A hybrid memetic-ANS optimization algorithm for the home health care and home care routing and re

TL;DR

A mixed integer linear programming (MILP) model is developed to cater to two groups of customers: pre-scheduled existing customers and same-day service new customers and a hybrid memetic-Adaptive Neighborhood Search (ANS) optimization algorithm is proposed to tackle the model.

Abstract

This paper addresses a realistic home health care and home care (HHC\&HC) problem which has become increasingly complex in the face of demographic aging and post-COVID-19 disruptions. The HHC\&HC sector, as the essential component of modern health care systems, faces unique challenges in efficiently scheduling and routing caregivers to meet the rising demand for home-based care services. Traditional approaches often fall short in addressing the dynamic nature of care requests, especially in accommodating new, same-day service requests without compromising scheduled visits. To tackle these issues, We define the problem as an HHC\&HC routing and rescheduling problem with rejection of new customers (HHC\&HCRRP-RNC), focusing on rescheduling for a single HHC\&HC caregiver in response to new customer requests within a single period. This problem is a variant of both the single-machine reschedule problem and the orienteering problem with mandatory visits (OPMV), where certain nodes must be visited while others are optional. A mixed integer linear programming (MILP) model is developed to cater to two groups of customers: pre-scheduled existing customers and same-day service new customers. The model emphasized maintaining minimal disruptions to the original schedule for existing customers as a constraint, highlighting the balance between adhering to scheduled visits and accommodating new customers. A hybrid memetic-Adaptive Neighborhood Search (ANS) optimization algorithm is proposed to tackle the model. This approach aims to minimize operational costs and opportunity costs while enhancing service quality and patient satisfaction. Through computational experiments, our proposed algorithm demonstrates notable performance, offering significant improvements in both efficiency and robustness within the problem domain.

Figures (9)

• Figure 1: An example of the Restricted Shortest Insertion operator, in which the unvisited node k with the highest payment is inserted into a position that increases the minimal increment of travel time
• Figure 2: An example of the Restricted Shortest Insertion operator, in which the unvisited node k is inserted so that the least increase in travel time is produced
• Figure 3: An example of the 2-opt operator which replaces two arcs $(i,i+1)$ and $(j,j+1)$ with $(i,j)$ and $(i+1,j+1)$
• Figure 4: An example of the Restricted Longest Removal operator in which three consecutive nodes $j$, $j+1$, and $j=2$ are relocated to a different position while keeping the sequence within this chain
• Figure 5: An example of the Restricted Longest Removal operator which removes the visited new customer node $j$ from the current route to produce the most decrease in travel time