Discrete Invasive Weed Optimization and Greedy Hybridization Algorithm for Home Care Multi-days Assignment Scheduling and Routing Problems

This article formulates a multi-day home care assignment scheduling and routing problem in which workload and distances are balanced between the employees. Additionally, constraints such as lunch breaks, maximum daily working hours, the maximum number of overtime hours, and the amplitude of the day are considered when solving the problem. The objective is to satisfy the clients' preferences, minimize the total distance traveled and the number of wasted and overtime hours, and balance the workload and the distance traveled between the employees. Since the proposed model is an NP-Hard problem, for solving large-scale problems, two resolution methods, a genetic algorithm approach, and a discrete invasive weed optimization with a greedy heuristic hybridization are presented. To validate the efficiency of the two approaches in solving the Home Care Multi-day Assignment, Scheduling, and Routing Problems, instances inspired by a real-life example of a home care center were tested. Moreover, they were compared to an exact mixed-integer linear programming method. The optimal results show the efficiency of our resolution methods; the solutions perform well as the multi-day home care assignment, scheduling, and routing problem can be solved in a reasonable time.