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Designing a resilient supply chain: An approach to reduce drug shortages in epidemic outbreaks


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INTRODUCTION: Supply network design is a long-studied topic that has evolved to address disruptive situations. The risk of supply chain disruption leads to the development of resilient supply chains that are capable of reacting effectively. OBJECTIVES: In the context of public health, drug supply networks face shortage challenges in many situations, such as current epidemic outbreaks such as COVID-19. Drug shortages can occur due to manufacturing problems, lack of infrastructure, and immediate reaction mechanisms. METHODS: The case study is solved with anyLogistix optimization and simulation software. RESULTS: We present the results of a hypothetical study on the impact of COVID-19 on a regional supply network. The results of this research are intended to be the basis for the design of resilient supply chains in epidemic outbreaks. CONCLUSION: Drug providers should consider strategies to prevent or reduce the impact of shortages as well as disruption spreads. Keywords Supply chain design, resilient supply chain, epidemic outbreaks, COVID-19, drug shortages, Dynamic Simulation
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Designing a resilient supply chain: An approach to
reduce drug shortages in epidemic outbreaks
Jose Antonio Lozano-Diez1, Jose Antonio Marmolejo-Saucedo2,and Roman Rodriguez-Aguilar3
1Universidad Panamericana. Augusto Rodin 498, Ciudad de México, 03920, México.
2Universidad Panamericana. Facultad de Ingenieria. Augusto Rodin 498, Ciudad de Mexico, 03920, Mexico.
3Universidad Panamericana. Escuela de Ciencias Económicas y Empresariales. Augusto Rodin 498, Ciudad de
México, 03920, México.
INTRODUCTION: Supply network design is a long-studied topic that has evolved to address disruptive
situations. The risk of supply chain disruption leads to the development of resilient supply chains that are
capable of reacting eectively.
OBJECTIVES: In the context of public health, drug supply networks face shortage challenges in many
situations, such as current epidemic outbreaks such as COVID-19. Drug shortages can occur due to
manufacturing problems, lack of infrastructure, and immediate reaction mechanisms.
METHODS: The case study is solved with anyLogistix optimization and simulation software.
RESULTS: We present the results of a hypothetical study on the impact of COVID-19 on a regional supply
network. The results of this research are intended to be the basis for the design of resilient supply chains in
epidemic outbreaks.
CONCLUSION: Drug providers should consider strategies to prevent or reduce the impact of shortages as well
as disruption spreads.
Received on 18 April 2020; accepted on 05 May 2020; published on 07 May 2020
Keywords: Supply chain design, resilient supply chain, epidemic outbreaks, COVID-19, drug shortages, Dynamic
Copyright © 2020 Jose Antonio Lozano-Diez et al., licensed to EAI. This is an open access article distributed under the
terms of the Creative Commons Attribution license (, which permits
unlimited use, distribution and reproduction in any medium so long as the original work is properly cited.
1. Introduction
The Mexican health system has gone through several
reforms, one of the most important being the reform
of the General Health Law of 2003 that gave rise to
the Social Protection System in Health, which would
operate through the Popular Insurance as a public
insurer ocially starting operations in 2004.
The configuration of the public health system in
Mexico was integrated by three large institutions, the
ISSSTE that provides social security to state workers,
the IMSS that provides coverage to workers in the
private sector, and the Popular Insurance that integrates
the open population without import your work or social
Corresponding author.Email:
In addition to these reforms, the demographic and
epidemiological profile of the Mexican population has
changed. The epidemiological transition that Mexico
is going through and the aging of its population
are determining factors in the demand for specific
health services, as well as the requirement for specific
medications to care for the population [1]. There are
additional risk factors such as for overweight and
obesity, as well as an increase in the prevalence of
chronic diseases. In 2018, it was recorded that 75.2%
of the adult population (20 years and over) had
problems with overweight or obesity. Further 10.3%
of the population had diabetes and 18.4% suer from
hypertension [2]. This implies an increase in overweight
and obese people, and people with chronic diseases,
aecting the mortality of the Mexican population and
generating significant pressures on the Health System.
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Concerning demographic transition in 2020, the
average age of the Mexican population was 29.2 years
in contrast to the year 2000 where the average age
of Mexicans was 22.9 years. According to data from
the Economic Commission for Latin America and the
Caribbean (ECLAC), the population aged 65 and over in
Mexico increased from 6.1% in 2010 to 7.6% in 2020 [3].
The increase in the adult population likewise generates
greater pressure. to the health system, in addition to
inverting the population pyramid. Fig. 1shows the
population pyramid of Mexico in 2012 and the data
projected to 2030 by the National Population Council
Figure 1. Mexico population pyramid, 2012-2030.
In a framework of limited resources, it generates
significant pressures on the financing of the system.
In 2017, health spending as a percentage of GDP
represented 5.5%, of which 52% corresponds to public
spending, 43% to pocket spending, and 5% to private
prepaid [4].
1.1. Analysis of drugs supply in the public sector
As part of the new configuration of the health system
in Mexico, the goal was to achieve universal coverage
through eective access to health services. Addressing
priority problems in the health sector, such as the
supply and complete supply of medicines in public
health services. The quality care process is completed
at the moment the patient receives the prescription
medications that will allow them to recover their state
of health.
The issue of drug supply and supply in Mexico is a
topic that has been worked on for many years, through
the implementation of various strategies that allow the
supply and supply of 100% of the drugs prescribed to
patients. In 2012, the percentage of full prescriptions
filled in the public sector was 65.2%, which implied
that 34.8% of the prescriptions were not filled. For
2018, this indicator was 69.9%, with 30.1% of recipes
not filled. The percentage of complete prescriptions
filled has improved in the last 6 years, however, the
established goal of 90% has not been reached (Fig. 2).
Various strategies have been implemented to improve
the medicine supply chain and to guarantee the supply
Figure 2. Percentage of a complete supply of drugs, 2012-2018.
and complete supply of prescriptions.As we can see
in Table 1, this table summarizes the main among
some strategies implemented to improve the supply and
supply of medicines in the public sector in Mexico [5].
Table 1. Policies implemented at the federal leve
Policies Description
Coordinating Commission for the Negotiation of
Medicine Prices and other Health Supplies
Intersectoral commission for the negotiation of
medicines and other single-source supplies.
Negotiations take place annually.
Consolidated purchase of medicines
Consolidated purchase of medicines integrating
the requirements of the main public health
institutions, as well as entities from the federal
and state levels.
