Staff dimensioning in homecare services with uncertain demands

Abstract

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) centre 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 optimisation problem very hard. Few studies are dedicated to staff dimensioning for HHC compared to patient to nurses assignment/sequencing and centres location problems. We propose an original two-stage approach based on integer linear stochastic programming, which 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 hospitalisation data (ATIH).

Keywords:

• homecare
• staff dimensioning
• stochastic programming
• stochastic vehicle routing problem

Notes

1 ATIH is the French technical agency for hospitalization information, http://www.atih.sante.fr. From the ATIH database, one can get the amount of patients of every region in France for every pathology and the treatment associated with. This data are public and three years of data (from 2010 to 2012) were used in this study.

2 GHM: Groupe Homogène des Malade is a classification of treatments used by French authorities to calculate reimbursements, hospital capacities, resources requirements and so on.