A network flow-based model for operations planning in home health care delivery

• Published date: 24 September 2020
• Date: 24 September 2020
• Pages: 68-95
• DOI: https://doi.org/10.1108/IJLM-02-2020-0073
• Subject Matter: Management science & operations,Logistics
• Author: Fabián Castaño,Nubia Velasco

A network flow-based model for

operations planning in home health

care delivery

Fabi

an Casta~

no

Civil and Industrial Engineering, Pontificia Universidad Javeriana,

Cali, Colombia, and

Nubia Velasco

School of Management, Universidad de los Andes, Bogota, Colombia

Abstract

Purpose –To solve the problem, a mathematical modelis proposed; it relies on a directed acyclic graph (DAG),

in which arcs are used to indicate whether a pair of appointments can be assigned to the same route or not (and

so to the same care worker). The proposed model aims at minimizing the personnel required to meet daily

demand and balancing workloads among the workers while considering the varying traffic patterns derived

from traffic congestion.

Design/methodology/approach –This paper aims at providing solution approaches for addressing the

problem of assigning care workers to deliverhome health-care (HHC) services, demanding different skills each.

First, a capacity planning problem is considered,where it is necessaryto define the number of workers required

to satisfy patients’requests and then, patients are assigned to the care workers along with the sequence

followed to visit them, thus solving a scheduling problem. The benefits obtained by permitting patients to

propose multiple time slots where they can be served are also explored.

Findings –The results indicate that the problem can be efficiently solved for medium-sizedinstances, that is,

up to 100 daily patient requests. It is also indicatedthat asking patients to propose several moments when they

can receive services helps to minimize the need for care workers through more efficient route allocations

without affecting significantly the balance of the workloads.

Originality/value –This article provides a new framework for modeling and solving a HHC routing problem

with multiskilled personnel. The proposed model can be used to identify efficient daily plans and can handle

realistic characteristics such as time-dependent travel times or be extended to other real-life applications such

as maintenance scheduling problems.

Keywords Home health care delivery, Multiskill personnel routing and scheduling, Network models, Benders’

decomposition

Paper type Research paper

1. Introduction

In traditional settings, the medical is provided in medical facilities and the patient has to move

from home to hospital and/or remain there to be monitored constantly. Boosted by an

insufficient capacity of the medical system and by the recent technological advances of

portable medical equipment, the idea of moving medical staff from health-care facilities to

those persons who need assistance has raised a growing interest (Cotta et al., 2001;Rodriguez-

Verjan et al., 2018). These services are known as home health care delivery (HHD).

HHD can be traced back to 1950 when Dr. Bluestone from Montefiore Hospital in New

York started what is known to be the first American experience in home health care

programs. The reasons for its creation were to decongest hospital rooms and provide patients

with a more humane and supportive environment (Cotta et al., 2001). This model was rapidly

adopted in the developed world for countries such as France, the United Kingdom, Sweden,

Italy and Canada (Terrade et al., 2012;Cotta et al., 2001).

Among the HHD there are two schemes: (1) domiciliary care delivery and (2) community

health-care programs. The first constitutes an effective strategy for addressing the weak

IJLM

32,1

68

The current issue and full text archive of this journal is available on Emerald Insight at:

https://www.emerald.com/insight/0957-4093.htm

Received 1 February 2020

Revised 5 August 2020

Accepted 30 August 2020

The International Journal of

Logistics Management

Vol. 32 No. 1, 2021

pp. 68-95

© Emerald Publishing Limited

0957-4093

DOI 10.1108/IJLM-02-2020-0073

coverage of the health-care systems, and it is also becoming a cost-effective and flexible

instrument in the social system (Cappanera and Scutell

a, 2015). Community health-care

programs provide care services to those living outside the financial and physical reach of the

standard health infrastructure (Brunskill and Lesh, 2010). HHD serves to avoid hospital stay

that constitutes a good option when hospital facilities and equipment should be prioritized for

the attention of emergencies, patients with serious diseases or surgical needs. The main

objective of HHD programs is to provide the required services at patients’homes, with the

advantage of allowing them to continue living in their own friendly environment. An

additional advantage can also be seen in the financial context, allowing health-care

institutions to more efficiently use the so often scarce resources (Rest et al., 2012).

To satisfy the growing demand for such services, the planning process requires

coordinating schedules for the care workers so as to allocate them the patient appointments in

order to satisfy demand requirements in an efficient manner (Fikar and Hirsch, 2016). As

ought to be expected, schedules should respect the estimated travel time between locations,

avoiding long journeys and/or prevent wasting staff members’working time. The success of

such a program might be measured in terms of the capacity to keep under control the total

resources spent on providing the desired services (Fikar and Hirsch, 2016). This is especially

the case when the cost of hiring highly skilled care workers or having them out of institutions

where they may be required is expensive.

Let us consider a set of available care workers with different and/or multiple skills and a

set of patients (people, municipalities, small villages, schools, etc.) demanding different types

of services. Each patient then specifies a set of time slots during which he/she prefers to be

serviced and programmers have to choose between the options expressed by patients. In

general, patients’preferences are respected as they cannot overlap with other activities and

waiting for the appointments may require some planning from their side. Every request

should be attended to by care workers having the specific skills necessary to provide the

services demanded. These individual skills involve certain costs, with the more expensive

services provided by highly qualified care workers.

The problems to address consist of assigning personnel to the different activities

(services) during a planning horizon. Nonperiodic visits are considered, so it is not required

for a patient to be pre-assigned to a given care worker. Nonetheless, other constraints for the

operation have to be considered: (1) two appointments cannot be assigned to one care worker

simultaneously; (2) the time between successive appointments allocated to the care workers

must respect the travel time required to move between patients’locations (that might depend

on the moment when the travel starts); (3) each patient should be visited over the course of a

day exactly once; (4) the care worker visiting a patient should match the skill required for

delivering the requested service. The home care context often involves joint assignment,

scheduling and routing decisions over a given planning horizon. Consequently, the problem

faced often combines well-known characteristics of well-known hard optimization problems

such as vehicle routing and staff rostering (Cappanera and Scutell

a, 2015).

To complicate things even more, traffic congestion in large urban agglomerations

makes the planning tasks even harder to solve. Congestion increases the pressure over

health-care services providers and makes it imperative to improve the planning processes

behindtheactivitiesrequiredtodelivertheexpected services appropriately while keeping

costs under control. Should technical services are to be delivered in large congested cities,

additional considerations have to be taken into account. In the first place, neglecting

congestion while planning the routes assigned to personnel in charge of visiting clients

might affect the capacity to respond to the increasing demand as care workers traveling in

vehicles might spend long time in traffic jams. Moreover, neglecting varying traffic

patterns can result in higher costs, missed deadlines, diminution of service levels and

worsened city congestion.

Home health

care delivery

69