Reference prices
Reference list for the purchase of medicines
financed with resources from the Social Health
Protection System, the objective is to reduce
the variance in the public purchase prices acquired
by the federal entities.
Generic release policy
Prioritization of the issuance of health records
for high-priority generic products. This will allow
there to be more competitors in the shorter term in
the market and will generate a decrease in the prices
of medicines whose patent has expired.
These policies have generated positive results in
the medicine supply chain in the health sector, but
according to the indicators, there are still important
gaps to be resolved. An example of this is household
out-of-pocket spending on medicines, since failing to
supply the public sector in the best of cases patients
must go to the private market to purchase their
medicines. According to data from the National Survey
of Household Income and Expenditure (ENIGH for
its acronym in Spanish) in 2018, Mexican households
spent around MXN$34,332 million on medicines. This
represents 31.3% of out-of-pocket spending on health of
Mexican households, which represented MXN 109,700
million in the same year, followed by spending on
outpatient care (28.0%) and hospital care (21.1%), fig.
The medicine supply chain is a complex process and
with a very particular operation unlike the supply chain
of other products. Both supply and demand interact
with various agents, who participate in the supply
process and those who participate in the patient care
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Figure 3. Out-of-pocket expenditure on household health in
Mexico, 20016-2018.
process (Fig. 4). In the case of the public sector, the
federation only controls part of the supply chain, so
there are inherent risks and the probability of failure
at each link in the supply chain. Furthermore, the
participation of the pharmaceutical industry is highly
relevant because it participates in the entire process
through various direct and indirect strategies. From
Figure 4. Drug supply process.
the analysis of the main problems presented in the
supply of medicines in the public sector, five main areas
of risk of failure in the operation were integrated: 1)
planning, 2) acquisition, 3) distribution, 4) prescription
and 5) dispensing. Any failure in any of these stages
compromises the ecient operation of the supply chain
and in turn, implies that the supply of prescription
drugs is not complete for all patients.
Fig. 5shows the analysis of possible problems in
the five stages considered, highlighting the distribution
process with delays in the delivery of medicines,
shortages in pharmacies of medical units, lack of
adequate communication between warehouses and
medical units as well as dierent models of drug
distribution. Distribution models refer to the scheme in
which the distribution of the drug is managed after its
acquisition, for example, the most widely used schemes
are outsourcing or direct distribution.
The analysis of the problems in the medicine
supply chain in the public sector shows areas of
opportunity at each stage. However, the main limitation
for establishing an ecient supply chain lies in the
Figure 5. Problematic of the full drug supply.
operation of multiple agents at each stage of the process.
Therefore, it is necessary to establish regulatory entities
that make it possible to integrate the operation of these
agents if it is not in the daily operation, but a framework
of a public health emergency such as an epidemic.
The Mexican health system is fragmented, this
determines a particular configuration in its operation
and therefore in the related medicine supply chain.
According to what is described in this section, it can
be seen that Mexico faces an important demographic
and epidemiological transition, as well as structural
problems in the supply of medicines in the public
sector. On average 30% of the recipes generated in
the public sector are not filled or are not filled.
Various strategies have been implemented to improve
the supply level; however, much remains to be done.
Therefore, it is necessary to be prepared in the face of
a disruptive event such as an epidemic and design a
supply chain for both supplies and medicines that allow
for an ecient response to contingencies.
2. COVID-19 pandemic in Mexico
In the context of an epidemic, it is necessary to have
a resilient medicine supply chain design. However, in
the case of Mexico, we start from a supply chain of
medicines with structural problems, since a percentage
of unsorted prescriptions derived from the structure of
the health system and the operation of the medicine
supply system is maintained. In this context, at
the beginning of 2020, Mexico faces an enormous
challenge due to the COVID-19 pandemic. According
to information issued by the Ministry of Health, as
of April 28, 77,005 possible cases were registered
[6]. Preliminary data subject to validation by the
Ministry of Health through the General Directorate of
Epidemiology. The information contained corresponds
only to the data obtained from the epidemiological
study of a suspected case of viral respiratory disease
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at the time it is identified in the medical units
of the Health Sector. The records are made by
sentinel surveillance, of the System of Health Units
for Monitoring Respiratory Diseases (USMER for its
Spanish acronym). The USMERs include first, second,
and third-level medical care units.
The information on suspicious cases reported to the
epidemiological surveillance system is validated based
on the tests carried out for the confirmation of positive
cases with COVID-19, the distribution of the data shows
that as of April 28 of the 77 thousand case records
16,752 were confirmed by diagnostic tests, 49,000 cases
were discarded as COVID-19, and 11,000 cases are
still pending confirmation due to the time required to
carry out the tests. Of the total confirmed cases, 42%
correspond to women and 58% to men. (Fig. 6).
Figure 6. Total cases registered by the epidemiological
surveillance system as of April 28, 2020.
The proportion of confirmed cases represents 22%,
negative 64%, and pending results 15%. It is important
to note that although only 22% of the total registrations
as of April 28 were positive, it was necessary to
give attention to the 77 thousand cases received. This
implies that given the health emergency, a greater
number of users go to health services due to the
suspicion of being infected with COVID-19, which in
turn generates a significant increase in the demand for
health services.
The distribution of cases by state entity shows Mexico
City (5,261 cases), the State of Mexico (1,966 cases),
and Baja California (1,410 cases) as the entities with
the highest number of confirmed cases. As of April
28, 2020, it is observed that cases are presented in all
the federal entities, with Colima (25 cases), Durango
(57 cases) and Nayarit (61 cases) being the entities
with the fewest confirmed cases (Fig. 7). According to
the confirmed cases, there is a distribution of their
severity, of the total of confirmed cases, 61% are
ambulatory cases, and 39% required hospitalization.
When analyzing the age groups of the confirmed cases,
we observe that there is a higher concentration of
Figure 7. Distribution of cases by state as of April 28, 2020.
cases in ages ranging from 30-54 years, concentrating
57% of the total number of cases, which implies that
the highest proportion of patients is concentrated in
patients in working age. Patients aged less than 30
years accumulate 14% of the total number of cases and
patients older than 54 years represent 30% of the cases.
(Fig. 8).
Figure 8. Distribution of cases by five-year age group as of April
28, 2020.
