The Homecare Problem appears when formal care started to be provided to persons in need of assisted living support. In short, this problem tackles the allocation of caregivers to patients simultaneously with the daily work schedule of each caregiver. Most of the published works on HHP assume that patients must be visited by the same caregiver or at most by two different persons – this feature is frequently named as loyalty. In our case, one of the objectives is exactly the opposite. One wants to define a plan that allows caregivers to rotate among patients on a weekly basis. This is to mean that every week patients should be visited by different caregivers. This work is motivated by a real case study of a Portuguese catholic parish. This community offers several social services to population that lives nearby: meal delivery, activities of the daily living, adult day care and transportation. The “non-loyalty” feature was a request made by the social assistant in charge of the service since she has noticed that a long patient/caregiver relationship usually leads to conflict situations. Nonetheless, the caregiver assigned each week should not change within the week. With a group of 66 patients, the daily schedule of teams of two caregivers has to be plan so that all patients’ requests are met. The request vary from twice a day to two days a week and may be of activities of the daily living (such as bathing, dressing, medication assistance, home cleaning) and/or transportation to (and from) the day care center. Patients live in two different urban areas. In each area, patients’ homes are within walking distance, but between the two areas the caregivers have to take public transportation. Each caregiver should depart from the Parish Social Center and return at the end of the day. At 1 p.m. they also go to the Parish Social Center to have lunch (lunch-break). One of the teams should arrive one hour earlier to help on deliver meals. In this presentation we will present a MILP formulation developed to address the characteristics mentioned above and the results achieved.

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Home healthcare problem, combinatorial optimization, real case study