Prioritizing high-risk sub-groups in a multi-manufacturer vaccine distribution program

• Published date: 08 May 2017
• Pages: 311-331
• DOI: https://doi.org/10.1108/IJLM-12-2015-0227
• Date: 08 May 2017
• Author: Sharon Hovav,Avi Herbon
• Subject Matter: Management science & operations,Logistics

Prioritizing high-risk sub-groups

in a multi-manufacturer vaccine

distribution program

Sharon Hovav and Avi Herbon

Department of Management, Bar Ilan University, Ramat Gan, Israel

Abstract

Purpose –Annual influenza epidemics cause great losses in both human and financial terms. The purpose of

this paper is to propose a model for optimizing a large-scale influenza vaccination program (VP). The goal is

to minimize the total cost of the vaccination supply chain while guaranteeing a sufficiently high level of

population protection. From a practical point of view, the analysis returns the number of shipments and the

quantity of vaccines in each periodic shipment that should be delivered from the manufacturers to the

distribution center (DC), from the DC to the clinics, and from the clinics to eachsub-group of customers during

the vaccination season.

Design/methodology/approach –A mixed-integer programming optimization model is developed to

describe the problem for a supply chain consisting of vaccine manufacturers, the healthcare organization

(HCO) (comprising the DC and clinics), and the population being vaccinated (customers). The model suggests

a VP that implemented by a nation-wide HCO.

Findings –The benefits of the proposed approach are shown to be particularly salient in cases of limited

resources, as the model distributes demand backlogs in an efficient manner, prioritizing high-risk sub-groups

of the population over lower-risk sub-groups. In particular, the authors show a reduction in direct medical

burden of consumers, such as the need for doctors, hospitalization resources, and reduction of indirect,

non-medical burden, such as loss of workdays.

Practical implications –Drawing from the extended enterprise paradigm, and, in particular, taking consumer

benefits into account, the authors suggest an operational-strategic model that creates impressive added value in a

highly constrained supply chain. The model constitutes a powerful decision tool for the deployment of large-scale

seasonal products, and its implementation can yield multiple benefits for various consumer segments.

Originality/value –The model proposed herein constitutes a decision support tool comprising operational-

tactical and tactical-strategic perspectives, which logistics managers can utilize to create an enterprise-

oriented plan that takes into account medical and non-medical costs.

Keywords Vaccination, Distribution problem, Influenza, Medical supply chain, MIP,

Prioritizing high-risk sub-groups

Paper type Research paper

Nomenclature

Indexes

jcustomer sub-groups, j¼1, …,G

iclinic index, i¼1, …,I

Lmanufacturer index, l¼1, …,L

tdiscrete time index, t¼1, …,T

Parameters

d

ijt

demand for vaccine units (doses) in

period tby sub-group jin clinic i

hCL

iclinic inventory holding cost, for

clinic i, per unit of vaccine in a single

time period

h

DC

DC inventory holding cost per unit of

vaccine per time period

Π

jτ

health benefits in monetary terms;

expected losses per a period for

unvaccinated customer in sub-group

jin period t

ρ

j

cost of bad reputation per a period as a

consequence of unsatisfied demand by

sub-group j

A

ij

service cost per customer in sub-group

jby clinic iThe International Journal of

Logistics Management

Vol. 28 No. 2, 2017

pp. 311-331

© Emerald PublishingLimited

0957-4093

DOI 10.1108/IJLM-12-2015-0227

Received 7 September 2015

Revised 9 December 2015

10 December 2015

14 January 2016

Accepted 14 January 2016

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

www.emeraldinsight.com/0957-4093.htm

The assistance and guidance of Professor Eugene Levner, programming work of Dmitry Tzadikovich,

and comments of Dr Hanan Tell are greatly acknowledged.

311

Prioritizing

high-risk sub-

groups

kDC

lcost of purchasing a single unit of

vaccine from manufacturer land

transporting it to the DC

k

DC

cost of purchasing a single unit of

vaccine from the manufacturer and

transporting it to the DC

KCL

icost of transporting a single shipment

of vaccines from the DC to clinic i

α

jt

minimum service level required for

sub-group jby time tin terms of

vaccine availability

C

DC

storage capacity at DC

CCL

istorage capacity in clinic i

CM

lt storage capacity in warehouse of

manufacturer lin period t.

n

j

average medical personnel treatment

time per customer in sub-group j

N

it

medical personnel hours available in

clinic iin period t(hours per day)

Mvery large number

Auxiliary variables

I

t

inventory (on hand) in the DC at the

end of period t,t¼1, …,T

I

it

inventory (on hand) in clinic iat the

end of period t,i¼1, …,I,t¼1, …,T

Decision variables

q

lt

quantity of vaccine units delivered

(shipped) from the manufacturer lto

the DC in period t

q

it

quantity of vaccine units delivered

from the DC to clinic iin period t

s

ijt

quantity of backlogged vaccine units

in clinic ilinked to group jin period t

w

ijt

quantity of vaccine units consumed in

clinic ilinked to group jin period t

Z

it

1 if shipment of vaccines from the DC

to clinic iin period tis transported,

0 otherwise

1. Introduction

Annual influenzaepidemics cause great losses in bothhuman and financial terms. According

to the National Institute of Allergy and Infectious Diseases (2008), in each influenza season

between 5 and 20 percent of Americans, both vaccinated and unvaccinated, contract the

disease, despitevaccination programs (VP). Molinari et al.(2007), relying on data from a 2003

survey of the US population, estimate that in 2003 influenza epidemics led to 3.1million days

of hospitalization and to 31.4 millionoutpatient visits, correspondingto direct medical costs of

10.4 billion dollars.Keogh-Brown et al. (2010) applieda macro-economic model to evaluate the

potential effect of a high-volume pandemic on gross domestic product (GDP) in the UK, and

determined that even a mild disease scenario would yield a 1.55 percent drop in GDPduring

the following quarter. Billions of dollars are spent yearly on preparedness for influenza

epidemics, including VP, in an attempt to prevent even greater losses.

Exploiting the maximum potential of the VP supply chain is considered to be a global

challenge (Chick et al., 2008). The efficiency of VP is associated with two main factors. The

first factor is the vaccination rate (i.e. the percentage of the overall population that is

vaccinated) which, according to Yoo (2011) depends on four determinants: ongoing influenza

epidemic level, media promotion, reimbursement rate for providers to administer vaccines

(Chick et al., 2008), and vaccine supply chain flow. The second factor is the timing of the

vaccination for individual sub-groups, and, in particular, the extent to which high-risk

groups are motivated to be vaccinated earlier (Yoo and Frick, 2005).

Herein, we propose a model, based on a mixed-integer programming methodology that

aims to improve the efficiency of a country-wide multi-manufacture vaccine distribution

program (VDP) run by a healthcare organization (HCO). We note that the concept of a VDP

is distinct from the more general concept of VP, in that it takes into account logistical

costs in addition to availability of operational resources (e.g. storage capacity and medical

human resources). The model developed herein considers all stakeholders in the supply

chain –including vaccine manufacturers, the HCO, and the population (and specific

sub-groups) being vaccinated –while focusing on two key agents, both of which are

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