Of the total confirmed cases, a total of 1,569
patients have died, which represents 9.4%, which
expressed in terms of a gross mortality rate per
1,000 inhabitants, represents 93.3 deaths per thousand
inhabitants. Presenting the highest number of deaths
in adults over 40 years. The highest mortality rates
are observed in the groups of 75-79 years with 230
deaths per 1000 inhabitants, the group of 80-84 with
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227 deaths per 1000 inhabitants, and the group of 90-
94 years with 222 deaths per 1000 population (Fig. 9).
Figure 9. Deaths and mortality rate by age groups as of April
28, 2020.
Based on the information generated up to April 28,
2020, some important elements are identified, referring
to the states with the highest number of cases, the
mortality observed in groups of older adults, as well
as the presence of diseases related to additional risk
factors. in patients identified as obesity, hypertension,
diabetes, and smoking. Of the total of confirmed cases,
30% developed pneumonia, 22% have hypertension,
and 18% diabetes. 21% of confirmed patients are obese
and 9% report smoking. About specialized services, a
low proportion of confirmed patients has required ICU
services 4.3% and 4.2% have been intubated (Table 2).
The evolution of the COVID-19 pandemic in Mexico
Table 2. Related diseases, risk factor and specialized care of
confirmed cases
Related diseases Cases %of confirmed cases*
Pneumonia 4,942 29.5%
Hypertension 3,640 21.7%
Diabetes 3,064 18.3%
Other complication 696 4.2%
Asthma 585 3.5%
Cardiovascular 473 2.8%
COPD 421 2.5%
Chronic kidney 388 2.3%
Immunosuppression 314 1.9%
Risk factors
Obesity 3,463 20.7%
Smoking 1,496 8.9%
Specialized care
ICU 720 4.3%
Intubated 709 4.2%
is still in evolution, there is no evidence that as of
April 28, 2020, the maximum peak of cases has been
reached, so it is necessary to follow up on the available
information issued by the Secretariat of health. The
available information shows an increase in the demand
for health services given the spread of the pandemic
and that service users come to present some related
symptoms. This implies that there is an unusual peak
in demand in public health services as well as supplies
and medicines. Since the registration of possible cases
implies some attention to the patient (Fig. 10).
Figure 10. Evolution of the cases registered in Mexico as of
April 28, 2020.
In the framework of a structural problem in the
supply chain of medicines (and supplies) in the
public sector in Mexico, it is necessary to define
alternative schemes to solve episodes of sanitary crises
such as the current one. For this, it is necessary
to opt for the integration of innovative technologies
and methodologies that allow a rapid response to a
contingency, seeking to lessen the impact on the health
3. Literature review
In the case of a Health system such as that of Mexico
that has structural problems and a 70% full supply
of medicines, facing a public health challenge such as
the COVID-19 pandemic implies making value-added
proposals that allow face contingencies like the current
one. The design of a resilient medicine supply chain
that can serve as a response to unexpected risks in the
health system requires the participation of the dierent
agents involved in the supply chain, in addition to the
stewardship of the health department that allows the
integration of wills and joint actions.
In the framework of an epidemic, it is necessary
to guarantee medical supplies (medicines, vaccines,
supplies, etc.) in addition to basic products (food,
water, etc.). To guarantee the supply and supply of
these products, it is necessary to have strategic storage
and distribution centers that communicate with the
expected demand points in the event of a contingency.
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It is precisely a problem of designing an emerging
logistics network in the face of disruptive events. For
this, it is necessary to define the number and location
of distribution and collection centers, unloading places
and the location of demand centers, and the selection of
optimal distribution algorithms that guarantee the best
performance of the network. As well as the definition
of the required optimal inventory levels, replacement
policies, transportation, and distribution according to
the health contingency that is being faced.
For the proper design of a network of this nature,
it is necessary to have precise estimates of the
demand required according to the contingency. Studies
have been carried out combining demand estimation
models related to epidemiological models of disease
progression. Authors such as [7] propose a multi-
objective programming model for the selection of
emergency centers and the quantities of drugs to be
transported from the supply sources to the demand
points. In [8], they extend the vision of multi-objective
programming towards a stochastic model using genetic
algorithms for its solution. In [9], they integrate the
analysis of system dynamics to model the dynamic
behavior of the refueling, reception, and dispensing
sources in the case of an anthrax attack. In [10], they
propose a dynamic optimization model with variable
replacement and transport times using heuristic
methods for its solution. Other approaches consider
logistics network designs with one-time supply and
replenishment points [11]. Similarly, there are dierent
versions of the modeling depending on the objective
of the network, which can be to minimize inventory
and transport costs or to minimize response time as a
priority [12] and [13].
Various studies use the hybrid approach where they
combine disease modeling through simulation and
supply chain design through optimization models, [14]
applies this approach to an anti-bioterrorism system. In
[15], they analyze the distribution of medical supplies
in aected areas considering a desirable minimum
level of supply as well as maximum response times
in addition to the associated costs. Similarly, vehicle
routing problems are integrated into a context of
epidemic control, works such as [16], [17] and [18] have
addressed this problem in their logistics designs.
In [19], they show the development of a coordi-
nated supply chain for the distribution of the influenza
vaccine. Taking into account the non-linear demand
given the behavior of the disease and the most eective
immunization strategies, combining the epidemiolog-
ical model with the supply chain. In addition to the
necessary coordination between the government and
the vaccine provider, through shared risk schemes.
The study shows in [20] presents a systematic review
of the health and disaster supply chain literature, espe-
cially in the case of natural disasters. They highlight the
development of methodologies to abort the problem,
based on operational management, information tech-
nology, inventory and control management, strategic
management, and service management. As well as the
application of new technologies for inventory manage-
ment such as the use of RFID.
In [21], they develop a systematic review of relief
distribution networks. Highlighting the contributions
made about three stages defined in an emergency:
a) preparedness and mitigation, b) response, and c)
recovery. To attend to each stage, methodological con-
tributions focused on location and network design,
transportation (relief distribution and casualty trans-
portation), and location and transportation are distin-
guished. Through exact and heuristic methods.
