Sourcing Decisions for Goods with Potentially Imperfect Quality under
the Presence of Supply Disruption
Laura Wagner and Mustafa C¸ agri G¨urb¨uz
MIT-Zaragoza International Logistics Program, Zaragoza Logistics Center, University of Zaragoza,
Ed. Nayade 5 C/Bari 55, Plaza, Zaragoza, Spain
1 STAGE OF THE RESEARCH
Research questions set and expected outcome
identified,
Methodology determined (stochastic Dynamic
Programming with periodic control and numeri-
cal analysis),
Literature review mostly completed, positioning
of the papers done,
Preliminary research on numerical analysis and
determination of ranges for input parameters
2 OUTLINE OF OBJECTIVES
In 2012, counterfeited versions of Avastin– an in-
jectable medicine used to treat cancer– had been (un-
intentionally) administered to patients in at least 19
clinics, hospitals and pharmacies in the US, poten-
tially harming patients due to a lack of the active in-
gredient, bevacizumab. Although the Food and Drug
administration (FDA) indicated that the supply of that
particular drug was adequate to meet demand, there is
an ongoing shortage of some cancer drugs that could
increase the incentive of counterfeiters to infiltrate
falsified products in legal supply chains (Hellerman,
2012). These types of incidences are quite recurrent.
According to a survey conducted by the Pharmaceu-
tical Security institute (PSI) close to 2000 counterfeit
incidents were reported in 2012 alone, involving some
100 countries with 523 differentpharmaceutical prod-
ucts in a wide array of therapeutic and organic system
categories (PSI, 2012).
The aim of this paper is to provide further insights
into the optimal periodic reviewreplenishment and al-
location policy of a dispenser having access to a pool
of alternative wholesalers who differ in their quality
protection efforts, delivery reliability and costs. In
particular, we are interested in the following research
questions:
What is the optimal replenishment and allocation
strategy when supply sources differ in their cost,
quality protection and reliability?
Under which circumstances would a dispenser
procure from sources where quality cannot be as-
certained?
Is multi-sourcing a valuable strategy against re-
current shortages at the expense of potentially re-
ceiving inferior product quality?
What is the impact of (post-sales) detection abil-
ity and timing of inferior quality goods on the op-
timal allocation policy?
What is the value of implementing a track-and-
trace system for the dispenser?
The analysis aims firstly to inform the policy makers
under which conditions medicines are sourced from
doubtful providers, and secondly, it will also provide
a decision support tool to dispensers on their willing-
ness to invest in a track-and-trace system.
3 RESEARCH PROBLEM
Complex pharmaceutical supply chains enable coun-
terfeiters to push fake products through the distribu-
tion channels. Although the prevalence of counter-
feits is not exactly known, FDA estimates that ap-
proximately 1% of all medicines consumed in de-
veloped countries and up to 30% in developing /
under-developed countries are fake medicines, caus-
ing grave social and financial damages to the societies
(WHO, 2010).
Counterfeit goods mimic genuine manufacturers’
original products in looks and packaging, however,
they possess inferior product attributes potentially
leading to resistance and/or adverse effects when (un-
intentionally) consumed. Recent examples of coun-
terfeited goods that garnered significant media at-
tention is the case of Heparin a blood-thinner pro-
vided by Baxter International that caused unexpected
10
Wagner L. and Gürbüz M..
Sourcing Decisions for Goods with Potentially Imperfect Quality under the Presence of Supply Disruption.
Copyright
c
2014 SCITEPRESS (Science and Technology Publications, Lda.)
allergic reaction in dialysis patients in 2007 as re-
ported by FDA. Another example is that of cough
medicine containing toxic syrup which was unknow-
ingly bought and dispatched by the Panamanian pub-
lic health sector, resulting in more than 78 deaths.
Manufactured in China, this medicine passed through
brokers and wholesalers in Asia and Europe and fi-
nally reached end-consumers in Latin-America (Pew-
Health-Group, 2011).
