*Proceeding Paper* **A Bi-Objective Scheduling Problem in a Home Care Business †**

**Isabel Méndez-Fernández 1,2,\*, Silvia Lorenzo-Freire 1,2 and Ángel Manuel González-Rueda 1,2**


**Abstract:** In this work we study a routing and scheduling problem for a home care business. The problem is composed of two conflicting objectives, therefore we study it as a bi-objective one. We obtain the Pareto frontier for small size instances using the AUGMECON2 method and, for bigger cases, we developed an heuristic algorithm. We also obtained some preliminary results that show the algorithm has good behaviour.

**Keywords:** optimization; scheduling; heuristic algorithms; operations research

## **1. Introduction**

Home care services aim to help elderly, sick or dependent people maintain their quality of life without having to leave their homes. The goal of a Home Care Scheduling Problem is to obtain the routes that the company's employees must follow, as well as the times at which each service has to be carried out.

In our problem, the users are the company's clients, and they require a number of services that need to be carried out, by the company's employees, throughout the week. To correctly address the users' needs it is essential that they define the characteristics of the services they request: the day of the week they belong to, their duration, a hard time window and a soft time window. These time windows are necessary because they are used to determine the schedule of each service. Hard time windows state the times within which services must be completed, to have a feasible plan. Soft time windows represent when the user prefers to be attended, even though it is not necessary to uphold them.

The caregivers are the company's employees and their work consists of visiting users at their homes to carry out the tasks required by them. Every caregiver has a contract, which states the maximum number of hours they can work during each day, and the number of hours that they are hired to work during the week. Caregivers' working days start at the beginning of the first service and end when the last one is finished. All breaks that caregivers have during the day are considered worked time, with the exception of the largest one—if it lasts two or more hours.

To maintain the users satisfaction, the company works with a list of 6 affinity levels that establish the compatibility between users and caregivers.