In [22], they present a literature review focused on
epidemic control and logistics operations. Highlight-
ing as a necessary attribute in the face of a health
contingency the need for a quick response and coor-
dination between the sectors involved to guarantee
the supply of medical supplies, human and financial
resources. Highlighting the time horizon in which you
intervene, pre-event, or post-event. Bioterrorism, natu-
ral outbreaks, and disaster aftermath are considered as
possible catastrophic events. The intervention considers
as basic stages: 1) Preparedness, 2) Outbreak, 3) inves-
tigation, 4) Response, and 5) Evaluation. Table 3shows
the main logistical operations and decisions during the
phases of an epidemic outbreak. The main methods
Table 3. Most important logistics operations and decisions during
the phases of the outbreak
Phase Most important logistic operations
Identification of sources
Contract management
Inventory management
Periodical review and updating of medical supplies
Facility location of stockpiling centers
Network design transportation/distribution
Selection of facilities/health
Availability of funds
Outbreak investigation
Provision of appropriate materials
Training of clinical workers
Provision of commodities and resources to the outbreak response
Collection, transportation, and storage of specimens
Procurement, handling, storing and distribution of laboratory commodities
Selection of facilities (PODs)
Review and updating of supplies
Transportation/distributionof supplies and commodities
Procurement of supplies once depleted
Dispensing of medical supplies, supplementary materials, and commodities to the public
Establishment of a cold supply chain for essential medical supplies
Management of human resources
Scheduling available vehicles
Adjustments to the capacity of health care facilities to hospitalize infected people
Management of patients in triage centers
Identification and assessments of possible bottlenecks of delays
Evaluation of timelines that should have been respected
Follow-up and monitoring of patients for the eectiveness of treatments
Identification of patients requiring dose modification of alternative treatment
Development of indicators to evaluate the performance of logisticscontrol operations
Assessment coordination issues
Establishment and operation of rehabilitation procedures
used to analyze the problems associated with the health
supply chain are simulation, game theory, mathematical
modeling, economic analysis, cost-eectiveness analy-
sis, optimization, and analysis of multi-criteria deci-
A recent study by [23] analyzes a reverse logistics
network design for the treatment of medical waste, in
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the framework of the COVID-19 pandemic in Wuhan
(China). The study is of great importance due to the
identification of a high rate of contagion as well as
the residence time of the virus in objects that had
contact with infected patients. Rapid response to the
management of these wastes represents an opportunity
to contain the spread of the epidemic. A multi-objective
and multi-period model of mixed-integer programming
is proposed for the design of the reverse logistics
The challenge is not less considering the complexity
in the prediction of epidemic outbreaks, however, based
on historical data, it has been possible to adequately
model the probability of occurrence and possible
scenarios of the magnitude of the problem. Stochastic
variables and dierent simulation approaches must
necessarily be included to obtain robust models. From
a technical point of view, it is necessary to integrate
innovative elements in supply chain management, such
as the integration of:
Multi-paradigm simulation schemes
Discreet simulation
Dynamic simulation
Agent-based simulation
Optimization algorithms
Disruption event modeling
Risk analysis in the supply chain
The use of data science tools, simulation, and
optimization methodologies will allow ecient and
timely management of the supply chain for medicines
and supplies in a contingency. Currently, there is a
specialized software that allows integrating dierent
paradigms into hybrid models that allow generating
technical evidence for public health decision-making.
4. Resilient supply chain model
In this section, we develop the supply chain design
model for a resilient supply network. We consider the
model into a generalized network. The model is a
mixed-integer linear problem.
Let Kbe the set of manufacturing plants. An element
kKidentifies a specific plant of the company. Let I
be the set of the potential cross-docking warehouses.
An element iIis a specific cross-docking warehouse.
Finally, let J be the set of distribution centers, a specific
distribution center is any jJ. Let Zdenote the set of
integers {0,1} .
4.1. Parameters
Qk= Capacity of plant k.
βi= Capacity of cross-docking warehouse i.
Fi= Fixed cost of opening cross-docking warehouse in
location i.
Gki = Transportation cost per unit of the product from
the plant kto the cross-docking warehouse i.
Cij = Cost of shipping the product from the cross-dock
ito the distribution center (CeDis) j.
dj= Demand of the distribution center j.
4.2. Decision variables
We have the following sets of binary variables to make
the decisions about the opening of the cross-docking
warehouse, and the distribution for the cross-docking
warehouse to the distribution center.
Yi=(1 If location iis used as a cross-docking warehouse,
0 otherwise,
Xij =(1 If cross-dock isupplies the demand of CeDis j,
0 otherwise,
Wki = The amount of product sent from plant kto the
cross-dock iis represented by continuous variables
We can now state the mathematical model as a (P)
problem. See [24].
Wki ,Yi,Xij
Gki Wki +X
Cij djXij
Subject to constraints:
Capacity of the plant
Wki Qk,kK(2)
Balance of product
djXij =X
Wki ,iI(3)
Single Cross-docking warehouse to distribution center
Xij = 1,jJ(4)
Cross-docking warehouse capacity
djXij βiYi,iI(5)
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Demand of items
Wki ,iI(6)
Wki 0,iI , kK(8)
Xij Z,iI , jJ(10)
The objective function (1) considers in the first term
the cost of shipping the product from the plant k
to the cross-docking warehouse i. The second term
contains the fix cost to open and operate the cross-
docking warehouse i. The last term incorporates the
cost of fulfilling the demand of the distribution center
j. Constraint (2) implies that the output of plant
kdoes not violate the capacity of plant k. Balance
constraint (3) ensures that the amount of products that
arrive to a distribution center jis the same as the
products sent from the plant k. The demand of each
distribution center jwill be satisfied by a single cross-
docking warehouse i, this is achieved by constraint
(4). Constraint (5) bounds the amount of products that
can be sent to a distribution center jfrom an opened
cross-docking warehouse i. Constraint (6) guarantees
that any opened cross-docking warehouse ireceives at
least the minimum amount of demand requested by a
given distribution center j. Constraint (7) ensures that
the minimum demand of each distribution center jis
considered. Finally, constraints (8), (9) and (10) are the
non-negative and integrality conditions.
5. Case study
In this section, we describe the case study. In particular,
we consider the pharmaceutical supply chain in Mexico.
The supply chain is made up of four echelons:
two factories, one central-distribution center, three
regional-distribution centers and thirty-two wholesale
drug distributors. These facilities and clients are
scattered throughout the country. Figs 11 and 12
represent the current structure of the supply chain.
The case study consists of finding a resilient solution
that allows the supply chain to react eciently to a
disruption. The distribution centers will be the facilities
subjected to hypothetical scenarios of disruption.
Table 4shows the disruption scenarios considered.
All network diagrams were implemented in
cytoscape software, see [25].
Figure 11. CDC-Factory links.
