arXiv subjects

Vincent T'kindt

Publications and source records attributed to Vincent T'kindt.

4 recordsLinked to original sources

arXiv2026

Solution of a bilevel optimistic scheduling problem on parallel machines

We consider the uniform parallel machines scheduling problem in the context of optimistic bilevel optimization, where two speed options are considered. In this scenario, the leader aims to minimize the weighted number of tardy jobs, while the follower seeks to minimize the total completion time on a set of uniform machines. This problem has practical applications in Industry 4.0. We show that this problem is NP-hard in the strong sense by providing a reduction from the Numerical 3-Dimensional Matching problem and we provide a moderately exponential-time dynamic programming algorithm. The problem is solved by means of a concise MIP formulation and a branch-and-bound algorithm that embeds a column generation approach for the lower bound computation. Computational experiments are presented for instances with up to 80 jobs and 4 machines while larger problems are out of reach for the proposed approaches.

math.OC↗

arXiv2024

Moderate Exponential-time Quantum Dynamic Programming Across the Subsets for Scheduling Problems

Grover Search is currently one of the main quantum algorithms leading to hybrid quantum-classical methods that reduce the worst-case time complexity for some combinatorial optimization problems. Specifically, the combination of Quantum Minimum Finding (obtained from Grover Search) with dynamic programming has proved particularly efficient in improving the complexity of NP-hard problems currently solved by classical dynamic programming. For these problems, the classical dynamic programming complexity in $\mathcal{O}^*(c^n)$, where $\mathcal{O}^*$ denotes that polynomial factors are ignored, can be reduced by a hybrid algorithm to $\mathcal{O}^*(c_{quant}^n)$, with $c_{quant} < c$. In this paper, we provide a bounded-error hybrid algorithm that achieves such an improvement for a broad class of NP-hard single-machine scheduling problems for which we give a generic description. Moreover, we extend this algorithm to tackle the 3-machine flowshop problem. Our algorithm reduces the exponential-part complexity compared to the best-known classical algorithm, sometimes at the cost of an additional pseudo-polynomial factor.

quant-ph↗

arXiv2023

Single machine rescheduling for new orders: properties and complexity results

Rescheduling problems arise in a variety of situations where a previously planned schedule needs to be adjusted to deal with unforeseen events. A common problem is the arrival of new orders, i.e. jobs, which have to be integrated into the schedule of the so-called old jobs. The maximum and total absolute time deviations of the completion times of these jobs are modeled as a disruption constraint to limit the change in the original schedule. Disruption constraints affect the shape of an optimal schedule, particularly with respect to the sequencing of old jobs and the insertion of idle time. We therefore give a classification into idle and no-idle problems for a set of single-machine rescheduling problems with different objective functions. We then prove the complexity of five rescheduling problems that have been left open in the literature.

cs.DM↗

arXiv2017

No-idle, no-wait: when shop scheduling meets dominoes, eulerian and hamiltonian paths

In shop scheduling, several applications exist where it is required that some components perform consecutively. We refer to no-idle schedules if machines are required to operate with no inserted idle time and no-wait schedules if tasks cannot wait between the end of an operation and the start of the following one. We consider here no-idle/no-wait shop scheduling problems with makespan as performance measure and determine related complexity results. We first analyze the two-machine no-idle/no-wait flow shop problem and show that it is equivalent to a special version of the game of dominoes which is polynomially solvable by tackling an Eulerian path problem on a directed graph. We present for this problem an O(n) exact algorithm. As a byproduct we show that the Hamiltonian Path problem on a digraph G(V,A) with a special structure (where every pair of vertices i,j either has all successors in common or has no common successors) reduces to the two-machine no-idle/no-wait flow shop problem. Correspondingly, we provide a new polynomially solvable special case of the Hamiltonian Path problem. Then, we show that also the corresponding $m$-machine no-idle no-wait flow shop problem is polynomially solvable and provide an O(mn log n) exact algorithm. Finally we prove that the 2-machine no-idle/no-wait job shop problem and the 2-machine no-idle/no-wait open shop problem are NP-Hard in the strong sense.

cs.DM↗