Multi-criteria assignment policies to improve global effectiveness of medico-social service sector

Abstract

In this paper, we propose a multi-criteria approach in order to reduce the waiting time on the assignment of users to medico-social institutions. The main goal is to ascertain whether alternative assignment policies can improve global response to users’ demands, and to assess the performances of each alternative (scenario) compared to the current practice. We propose a mathematical model of user assignment to medico-social structures and professionals, under constraints of resource capacity, professionals’ skills and user requirements (formulated in an individual support project). With alternative assignment policies, users’ needs could be covered partially. They also authorize the involvement of several structures and several professionals in the response to the request. A mixed integer linear programming solver is used to solve this assignment problem, following a lexicographic approach in case of partial coverage policy. For some assignment policies that have long calculation times, we propose a simulated annealing approach in order to speed up the resolution. In order to validate simulated annealing approach, we compared it with a greedy randomized adaptive search procedure. The problem is solved for instances where we have real size data for a set of institutions for disabled children and teenagers. We present and compare computational results over several scenarios, highlighting the improvement provided by each alternative assignment policy.

Introduction

The medico-social sector is composed of a wide range of services and institutions (also called medico-social structures or structures throughout the study) that support vulnerable people such as disabled children, teenagers or adults, people in precarious situations or in social difficulty such as situations of exclusion or dependency, and the elderly. Today, this sector faces a quantitative and qualitative supply deficit, manifested especially in the exclusion of frail and disabled people. When the need for an accompaniment (or support) is identified, a request for admission is sent to one or several medico-social institutions, which then accept or refuse the person, according to his or her particular needs as described in the ISP (Individual Support Project), the specialization of the structures and the availability of the healthcare practitioners and social workers (social educators, special needs teachers, nurses, physicians, psychologists, speech therapists, etc.), that we refer to as ‘professionals’ throughout the paper. This current assignment process is not satisfactory. A recent French national report (Piveteau et al., 2014) highlights the difficulty of finding support for a large number of people with heavy needs (called “zero solutions”). This causes a break in the person's life path, with consequences on both the person and his or her immediate environment (loneliness, risk of crisis, need for hospitalization, etc.). Apart from deteriorating living conditions, the lack of support can lead to situations involving high expenses (in case of hospitalization for example). The same report emphasizes the sense of solidarity: “Contrary to rupture, it is not ‘everything and immediately’ but ‘always something with an ever outstretched hand’”. This report points out the multiple origins of the problem: (1) the medico-social offer is not qualitatively and quantitatively sufficient (Vachey et al., 2012); (2) there is a lack of coordination between the offer and users’ needs; and (3) current assignment policy consists in finding a solution that covers all support needs in a single institution. In order to improve response to people's need for support, we have chosen to tackle the third point above. We explore the track consisting in the search for alternative assignment policies that are more flexible and that may, for example, partially cover the user's needs, or that authorize involvement of several structures and several professionals in meeting the need. The problem is to assign users to professionals and structures, according to their needs in several domains, while respecting constraints such as resource capacity, professionals’ skills or need coverage. In this Multidimensional Assignment Problem (MAP), the number of admitted users (assigned to one single structure) is the main criterion to optimize, as it results in a total coverage of user needs. However, an alternative to this assignment policy could be to relax constraints related to the assignment of users to one single structure with one single professional for each domain requested by the user in his ISP. Another relaxed constraint could be to cover needs partially (i.e., we allow the admission of a user even if all their requirements for each area of the ISP are not completely covered). In this case, a secondary objective would aim to maximize the minimum coverage rate for all users.

In this paper, we evaluate alternative assignment policies compared to the current policy, in order to determine whether, under more flexible policies, we can achieve a better use of human resources and thus increase the number of users admitted. The main purpose is to decrease the waiting time for users to access services and thereby to reduce the risk of interrupting the support they receive. A previous work presented a first model and a first exact resolution method (Osorio et al., 2015a). In this paper, we propose an extended model of multi-criteria assignment policies and a metaheuristic-based approach to solve problems that have prohibitive calculation time.

The paper is organized as follows. The next section presents a review of the literature on the Multidimensional Assignment Problem, to which our problem is linked. In Section 3 we then present the formulation of the problem of assigning users to medico-social structures as a mathematical model. This model is designed to be able to translate each proposed alternative policy by changing only few parameters. In Section 4 the experimental approach is described. This section presents all the scenarios that are compared, along with how the input data have been generated and how each case is solved. It presents an algorithmic approach based on simulated annealing for reducing the computation time, especially for scenarios involving partial need coverage. Section 5 gives the results obtained, compares the performances of the assignment policies according to performance indicators, and gives some managerial assessments. Finally, Section 6 draws conclusions and defines some future research tracks.