Table 4. Scenarios addressed in the case study
Scenario Disruption Breakdown time
I One factory is closed due to health contingency 45 days
II One DC is closed 30 days
III All facilities are closed 15 days
5.1. Solution methodology
The solution methodology used in this research is based
on simulation-optimization. The anylogistix software
was used to develop the "what if" methodology. This
software uses CPLEX as an optimization engine to find
the best solutions within a set of possible solutions.
First, the current situation of the pharmaceutical
company’s supply chain is modeled. Subsequently,
the elements or facilities that make up the supply
network are optimized. Several operating policies of
the chosen supply network are simulated. Finally,
disruptive events are generated to test the resilience
of the proposals to the previously defined disruption
scenarios, see fig 13.
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Figure 13. Inventory Policies and Demand
5.2. Computational results
Considering the three dierent scenarios, it was found
that scenarios I and II are those that cause the
greatest negative impact on the operation of the supply
chain. For this, and for reasons of extension of the
document, analysis of results shows the performance
indicators for scenario I and scenario II. After running
the optimization and simulation routines, the results
obtained are as follows.
In the first instance, performance indicators for
the current structure of the company were analyzed
without disruption. Afterwards, the various scenarios
were simulated. The variation experiment function,
incorporated in ALX, was used to compare various
key performance indicators. Fig. 15 shows the current
supply chain network structure.
For scenario I, the service level by product, the
available inventory of all the facilities and the average
delivery time are shown in figs. 17,18 and 19,
Scenario II, see fig. 12, as mentioned above, was
the one with the greatest disruptive eects and it is
the scenario that generates less profits. As seen in fig.
20, the level of service deteriorated to levels of 60%
and 40% for each product. Figs. 21 and 22, shows the
available inventory and lead-time.
Once scenario II has been optimized, see fig. 14, the
results of the key performance indicators are reflected
in Table 5. In this scenario, the highest profits are
generated with a service level above 95%, see fig. 23.
The available inventory and lead time are shown in figs.
24 and 25. Finally, the proposal to optimize scenario II
is shown in fig. 16.
6. Conclusions
According to the scenarios outlined for the company,
the epidemic outbreak of COVID-19 in Mexico caused
several disruptions in the supply chain of medicines.
Table 5. Key performance indicators of proposal solution
Available Inventory 682342.6764 pcs
Demand (Products Backlog) 0 pcs
Demand Placed (Products) by Customer 1061896.722 pcs
Demand Received (Products) 2483056.467 pcs
Fulfillment Received (Products On-time) 1050395.745 pcs
Fulfillment Received (Products) 1421159.745 pcs
Fulfillment Shipped (Orders) 393 Order
Peak Capacity 989528 pcs
Products Produced 1545502.421 pcs
Profit 3.52E+08 USD
Service Level by Products 0.989169401 Ratio
Total Cost 3715253.767 USD
Transportation Cost 3715253.767 USD
Traveled Distance 41252.88728 km
Figure 14. Several CDCs.
Figure 15. Current Supply Chain Network.
Figure 16. Supply Chain Network proposal.
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Figure 17. Service Level of Scenario I.
Figure 18. Available Inventory of Scenario I.
Figure 19. Lead-Time of Scenario I.
Figure 20. Service Level of Scenario II.
The solution methodology based on a simulation-
optimization approach, allows analyzing the impacts
Figure 21. Available Inventory of Scenario II.
Figure 22. Lead-Time of Scenario II.
Figure 23. Service Level of Scenario II Optimized.
Figure 24. Available Inventory of Scenario II Optimized.
of the dierent recovery strategies for a subsequent
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Designing a resilient supply chain: An approach to reduce drug shortages in epidemic outbreaks
Figure 25. Lead-Time of Scenario II Optimized.
epidemiological outbreak. Additionally, the proposed
approach allows enable a comprehensive view of the
supply network, as well as fast and ecient responses
to risky situations and changing.
Mexico has great health challenges, it is going
through a demographic and epidemiological transition
where chronic degenerative diseases predominate. The
public sector medicine supply chain in Mexico has sev-
eral structural problems related to the characteristics
of the Health System. In 2018, the percentage of a full
supply of medications represented 70%, historically
maintaining a percentage of prescriptions not filled,
which implies that the patient must expend out-of-
pocket expenses to acquire their medications or not take
Starting from this deficient structure of the medicine
supply chain in the public sector, facing an epidemic
such as the case of COVID-19 represents a very
important challenge for the Mexican health system. The
present pandemic has represented a significant increase
in the demand for public health services. As of April
28, 2020, a total of 77 thousand probable cases were
registered in the epidemiological surveillance system,
of which 16,752 cases were positive with COVID-19.
The crude mortality rate represented 93.3 deaths per
1000 inhabitants, and adults and older adults with some
chronic disease are mainly aected.
In this context, the need for a supply chain for
medicines and supplies that allows dealing with
external events such as a pandemic is evident. For
this, it is necessary to take into account innovative
concepts of supply chain management, simulation, risk
analysis, and optimization. Being able to have robust
and ecient designs will allow us to react quickly to
a contingency.
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... Simulation and optimization software integrates multiple functions such as simulation, design, and optimization. They have also been proven to be an effective tool for designing a resilient supply chain network [40,41]. Our paper enriches and extends the research on supply chain resilience by simulating the mask supply chain during the pandemic. ...
... Kaur, Pasricha and Kathuria [40] used AnyLogistix simulation software to find out the number of optimal distribution centers in the food supply chain of first-tier cities in India so as to improve the stability of the food supply chain during the epidemic. Taking the drug supply chain disruption in Mexico as an example, Lozano-Diez, Marmolejo-Saucedo and Aguilar [41] and Marmolejo-Saucedo et al. [54] developed the supply chain design model for a resilient supply network using AnyLogistix simulation software to reduce drug shortages in epidemic outbreaks. Prosser et al. [55] used Supply Chain Guru (Madagascar and Niger) and AnyLogistix (Guinea) modeling software to analyze and optimize the vaccine supply chain to provide decision-making guidance for improving vaccine availability in each country. ...
