For a variety of routing and scheduling problems in aviation, shipping, rail, and

road transportation, the state-of-the-art solution approach is to model the prob-

lem as a set coverin

Dalmeijer, K. (Kevin)

Hoogendoorn, Y.N. (Ymro)

For a variety of routing and scheduling problems in aviation, shipping, rail, and

road transportation, the state-of-the-art solution approach is to model the prob-

lem as a set covering type problem and to use a branch-price-and-cut algorithm to

solve it. The pricing problem typically takes the form of a Shortest Path Problem

with Resource Constraints (SPPRC). In this context, valid inequalities are known

to be `robust' if adding them does not complicate the pricing problem, and `non-

robust' otherwise. In this paper, we introduce `resource-robust' as a new category

of valid inequalities between robust and non-robust that can still be incorporated

without changing the structure of the pricing problem, but only if the SPPRC

includes specic resources. Elementarity-robust and ng-robust are introduced as

widely applicable special cases that rely on the resources that ensure elementary

routes and ng-routes, respectively, and practical considerations are discussed. The

use of resource-robust valid inequalities is demonstrated with an application to the

Capacitated Vehicle Routing Problem. Computational experiments show that re-

placing robust valid inequalities by ng-robust valid inequalities may result in better

lower bounds, a reduction in the number of nodes in the search tree, and a decrease

in solution time

Erasmus University Digital Repository

Resource-robust valid inequalities for set covering and set partitioning models

https://repub.eur.nl/pub/134553/EI2020-08-herziene-versie.pdf

Resource-robust valid inequalities for set covering and set partitioning models

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