arXiv subjects

Thierry Garaix

Publications and source records attributed to Thierry Garaix.

4 recordsLinked to original sources

arXiv2023

Traveling salesman problem with time slots: Asymptotic analysis and resolution algorithm

We develop an asymptotic approximation and bounds for the traveling salesman problem with time slots, i.e. when the time windows of points to visit are a partition of a given time horizon. Although this problem is relevant in several delivery applications, operational research researchers did not pay close attention to it, contrary to the extensively studied general formulation with time windows. Exploiting the specificity of this problem allows to solve more efficiently instances which may be hard to solve by specifically designed algorithms for the traveling salesman problem with time windows. The asymptotic analysis of the traveling salesman problem with time slots is a step toward developing new approximations for the general problem with time windows.We discuss this case. We equally provide a formulation of the asymptotic approximation under a worst-case demand distribution of the points to visit, based on the principle of the maximum entropy. Computational results are given for the benchmarks of the literature for which the time slots are randomly generated.

math.OC↗

arXiv2018

Staff dimensioning in homecare services with uncertain demands

The problem addressed in this paper is how to calculate the amount of personnel required to ensure the activity of a home health care (HHC) center on a tactical horizon. Design of quantitative approaches for this question is challenging. The number of caregivers has to be determined for each profession in order to balance the coverage of patients in a region and the workforce cost over several months. Unknown demand in care and spatial dimensions, combination of skills to cover a care and individual trips visiting patients make the underlaying optimization problem very hard. Few studies are dedicated to staff dimensioning for HHC compared to patient to nurses assignment/sequencing and centers location problems. We propose an original two-stage approach based on integer linear stochastic programming, that exploits historical medical data. The first stage calculates (near-)optimal levels of resources for possible demand scenarios , while the second stage computes the optimal number of caregiver for each profession to meet a target coverage indicator. For decision-makers, our algorithm gives the number of employees for each category required to satisfy the demand without any recourse (overtime, external resources) with fixed probability and confidence interval. The approach has been tested on various instances built from data of the French agency of hospitalization data (ATIH).

cs.CY↗

arXiv2018

Iterated local search and very large neighborhoods for the parallel-machines total tardiness problem

We present computational results with a heuristic algorithm for the parallel machines total weighted tardiness problem. The algorithm combines generalized pairwise interchange neighborhoods, dynasearch optimization and a new machine-based neighborhood whose size is non-polynomial in the number of machines. The computational results significantly improve over the current state of the art for this problem.

cs.DC↗

arXiv2018

Proactive On-call Scheduling during a Seasonal Epidemic

Overcrowding in Emergency Departments (EDs) is particularly problematic during seasonal epidemic crises. Each year during this period, EDs set off recourse actions to cope with the increase in workload. Uncertainty in the length and amplitude of epidemics make managerial decisions difficult. We propose in this study a staff allocation model to manage the situation using on-calls. An on-call scheduling policy is proposed to best balance between demand coverage and labor cost under legal constraints of working time. The problem is modelled as a two-stage stochastic Integer Linear Program (ILP) and solved using a Sample Average Approximation (SAA) method. Several epidemic scenarios are defined with data from an ED in Lille, France.

physics.soc-ph↗