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The COVID-19 pandemic has caused severe consequences such as long-term disruptions and ripple effects on regional and global supply chains. In this paper, firstly, we design simulation models using AnyLogistix to investigate and predict the pandemic’s short-term and long-term disruptions on a medical mask supply chain. Then, the Green Field Analysis experiments are used to locate the backup facilities and optimize their inventory levels. Finally, risk analysis experiments are carried out to verify the resilience of the redesigned mask supply chain. Our major research findings include the following. First, when the pandemic spreads to the downstream of the supply chain, the duration of the downstream facilities disruption plays a critical role in the supply chain operation and performance. Second, adding backup facilities and optimizing their inventory levels are effective in responding to the pandemic. Overall, this paper provides insights for predicting the impacts of the pandemic on the medical mask supply chain. The results of this study can be used to redesign a medical mask supply chain to be more resilient and flexible.
... This has increased due to COVID-19. Moreover, decreasing production capacity and workforce unavailability may cause production planning problems according to Lozano-Diez et al. (2020); this is also in agreement with our study. Lozano-Diez et al. (2020) stated that these problems occurring in SCs are among the major threats to resilience and sustainability of a SC. ...
... Moreover, decreasing production capacity and workforce unavailability may cause production planning problems according to Lozano-Diez et al. (2020); this is also in agreement with our study. Lozano-Diez et al. (2020) stated that these problems occurring in SCs are among the major threats to resilience and sustainability of a SC. ...
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In rapidly changing business conditions, it has become extremely important to ensure the sustainability of supply chains and further improve the resiliency to those events, such as COVID-19, that can cause unexpected disruptions in the value supply chain. Although globalized supply chains have already been criticized for lack of control over sustainability and resilience of supply chain operations, these issues have become more prevalent in the uncertain environment driven by COVID-19. The use of emerging technologies such as blockchain, Industry 4.0 analytics model and artificial intelligence driven methods are aimed at increasing the sustainability and resilience of supply chains, especially in an uncertain environment. In this context, this research aims to identify the problematic areas encountered in building a resilient and sustainable supply chain in the pre-COVID-19 era and during COVID-19, and to offer solutions to those problematic areas tackled by an appropriate emerging technology. This research has been contextualized in the automotive industry; this industry has a complex supply chain structure and is one of the sectors most affected by COVID-19. Based on the findings, the most important problematic areas encountered in SSCM pre-COVID-19 are determined as supply chain traceability, demand planning and production management as well as purchasing process planning based on cause and effect groups. The most important issues to be addressed during COVID-19 are top management support, purchasing process planning and supply chain traceability, respectively.
... Several scholars have utilized simulation modelling to predict the COVID-19 effects and demonstrate the necessity for real-time visibility and structurally adaptable supply chains during a pandemic (Zhu and Krikke, 2020;Ivanov and Dolgui, 2021). Several studies have applied mathematical modelling techniques such as mixed-integer linear modeling (Lozano-Diez et al., 2020), game-theoretical modelling (Kargar et al., 2020), stochastic optimization (Mehrotra et al., 2020), etc. An integrated mathematical and simulation model was used by Lozano-Diez et al. (Lozano-Diez et al., 2020) to suggest the best ways for reducing the shortage of medicines. ...
... Several studies have applied mathematical modelling techniques such as mixed-integer linear modeling (Lozano-Diez et al., 2020), game-theoretical modelling (Kargar et al., 2020), stochastic optimization (Mehrotra et al., 2020), etc. An integrated mathematical and simulation model was used by Lozano-Diez et al. (Lozano-Diez et al., 2020) to suggest the best ways for reducing the shortage of medicines. ...
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The COVID-19 pandemic has caused a confounding collection of transportation, supply chains, and logistical disruptions, which needs to be well addressed by businesses and governments. During this pandemic, several researchers have concentrated on the sustainability and resilience of supply chains in various industry sectors. Nevertheless, the impacts of the pandemic on sustainability pillars, technological change and uncertainties, and resilience approaches in various sectors have not been clarified yet. More specifically, the agricultural biomass sector has experienced serious disruptions induced by the COVID-19. This paper aims to analyze and assess the agricultural biomass supply and production systems during the COVID-19 and their recovery in post-COVID-19. To the best of our knowledge, this is the first study to evaluate the economic, environmental, social, and technological change effects of the COVID-19 on Biomass Supply Chain resilience. Uncertainties of oil and palm energy demand, price, consumption, export, and production of leading producers and suppliers worldwide are analyzed considering the pre-COVID-19 and current COVID-19 period. It is then followed by recommendations for specific strategies, policies for the biomass industry, and general action plan to overcome the problems of resilience in medium, short, and long-term horizon plans. The findings from this study are valuable resources for the governments, biomass industry, and other stakeholders to provide cleaner post-pandemic energy production and supply and enhance the employees’ engagement.
... In response to the current vulnerability of the entire supply system, several resilience strategies have been suggested to mitigate the impacts of Covid-19 and to recover from the current pandemic (see, e.g. Paul and Chowdhury, 2020a;Taqi et al., 2020;De Silva et al., 2021;Lozano-Diez et al., 2020;Paul and Chowdhury, 2020b;Deaton and Deaton, 2020;Ivanov and Das, 2020;Remko, 2020, among others). The rapid spread of Covid-19 has also significantly affected sustainability, raising several environmental, economic, and social issues (Dente and Hashimoto, 2020;van Barneveld et al., 2020;Sarkis, 2020;Sharma et al., 2020;Queiroz et al., 2020;Rendana et al., 2021;Ibn-Mohammed et al., 2021). ...
The current Covid-19 pandemic is severely affecting public health and global economies. In this context, accurately predicting its evolution is essential for planning and providing resources effectively. This paper aims at capturing the dynamics of the positivity rate (PPR) of the novel coronavirus using the Heterogeneous Autoregressive (HAR) model. The use of this model is motivated by two main empirical features arising from the analysis of PPR time series: the changing long-run level and the persistent autocorrelation structure. Compared to the most frequently used Autoregressive Integrated Moving Average (ARIMA) models, the HAR is able to reproduce the strong persistence of the data by using components aggregated at different interval sizes, remaining parsimonious and easy to estimate. The relative merits of the proposed approach are assessed by performing a forecasting study on the Italian dataset. As a robustness check, the analysis of the positivity rate is also conducted by considering the case of the United States. The ability of the HAR-type models to predict the PPR at different horizons is evaluated through several loss functions, comparing the results with those generated by ARIMA models. The model confidence set is used to test the significance of differences in the predictive performances of the models under analysis. Our findings suggest that HAR-type models significantly outperform ARIMA specifications in terms of forecasting accuracy. We also find that the PPR could represent an important metric for monitoring the evolution of hospitalizations, as the peak of patients in intensive care units occurs within 12–16 days after the peak in the positivity rate. This can help governments in planning socio-economic and health policies in advance.
