This study presents an innovative extension to Home Healthcare Scheduling and Routing Problem (HHCRSP), introducing an Optional Starting Point (OSP) that allows for personalization of routes from the caregivers’ homes directly to patients. We developed a model using Mixed Integer Linear Programming (MILP) and a metaheuristic method inspired by the Greedy Randomized Adaptive Search Procedure (GRASP). This combination aims to make scheduling and routing more efficient, saving time and improving the quality of care for patients at home. Our results show that this new method can significantly enhance how home healthcare is delivered, making it more flexible and effective for both caregivers and patients.

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.

Home health care optimization is a trending research topic in the recent years since the demand for home health care rises. An important aspect of the problem is the workload balancing among caregivers that must be fair. However, the workload can be defined differently since the work of a caregiver can be composed of different activities: traveling time, time spent providing cares and idle time. Moreover, the home health care routing and scheduling problem with workload balancing is a multi-objective problem leading the working time balancing to increase the value of the total working time and soft patients time window and shared visits non-satisfaction. In order to obtain a good balance between all objectives, we perform an impact analysis of the caregivers activities balancing in order to identify the appropriate activities to balance instead of the whole working time. A mixed-integer programming representation of the problem is proposed and a memetic algorithm is used to evaluate the model on literature instances. An analysis of the results reveals the importance of the choice of the balanced activities in order to obtain an acceptable balance between workload balancing and the other objectives according to decision-makers strategy.

Considerable attention had previously been given to the single-vendor single-customer integrated inventory problem, but there had been very little work on the integrated single-vendor multi-customer and multi-product consideration. Here, we develop a generalized single-vendor multi-customer with multi-product consideration supply chain model with one transporter available to deliver the products from the supplier to the customers.The objective is to solve the proposed model and to find the minimized total cost, while guaranteeing a certain customer service level. A mathematical formulation of the problem is given in a general way. Then, we propose a branch and bound algorithm as an exact method and an efficient heuristic greedy algorithm. Both procedures are then compared through computational experiments which show that the heuristic algorithm is capable of generating near-optimal solutions within a short amount of CPU time.