A Stochastic Optimization Approach to the Long-Term Care Structure Assignment Problem for Elderly People

The growing number of elderly people (EP) has become one of the most important problems in recent years. This part of the population is often dependent and does not tolerate environmental changes well, so long-term care (LTC) structure assignments should be well prepared. This article proposes a stochastic optimization approach to solve the LTC structure assignment problem for a population of EP while taking into account health state changes and uncertain future demand. The objective of this approach is to make the best assignment decision among several structures or to wait for a better solution if no suitable structure is available. The model is validated and calibrated on the basis of stakeholder objectives and territorial special features through simulation. We propose a numerical analysis based on both quantitative and qualitative analyses to compare our model with simple assignment policies.
Note to Practitioners
—The increase in the elderly and dependent population and the lack of a long-term structure to address this aging population make it difficult to assign EP to the appropriate LTC. This decision often determines the quality of the end of life. Several parameters must be taken into account to choose the best solution: the health situation, geographic location, and financial resources. If the elderly person stays too long in a situation not suited to his/her condition, then his/her risk of a decline in health is significant. The dilemma is whether to choose: 1) to wait to have the structure most adapted to the health of the state or 2) to assign the elderly person to the most suitable structure available. We propose a stochastic optimization approach to help stakeholders assign EP to an LTC structure in a given territory. The model uses projections of the health state of the population over a time horizon to make decisions and considers elderly care requirements and characteristics, such as geographic compatibility and financial resources. The model performs better than a greedy algorithm (based on the first-in-first-out approach) and an optimization model without time projections.