... e proposed mathematical model is based on the formulation developed to provide a problem of distributing mass consumer products presented in [32,33]; the methodology was later developed to attend other problematic as resilient supply chain model as we can see in [34]. e mathematical model is flexible and can be adapted to different problems with excellent results. ...
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Coronavirus disease 2019 (COVID-19) has been the most recent disease, with millions of deaths worldwide. Fortunately, vaccines have been developed to immunize the population. However, the distribution of the vaccine is also a significant challenge. Generally, each country defines its strategy to bring it closer to the target population, considering the adequate transport for their conservation, depending on the type of vaccines defined. In this work, a mathematical model is proposed for the distribution of different COVID-19 vaccines in Mexico. Our results suggest an efficient strategy to meet demand in a given period.
This project is the result of a volunteer program that took place in the Republic Guinea-Bissau (RGB) at the Paediatric Hospital. The Paediatric Hospital was working with the same technologic skills as Portugal in the 70’s years. There was no wired network between departments, no informatic system and all work was handmade. The physicians received incomplete clinical reports and, sometimes, with gross errors. There was no triage neither outpatient short list during the medical urgency period. The outpatients needed to wait for long time to get the analytical report and most time without meal or single bread. On the Clinical Analysis Laboratory, the biologic sample identification and the manual data report were lower changes to be credible and there was no final checklist. This paper describes the improvements made by the authors in the hospital logistical processes and in the development and implementation of an information system that was started in March 2018. These improvements were developed based on lean manufacturing principles, on methods and best practices for some referenced case studies fromAmerica, Saudi Arabia, Italy and England. As a result, the hospital reduced outpatient waiting time, improved Hospital, Laboratory and outpatient outcomes, increased confidence work for physicians and laboratory technics
Available studies and reports, as well as real-time experiences, attest to profound, extensive, long-lasting effects on the supply chain caused by the pandemic. It is thus paramount to rethink the supply chain for medication and health care supplies to build a more resilient and adaptable management process. Data obtained from the NHS portal monthly reports from January 2017 to August 2020 – indicates that at the hospital level the impact was felt the most on the scheduling of medical appointments and prescriptions. Two forecasting methods were selected for this study: Simple Linear Regression and Holt-Winters with the trend and additive seasonality. There was a change in the behavior of hospital patients in the first year of COVID-19 pandemics. This change was shown in two main indicators, the number of hospital consultations and medication expenses. This changed behavior resulted in a decrease in demand for scheduled hospital services, 1.9M less than would be expected under normal conditions, and a foreseeable increase of €432M in the consumption of medicines in the last quarter of 2020, €103M more than in the same period. from the previous year.
The integration of inventory and transportation operations is a challenging task in multi-echelon supply chain management. Uncertainties in customer demands can have serious consequences, such as inventory fluctuations and transportation changes. Policies of integrated inventory and transportation management aim to find a balance between supply and demand and can minimize the total operating cost for the entire supply chain. In this study, we propose a scenario-based economic model predictive control (EMPC) framework for integrated inventory and transportation management of multi-echelon supply chains with stochastic demands. The proposed scenario-based EMPC framework can provide real-time optimal operations for automated inventory and transportation management with a minimum operating cost and a guaranteed risk probability. As the number of scenarios is linked with the risk probability, we develop a design condition to choose the number of scenarios and ensure that optimal operations from the proposed framework can guarantee the desired risk probability. Finally, we present a case study of a three-echelon supply chain benchmark to demonstrate the effectiveness of the proposed EMPC framework and provide several comparison results to show its performance.
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The COVID-19 pandemic has wreaked havoc across supply chain (SC) operations worldwide. Specifically, decisions on the recovery planning are subject to multi-dimensional uncertainty stemming from singular and correlated disruptions in demand, supply, and production capacities. This is a new and understudied research area. In this study, we examine, SC recovery for high-demand items (e.g., hand sanitizer and face masks). We first developed a stochastic mathematical model to optimise recovery for a three-stage SC exposed to the multi-dimensional impacts of COVID-19 pandemic. This allows to generalize a novel problem setting with simultaneous demand, supply, and capacity uncertainty in a multi-stage SC recovery context. We then developed a chance-constrained programming approach and present in this article a new and enhanced multi-operator differential evolution variant-based solution approach to solve our model. With the optimisation, we sought to understand the impact of different recovery strategies on SC profitability as well as identify optimal recovery plans. Through extensive numerical experiments, we demonstrated capability towards efficiently solving both small- and large-scale SC recovery problems. We tested, evaluated, and analyzed different recovery strategies, scenarios, and problem scales to validate our approach. Ultimately, the study provides a useful tool to optimise reactive adaptation strategies related to how and when SC recovery operations should be deployed during a pandemic. This study contributes to literature through development of a unique problem setting with multi-dimensional uncertainty impacts for SC recovery, as well as an efficient solution approach for solution of both small- and large-scale SC recovery problems. Relevant decision-makers can use the findings of this research to select the most efficient SC recovery plan under pandemic conditions and to determine the timing of its deployment.
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The outbreak of an epidemic disease may pose significant treats to human beings and may further lead to a global crisis. In order to control the spread of an epidemic, the effective management of rapidly increased medical waste through establishing a temporary reverse logistics system is of vital importance. However, no research has been conducted with the focus on the design of an epidemic reverse logistics network for dealing with medical waste during epidemic outbreaks, which, if improperly treated, may accelerate disease spread and pose a significant risk for both medical staffs and patients. Therefore, this paper proposes a novel multi-objective multi-period mixed integer program for reverse logistics network design in epidemic outbreaks, which aims at determining the best locations of temporary facilities and the transportation strategies for effective management of the exponentially increased medical waste within a very short period. The application of the model is illustrated with a case study based on the outbreak of the coronavirus disease 2019 (COVID-19) in Wuhan, China. Even though the uncertainty of the future COVID-19 spread tendency is very high at the time of this research, several general policy recommendations can still be obtained based on computational experiments and quantitative analyses. Among other insights, the results suggest installing temporary incinerators may be an effective solution for managing the tremendous increase of medical waste during the COVID-19 outbreak in Wuhan, but the location selection of these temporary incinerators is of significant importance. Due to the limitation on available data and knowledge at present stage, more real-world information are needed to assess the effectiveness of the current solution.