Even though the distribution channels are dominated
by few large wholesalers handling most of the drugs,
thousands of smaller distributors exist who buy ex-
cess products, repackage and sell them amongst each
other. In times of shortages (unavailability of the gen-
uine manufacturer), these distributors are the prime
source for downstream buyers, providing the essen-
tial drugs at inflated prices. The scattered landscape,
combined with high margins and the lack of trans-
parency invite fake producers to mingle their falsified
products with the original ones, subsequently harm-
ing end-consumers if these counterfeits are not de-
tected beforehand. As technology advances to detect
these illegal products, fake producers respond quickly
by using sophisticated methods to pass inspections,
thus rendering new detection methods ineffective.
In addition to random quality checks performed by
local health authorities such as FDA (Food and Drug
Administration) in the US, the health care soci-
ety has allocated significant resources for consumer
awareness programs to train medical personnel and
end-consumers about the perils associated with fake
medicines, including identification of falsified prod-
ucts.
The end-consumer efforts to detect and protect them-
selves from inferior products, however, rely heavily
on subjective measures such as perceived changes in
smell, taste or packaging, hence these methods are at
best noisy signals for inferior quality. Likewise, med-
ical personnel trained to observe lack of drug effec-
tiveness (LODE) in patients might suspect counterfeit
products as a cause, when informed about this poten-
tial harm.
To combat against counterfeiting the pharmaceuti-
cal industry recently discussed the implementation of
track-and-trace systems to increase end-to-end sup-
ply chain visibility. This method, once it is prevalent
world-wide, will allow the purchaser to gain informa-
tion about each drug’s source and history.
4 STATE OF THE ART
Our work is closely related to the procurement
models with dual/multiple sourcing under supply
disruption, random yield models, models with
product returns where the quality of the product is
questionable, and also models analyzing the impact
of counterfeit goods on supply chains.
Inferior quality products, if detected at the source,
may lead to low yields, high lead times for making
the product available to end-consumer, and/or pro-
curement disruption. Mitigation strategies against
these supply uncertainties have gained increasing
attention from practitioners and researchers alike.
One of the first papers analyzing the advantages of
dual sourcing in the context of supply disruption are
provided by (Parlar and Perry, 1996) and (G¨urler and
Parlar, 1997). Both authors consider a firm that can
allocate its replenishment among two suppliers with
identical costs and with infinite capacity to serve
deterministic demand. (Tomlin, 2006), extends this
research stream by analyzing a setting where a firm
can procure from one unreliable low cost supplier
and/or one costly back-up supplier to serve a random
amount of end-consumers. In a setting where the
back-up supplier may offer volume flexibility, the
author characterizes the conditions under which
single sourcing, dual sourcing or volume flexibility is
optimal.
Similarly, multi-sourcing has been shown beneficial
in supply uncertainties such as production yield and
lead-time. Examples of authors analyzing the benefit
of such mitigation strategies are (Veeraraghavan
and Scheller-Wolf, 2008) and(Federgruen and Yang,
2011).
However, in case the detection process is insuffi-
cient or imperfect, defective products might reach
end-consumers. Depending on the physical/financial
harm these products cause, such situations may
not only lead to losing customers forever, but also
to significant penalties on the immediate sellers
and/or on other upstream providers. Firms that offer
warranties for such products share the risk of these
post-consumption failures with the end-consumers.
As warranty models constitute an extensive body
of literature, we reviewed only the most relevant
ones. (Dai et al., 2012) explores the trade-off
between an extended warranty protection period
to boost sales and the associated warranty costs
in case of poor product quality in a single period
decentralized supply chain. The authors determine
under which conditions quality improvement and
warranty extensions should be provided. (Huang
et al., 2008) explore periodic inventory systems
with replacement warranties. The authors consider
stochasticity from two sources, namely from demand
and product returns. Under these conditions the
authors characterized the system as a warranty
SourcingDecisionsforGoodswithPotentiallyImperfectQualityunderthePresenceofSupplyDisruption
11
length-dependent threshold policy. An overview of
this literature stream is provided by (Murthy and
Djamaludin, 2002).
