Solving a More Flexible Home Health Care Scheduling and Routing Problem with Joint Patient and Nursing Staff Selection

Jamal Nasir,Chuangyin Dang

doi:10.3390/su10010148

Abstract

Development of an efficient and effective home health care (HHC) service system is a quite recent and challenging task for the HHC firms. This paper aims to develop an HHC service system in the perspective of long-term economic sustainability as well as operational efficiency. A more flexible mixed-integer linear programming (MILP) model is formulated by incorporating the dynamic arrival and departure of patients along with the selection of new patients and nursing staff. An integrated model is proposed that jointly addresses: (i) patient selection; (ii) nurse hiring; (iii) nurse to patient assignment; and (iv) scheduling and routing decisions in a daily HHC planning problem. The proposed model extends the HHC problem from conventional scheduling and routing issues to demand and capacity management aspects. It enables an HHC firm to solve the daily scheduling and routing problem considering existing patients and nursing staff in combination with the simultaneous selection of new patients and nurses, and optimizing the existing routes by including new patients and nurses. The model considers planning issues related to compatibility, time restrictions, contract durations, idle time and workload balance. Two heuristic methods are proposed to solve the model by exploiting the variable neighborhood search (VNS) approach. Results obtained from the heuristic methods are compared with a CPLEX based solution. Numerical experiments performed on different data sets, show the efficiency and effectiveness of the solution methods to handle the considered problem.

Highlights

In the case of variable neighborhood search (VNS), the relative gap is less than 9%, where the optimal solution is available from CPLEX, while it is less than 30% for all instances of type A when the relative gap is computed using the lower bound
The results indicate that the VNS performed better for type A instances as compared to self-correcting variable neighborhood search (SCVNS) in terms of the optimality gap
An mixed-integer linear programming (MILP) model was developed and heuristic solution methods were suggested for the daily health care (HHC) planning problem in this paper

Summary

Introduction

The provision of health care services at home has been a rapidly developing area of the global economy in the last two decades, with more than 10,000 firms providing therapeutic, rehabilitative and palliative services in the United States alone [1]. This is evident from the fact that many new organizations have been registered in this area of HHC in every developed country. In response to the increasing competitive pressures in all businesses, service providers must discover new ways to decrease their cost, improve quality and enhance productivity [2]. Every HHC service system should be efficient, sustainable and flexible to incorporate the demand and supply patterns

Objectives

Results

Conclusion