objective of this tool is to provide reliable and solid support to pharmacists for the verification of prescriptions so as to optimize and meet the hospital’s accreditation criteria. Various pharmaceutical validation algorithms were thus constructed, and the computer validation tool was developed and tested on these bases which generated very encouraging results.
Simulation of Countermeasures in the Face of Covid-19 Using a Linear Compartmental Model, by Alain GUINET.
Since the start of 2020, the whole world has been confronted by a pandemic, which led to the confinement of over half of the world’s inhabitants. We are disarmed in the face of the coronavirus (SARS-CoV-2), and containment seems to be the only countermeasure capable of containing the pandemic despite the consequential economic cost. This chapter presents a simulation of the epidemic based on the SIR (Susceptible–Infected–Recovered) model, which is known as a compartmental model in epidemiology. This simulation makes it possible to calculate, by period, the people at different stages of the disease, receiving different medical treatment, and to propagate the flows of people between the states by period. A discrete representation of the SIR model over a horizon of daily periods was used. The results showed the effectiveness of the health countermeasure chosen by half of the world’s countries to deal with the Covid-19 pandemic. Containment of the population seems to be a well-suited action in the absence of an efficient treatment, such as viral treatment or a vaccine.
1
Towards a Prototype for the Strategic Recomputing of Schedules in Home Care Services
1.1. Introduction
Home healthcare agencies are an alternative to standard medical or paramedical organizations, providing services directly to the beneficiary’s home. The aging of Western populations is accompanied by an increase in the number of vulnerable people and an explosion in demand for home healthcare and associated services (Guinet 2014), to which the organizations concerned must adapt. Service routing and scheduling is usually done by hand by experienced employees but this is time-consuming and extremely complex on a large scale. The design of decision support tools is becoming essential to automate the routing and scheduling process and build schedules that are satisfactory for the employer, the careworkers and the beneficiaries.
Having effective solutions to plan interventions is unfortunately not always sufficient to meet the challenge of routing and scheduling in the home care sector. Indeed, many eventualities can make a theoretically optimal schedule unfeasible. It is thus necessary to update the schedules to compensate for these unforeseen events. We are particularly interested in changes in the configuration of staff and beneficiaries of a home healthcare organization. Over the weeks, a beneficiary’s state of health can deteriorate, which in turn leads to changes in their needs and therefore in the services required, or even bidding farewell to the organization in the event they require hospitalization, for example. When beneficiaries leave, the establishment can, if the number of careworkers is high enough, accept new beneficiaries who will have to be included in the schedules. Likewise, there is a high turnover of staff because the careworkers are often subjected to difficult, stressful working conditions.
From a strategic, decision-making point of view, it would be inappropriate to recalculate optimal routes every time the schedules are disrupted. In a context where the human aspect is essential, it is necessary to take into account the schedule in progress, the assignments of careworkers or even the start time of the interventions, in order to satisfactorily reconstruct disrupted routes. Indeed, continuity is a key factor in patient satisfaction. Consequently continuity of care constraints must be respected by, on the one hand, keeping fixed start and end times (these are also defined contractually) and on the other hand, always assigning the same group of careworkers to the same patients. In order not to aggravate these instabilities, it is also crucial to take careworker satisfaction into account. Schedules that are not satisfactory for the staff increase staff turnover, which impacts the company’s quality of service. In a field where competition is increasingly fierce (Béguin 2018), providing good working conditions is not only a central argument for recruiting qualified careworkers but it also plays a decisive role in limiting turnover.
It is important to note that updating long-term schedules consists of creating new sustainable weekly or monthly schedules, in line with changes to staff and beneficiaries, while short-term rescheduling instead aims to provide a quick fix to the problem; for example, a daily schedule compromised by a one-off disruption, such as the sudden absence of a worker for a day.
In this chapter, we present a prototype developed to respond to a long-term weekly rerouting and rescheduling problem encountered by a home care services company operating in Auvergne Rhône-Alpes, France: Adomni-Quemera. We first offer a brief review of existing work on this theme in the literature, followed by a more specific description of the problem under consideration. In section 1.4, we briefly advance our resolution strategy, before presenting the prototype developed to propose solutions in a practical setting in section 1.5. The experiments carried out on real data are detailed in section 1.6. Finally, we approach avenues of research for future work in section 1.7.
1.2. Literature review
The Home Health Care Routing and Scheduling Problem (HHCRSP), i.e. the problem of planning home care routes, appears for the first time – to our knowledge – in 1997 in the article by Begur et al. (1997). Their method is based on adaptations of heuristics derived from algorithms for solving vehicle routing problems (VRP); in particular the classical methods developed in Clarke and Wright (1964) and Lin and Kernighan (1973). The modeling of the HHCRSP as a variant of the VRP is quite classic and Cheng and Rich (1998) were the first to adapt it to mixed-integer linear programming. They model the problem through a multi-depot vehicle routing problem (MDVRP) with multiple time windows, over a single-period horizon. The goal is to minimize overtime and tests are conducted on small case studies, made up of 4 nurses and 10 patients.
Since then, much research has focused on solving such problems, as they constitute a topical issue, both in practice and in the field of research with real scientific obstacles. For further details, the reader can refer to recent literature reviews: Cissé et al. (2017), Fikar and Hirsch (2017), Grieco et al. (2020) and Di Mascolo et al. (2021).
The problem is NP-hard, and thus difficult to solve in practice due to the presence of numerous business and industry-specific constraints, which are often treated with metaheuristics (Decerle et al. 2018) or with decomposition methods, such as the approach developed in the prototype presented here. In Grenouilleau et al. (2017), the authors propose a two-step algorithm to solve the routing and scheduling problem with minimization of overtime, staff qualification constraints and the possibility of not providing all the services requested. An LNS algorithm makes it possible to generate feasible routes, then a set partitioning model whose linear relaxation is repaired through a constructive heuristic, making it possible to select the routes that constitute the final schedule. In Fikar and Hirsch (2015), identification of potential routes precedes the overall scheduling optimization phase. The problem can also be broken down into a first step of assigning services to careworkers, then solving a traveling salesperson (TSP) problem for each of them. Issaoui et al. (2015) add a third step to this decomposition, in which they improve the routes obtained using a heuristic.
Most of the time, the objectives studied relate to the economic aspects of the problem, namely cost minimization (Fathollahi-Fard et al. 2019). However, there is also a particular interest in patient satisfaction (Mosquera et al. 2019). Careworker satisfaction, which is rarely studied, mainly consists of balancing the workload of careworkers (Cappanera and Scutellà 2014). The three stakeholders of the problem, namely the careworkers, the beneficiaries and the employer of