This paper concentrates around a particular quality
issue and its mitigation strategies, namely the in-
creasing presence of counterfeit products in complex
supply chains, with imperfect post-consumption
detection.
Recently, some articles have emerged that analyze the
potential harm of counterfeit trading. The research
stream can be broadly classified into two categories,
namely deceptive and non-deceptive counterfeiting.
While the latter is concerned with the existence of
gray markets in which consumers deliberately buy
goods from illegal sources, the former category
is composed of goods where the inferior quality
counterparts cannot be distinguished by consumers a-
priory. Dating back to 1988, (Grossman and Shapiro,
1988) showed that non-deceptive counterfeits can
contribute positively to consumer welfare assuming
that the illicit market offers inferior products at
a lower price. This however is unlikely the case
for deceptive goods, such as for pharmaceutical
counterfeiting, as consumers do not deliberately buy
inferior quality goods as is the case for non-deceptive
goods. Since consumers can not distinguish the
genuine product from the fake ones price discounts
are usually not transfered.
(Soo-Haeng et al., 2011) addressed these dis-
tinct supply distribution systems in a game-theoretic
setting and discussed the sensitivity of each counter-
feit system with respect to various anti-counterfeit
actions. Similar analyses have been provided by
(Zhang et al., 2012), (Lybecker, 2007) and (Zhang,
2011). A literature review composed of empirical
and modeling approaches discussing counterfeiting
is provided by (Staake et al., 2009). While the
aforementioned papers all propose a game-theoretic
model in which the decision maker is deliberately
choosing its quality product mix, they neglect the
operational decisions (e.g. inventory decisions).
(Liu et al., 2004) take this operational view point
by studying a one-period newsvendor model. The
authors assume that the buyer deliberately chooses
the quality based on cost margins, while random
checks hinder the decision-maker from acquiring
inferior quality products.
5 METHODOLOGY
In an environment where numerous entities are in-
volved in distributing and handling medicines and
medical shortages are recurrent, security breaches ex-
ists. This section analyses the optimal periodic review
replenishment and sourcing policy from the perspec-
tive of a dispenser having access to multiple sources
that differ in their cost, disruption and quality reli-
ability. In particular, we discuss conditions under
which dispensers might be compelled to procure the
needed drug from potential inferior sources as a miti-
gation strategy against supply uncertainties. In a set-
ting where quality can be at best revealed after end-
consumers’consumption– potentially leading to med-
ication errors–fake drugs not only result in social tolls
for individuals but also in financial costs including
higher operational expenses and/or law suits against
dispensers. We proceed by quantifying the informa-
tion gain obtained by the dispenser when track-and-
trace systems are implemented. The later analysis
aims to inform the health care society to set appropri-
ate incentives in order to fasten the adaptation of such
systems that can protect patients from the perversive
risk of counterfeit products.
We use the following mathematical notation in
this paper: [x]
+
= max{x, 0}, [x]
= min{x, 0}.
Further, we let x = (x
0
, x
1
, . . . , x
n
) denote a vec-
tor and x =
n
i=0
x
i
refers to the sum of its
components, unless otherwise indicated. x
i
=
(x
0
, x
1
, . . . , x
i1
, x
i+1
, . . . , x
n
) is used to indicate the
vector of components other than i.
5.1 Model
We concentrate our study on the optimal periodic re-
plenishment policy of a single product from the per-
spective of a cost minimizing dispenser (e.g. hos-
pitals/pharmacies) serving a random number of ho-
mogeneous end-consumers over a finite horizon with
length denoted by T. We assume that the poten-
tial number of end-consumer to be treated is large
and the requests are independent across different pe-
riods, which essentially allows us to represent the
end-consumers’ request by a random variable D with
probability distribution f
D
(ξ). The dispenser has ac-
cess to N sources, namely a genuine manufacturerand
various wholesalers. We represent the vector of all
suppliers by W = (0, 1, 2, . . . , N 1), where j W
denotes the j’th wholesaler and j = 0 is associated
with the genuine manufacturer.
