielle; Figueiredo, Rosa; Hvattum, Lars Magnus; Poss, Michaël; Requejo, Cristina

doi:10.1007/978-3-642-32147-4_23

Cited by 22 publications

(36 citation statements)

References 20 publications

(45 reference statements)

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“…Prior to our recent note [1], Sungur et al [25] were the first to mention a robust vehicle routing problem with time windows and uncertain travel times (T -V RP T W ). However, their modeling assumption led to all travel times taking their maximum values, yielding an over-conservative model.…”

Section: Introductionmentioning

confidence: 99%

“…Our recent note [1] presents the first general approach to the robust vehicle routing problem with time windows and uncertain travel times. Travel times belong to a demand uncertainty polytope, which makes the problem harder to solve than its deterministic counterpart.…”

Section: Introductionmentioning

confidence: 99%

“…Travel times belong to a demand uncertainty polytope, which makes the problem harder to solve than its deterministic counterpart. The benefit of the addition in complexity is that the model from [1] is more flexible than the one from [25] and leads to less conservative robust solutions. The work presented in [1] focuses on applying the classical dualization technique for robust programming which yields a very large formulation that are hardly solved for instances with more than 20 nodes.…”

Section: Introductionmentioning

confidence: 99%

“…The benefit of the addition in complexity is that the model from [1] is more flexible than the one from [25] and leads to less conservative robust solutions. The work presented in [1] focuses on applying the classical dualization technique for robust programming which yields a very large formulation that are hardly solved for instances with more than 20 nodes. The limited results obtained in [1] motivate us to tackle the T -V RP T W with the more sophisticated robust approaches used in this paper.…”

Section: Introductionmentioning

confidence: 99%

“…The work presented in [1] focuses on applying the classical dualization technique for robust programming which yields a very large formulation that are hardly solved for instances with more than 20 nodes. The limited results obtained in [1] motivate us to tackle the T -V RP T W with the more sophisticated robust approaches used in this paper. Our first approach uses adjustable robust optimization, while the second one substitutes robust constraints with canonical cuts.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

The robust vehicle routing problem with time windows

Agra

Christiansen

Figueiredo

et al. 2013

Computers & Operations Research

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158

107

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This paper addresses the robust vehicle routing problem with time windows. We are motivated by a problem that arises in maritime transportation where delays are frequent and should be taken into account. Our model only allows routes that are feasible for all values of the travel times in a predetermined uncertainty polytope, which yields a robust optimization problem. We propose two new formulations for the robust problem, each based on a different robust approach. The first formulation extends the well-known resource inequalities formulation by employing adjustable robust optimization. We propose two techniques, which, using the structure of the problem, allow to reduce significantly the number of extreme points of the uncertainty polytope. The second formulation generalizes a path inequalities formulation to the uncertain context. The uncertainty appears implicitly in this formulation, so that we develop a new cutting plane technique for robust combinatorial optimization problems with complicated constraints. In particular, efficient separation procedures are discussed. We compare the two formulations on a test bed composed of maritime transportation instances. These results show that the solution times are similar for both formulations while being significantly faster than the solutions times of a layered formulation recently proposed for the problem.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

The robust vehicle routing problem with time windows

Agra

Christiansen

Figueiredo

et al. 2013

Computers & Operations Research

Self Cite

158

107

View full text Add to dashboard Cite

show abstract

Robust constrained shortest path problems under budgeted uncertainty

et al. 2015

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We study the robust constrained shortest path problem under resource uncertainty. After proving that the problem is N P-hard in the strong sense for arbitrary uncertainty sets, we focus on budgeted uncertainty sets introduced by Bertsimas and Sim (2003) and their extension to variable uncertainty by Poss (2013). We apply classical techniques to show that the problem with capacity constraint can be solved in pseudo-polynomial time. However, we prove that the problem with time windows is N P-hard in the strong sense when Γ is not fixed, using a reduction from the independent set problem. We introduce then new robust labels that yield dynamic programming algorithms for the problems with time windows and capacity constraints. The running times of these algorithms are pseudo-polynomial when Γ is fixed, exponential otherwise. We present numerical results for the problem with time windows which show the effectiveness of the label-setting algorithm based on the new robust labels. Our numerical results also highlight the reduction in price of robustness obtained when using variable budgeted uncertainty instead of classical budgeted uncertainty.

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