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A method to solve the design of a distribution network for bottled drinks company is introduced. The distribution network proposed includes three stages: manufacturing centers, consolidation centers using cross-docking, and distribution centers. The problem is formulated using a mixed-integer programming model in the deterministic and single period contexts. Because the problem considers several elements in each stage, a direct solution is very complicated. For medium-to-large instances the problem falls into large scale. Based on that, a primal-dual decomposition known as cross decomposition is proposed in this paper. This approach allows exploring simultaneously the primal and dual subproblems of the original problem. A comparison of the direct solution with a mixed-integer lineal programming solver versus the cross decomposition is shown for several randomly generated instances. Results show the good performance of the method proposed.
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Healthcare and disaster supply chain have becoming a more important and popular research issues recently. However, only a few of paper is known about the current issues both healthcare and disaster supply chain especially in natural disaster case. This paper is a preliminary report of a research on healthcare and disaster supply chain. The paper intends to review and analyse several papers on above topic published during the last ten years. Published papers on healthcare and disaster supply chain research from 2005 and 2014 were classified into three main themes: (1) healthcare supply chain, (2) disaster supply chain and (3) healthcare supply chain in natural disaster. The topic issues in each main themes include operational management, information technology, inventory and control management, strategic management, and service management. Besides, the type of research methods contain empirical study, case study, modelling and simulation, literature review, and conceptual theory. Result of the review will provide the basis for the direction of future research in these three themes.
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Outbreaks of epidemics account for a great number of deaths. Communicable or infectious diseases are also a major cause of mortality in the aftermath of natural or man-made disasters. Effective control of an epidemic outbreak calls for a rapid response. Available resources such as essential medical supplies and well-trained personnel need to be deployed rapidly and to be managed in conjunction with available information and financial resources in order to contain the epidemic before it reaches uncontrollable or disastrous proportions. Therefore, the establishment and management of an emergency supply chain during the containment effort are of paramount importance. This paper focuses on defining the role of logistics operations and their management that may assist the control of epidemic outbreaks, critically reviewing existing literature and pinpointing gaps. Through the analysis of the selected literature a series of insights are derived and several future research directions are proposed. In conclusion, this paper provides both academics and practitioners with an overview of literature on epidemics control and logistics operations aiming at stimulating further interest in the area of epidemics control supply chain management.
When a public health emergency, such as an anthrax attack, happens in many areas, it is necessary to deploy the medical supplies to the affected people quickly. In this condition, the emergency logistics network based on integrated supply chain, which is made up of the points of dispensing, emergency centers, and replenishment sources, is proposed to response to the emergency. In order to compare its effect, the traditional emergency logistics network is introduced. Then multi-objective programming models for the two kinds of networks under many scenarios about the anthrax attack are constructed. From the practical example, we can draw up that: the cost of the integrated mode is always lower than the traditional mode. The transportation duration of the integrated mode is higher than the traditional mode when the treatment rate is 0.4. However, the integrated mode is lower than the traditional mode as the treatment rate increases.
To optimize the process of materials distribution in anti-bioterrorism system and improve the emergency relief timeliness, emergency materials distribution problem in system of anti-bioterrorism was constructed to be a multiple traveling salesman problem (MTSP) in paper the authors have done before. In that paper, knowledge of graph theory was used to transform the MTSP to be a TSP, then such TSP route was analyzed and proved to be the optimal Hamilton route theoretically. Besides, a new hybrid genetic algorithm was designed for solving the problem. However, only length of the route was considered as the objective function, while time windows, another much more important factor was neglected. In this paper, the MTSP with time windows is studied, and the best equilibrium solution of emergency materials distribution is obtained via numerical simulation. Moreover, combine with the SIR epidemic model, relationship between the parameters and the results are discussed. The research results show that the best emergency materials distribution scheme can be found by the method proposed in this paper effectively, which have a certain guiding significance for the actual emergency rescue work.
In the last 20 years, Emergency Management has received increasing attention from the scientific community. Meanwhile, the study of relief distribution networks has become one of the most popular topics within the Emergency Management field. In fact, the number and variety of contributions devoted to the design or the management of relief distribution networks has exploded in the recent years, motivating the need for a structured and systematic analysis of the works on this specific topic. To this end, this paper presents a systematic review of contributions on relief distribution networks in response to disasters. Through a systematic and scientific methodology, it gathers and consolidates the published research works in a transparent and objective way. It pursues three goals. First, to conduct an up-to-date survey of the research in relief distribution networks focusing on the logistics aspects of the problem, which despite the number of previous reviews has been overlooked in the past. Second, to highlight the trends and the most promising challenges in the modeling and resolution approaches and, finally, to identify future research perspectives that need to be explored.
To find the efficient logistics strategy for the anthrax attack, the anthrax progression model and emergency logistics model under the traditional and collaboration modes are constructed based on the System Dynamics (SD) approach. Then, a combination mode that integrates the two modes is proposed. Through the simulation, we analysed some factors which can affect the rescue effect, and we studied which mode is the best logistics strategy response to the anthrax attacks. This study provides insights for the decision-makers who cope with the emergency events, such as the bioterrorists attacks.
Demand for emergency resources is usually uncertain and varies quickly in anti-bioterrorism system. Besides, emergency resources which had been allocated to the epidemic areas in the early rescue cycle will affect the demand later. In this article, an integrated and dynamic optimisation model with time-varying demand based on the epidemic diffusion rule is constructed. The heuristic algorithm coupled with the MATLAB mathematical programming solver is adopted to solve the optimisation model. In what follows, the application of the optimisation model as well as a short sensitivity analysis of the key parameters in the time-varying demand forecast model is presented. The results show that both the model and the solution algorithm are useful in practice, and both objectives of inventory level and emergency rescue cost can be controlled effectively. Thus, it can provide some guidelines for decision makers when coping with emergency rescue problem with uncertain demand, and offers an excellent reference when issues pertain to bioterrorism.
Quick and accurate response to the relief demand is vital to an emergency logistics network under disaster spreading. In this paper, we first characterize the disaster spreading process to forecast the time-varying relief demand, by using an epidemic model to analyze the relationships among three groups of affected individuals. Then, a new three-tiered emergency logistics network equilibrium model is formulated to satisfy the predicted urgent demand with the least relief cost, in particular the time cost. We perform numerical simulation to demonstrate the effectiveness of our model, and discuss the impact of the important parameters.