Although the genuine manufacturer certainly sells
only high quality products, it also randomly an-
nounces shortages. When this happens, the genuine
manufacturer is unavailable, leaving the dispenser
with the option to operationally insure supply through
the remaining N 1 wholesalers. We will refer to
such a situation as a “down” period with procurement
ICORES2014-DoctoralConsortium
12
option W
0
= (1, 2, . . . , N 1) and indicate the avail-
ability of the genuine manufacturer by an “up” pe-
riod (with sourcing option W). We model the gen-
uine manufacturer’s availability as being in one of the
two states, which we denote by δ {0, 1}: either he
is available (in an “up” state δ = 0) with some prob-
ability π or not (i.e. in a “down” state δ = 1) with
probability (1 π), where π is the parameter of a
Bernoulli distribution known before a sourcing deci-
sion is made.
These wholesalers, although available at all times
with ample capacity, differ in their safety efforts,
hence potentially carry inferior quality products. That
is, wholesalers might have procured a sufficient
amount of goods from genuine manufacturers prior to
a shortage announcement to profit from the increased
margin that can be obtained when supply is scarce
and/or use non-secure channels risking fake products
to enter.
In any case, when procuring from wholesaler j
a random proportion Θ
j
[0, 1] of the procurement
quantity will be of inferior quality with mean β
j
for
all j W. The probability distribution g
j
(θ) is as-
sumed to be time invariant and independent of the or-
der quantity. This assumption is consistent with pro-
portional random yield models. For notational rea-
sons, we indicate j = 1 as the wholesaler with the low-
est mean of delivering inferior products and ranking
the remaining ones accordingly from lowest to high-
est. That is β = (β
0
, β
1
, . . . β
j
, . . . , β
N1
) represents
an ordered vector of inferior quality procurement as-
sumed to be time invariant with the genuine manu-
facturers’ expected quality unreliability normalized to
zero (β
0
= 0) such that β
0
< β
1
, < β
2
< . . . , < β
N1
.
The procurement cost of each source is denoted by
c
j
for all j W. Although it is possible that some
sources might offer the desired product for a lower
price than the genuine manufacturer itself, we assume
that the cost of procuring from the genuine manufac-
turer j = 0 is at most the cost of any other source
(c
0
c
j
j W
0
). This allows us to approx-
imately capture the steep price increase offered by
wholesalers when shortages persist and ensures that
the genuine manufacturer, when available, will be se-
lected as one of the primary sources.
It is questionable whether prices offered by whole-
salers can signal inferior product quality in times of
shortages. For instance a survey conducted by (Bate
et al., 2012) suggests that less protected sources of-
fer almost no price-discount relative to the original
genuine manufacturer. According to the authors, non-
price signals such as chain affiliation of the whole-
salers or pharmacies may lead to more accurate re-
sults when assessing drug quality, although do not en-
sure either high quality procurement with certainty.
This findings suggests that the procurement prices c
j
in times of shortages may be arbitrary with respect
to the perceived amount of counterfeits a wholesaler
may carry, while the perceived amount of acquiring
falsified versions from wholesaler j, may be formed
by the particular dispenser based on other factors.
Assumption 1a: In times of genuine manufacturers’
shortage announcement metrics other than costs form
the the dispenser’s belief about the sources protection
capability: c
j
for each j W
0
is arbitrary relative to
other sources’ procurement costs.
This assumption states, that a price discount from a
source is not necessarilya signal for potential lower
quality goods.
However, due to the complexity of the pharmaceuti-
cal supply chain, it might be difficult or almost im-
possible for a dispenser to perform a thorough qual-
ity assessment of the source, especially in times when
medications are needed instantaneously. In this case,
costs might still be used to assess the quality of the
source.
Assumption 1b: In times of genuine manufacturers’
shortage announcement, the dispensers’ belief about
the wholesalers’ protection effort is based on the pro-
curementcosts: c
1
> c
2
> . . . > c
N1
This assumption
on the other hand states, that when for instance an of-
fer is belowthe market value, the dispenser might sus-
pect a higher percentage of inferior goods.
Therefore, we will separately analyze both, a cost and
a non cost metric to assess the perceived protection
efforts of wholesalers:
The dispenser, in any period t (0, . . . T), first ob-
serves the state of the genuine manufacturer δ used
to decide from whom to procure the desired quan-
tity, to be able to serve the random number of end-
consumers. We assume that the lead-time is zero, that
is, goods ordered in period t arrive in the same pe-
riod and can be used to meet end-consumers demand
within that period while unmet demand is lost. Fur-
ther, let the on-hand inventory in period t be indicated
by x
t
= (x
0,t
, x
1,t
, . . . , x
N1,t
) with x
j,t
representing the
amount of products in stock from supplier j. We fur-
ther denote with x
t
the total on-hand inventory in pe-
riod t before the receipt of current orders. Likewise,
let y
t
= (y
0,t
, y
1,t
, . . . , y
N1,t
) represent the vector of
orderings in period t and let z
t
= (z
0,t
, z
1,t
, . . . , z
N1,t
)
account for the amount of inventory after ordering be-
fore demand realizes.
The total on-hand inventory after ordering, z
t
, in pe-
riod t is given by:
z
t
= x
t
+ y
t
=
N1
j=0
x
j,t
+
N1
j=0
y
j,t
(1)
SourcingDecisionsforGoodswithPotentiallyImperfectQualityunderthePresenceofSupplyDisruption
13
In addition, we assume that the dispenser will deplete
the drugs with decreasing order of perceived quality
reliability. For instance, the dispenser will first use the
stock from the wholesaler, perceived to be the most
quality-protected one and in case of insufficient stock
he will proceed with depleting inventory from whole-
salers’ j = 1, 2, . . . , N 1 procurements. The inven-
tory dynamics x
t+1
can be described as follows:
x
0,t+1
=(z
0,t
D)
+
x
j,t+1
=(z
j,t
(D
j1
i=0
z
i,t
)
+
)
+
j = 1, . . . , N 1
(2)
That is, all demand not filled by stock from presum-
ably higher quality protected sources will be filled by
lower ones given its instock availability.
We denote the per period per unit inventory hold-
ing cost incurredthroughpurchases from wholesaler j
by h
j
and assume that unmet demand is lost, resulting
in a lost sales cost of p. In the situation of essential
drugs this per person lost sales cost can be substan-
tial, especially when the interruption of medical treat-
ments may result in long lasting consequences such
as is the case of antivirals used for HIV patients. Un-
less strategically interrupted treatments are prescribed
by medical professionals, the non-adherence to daily
dosages of antivirals may lead to patients developing
resistance against the drug in use, and in turn may re-
sult in high switching costs from first to second line
treatments (Chesney MA, 1999).
Model without Track-and-Trace System
In this section we analyze the dispenser’s optimal pro-
curement and allocation strategy under the circum-
stances of not having a track-and-trace system im-
plemented as is the case of todays’ pharmaceutical
distribution chains. The dispenser in this situation is
unable to discover counterfeits before administering
fake drugs to patients, hence relies on the feedback
from patients and medical personnel.
Administering inferior quality goods to patients po-
tentially render treatments ineffective and may cause
medication errors. In a recent study conducted by
McKinsey, (Ebel et al., 2013), medication errors in-
duced by dispensers can have several roots, including
unintentional fake drug prescription. It is estimated
that these errors occur in 10 20% of all inpatient
hospital admissions, one third of which result in ad-
verse drug events (ADE). Each of these ADE’s not
only result in high social tolls but also in direct finan-
cial costs estimated to amount to USD 4000 to 8000
per person in the US.
For our study we consider only the measurable costs
associated directly to the procurement of counterfeits
by the dispenser. Though we are aware that the true
social and financial harm induced by fake products is
far higher, estimating these global economic and so-
cial costs of drug-counterfeiting is a challenge to the
health community. These costs include but are not
only limited to tax related costs, reputation damage,
lost sales, operational expenses, quality assurance and
social harm.
In addition to these estimation difficulties, counterfeit
drugs, even when consumed, can go undetected by
individuals due to the subjective measures of coun-
terfeits like changes in smell, taste or packages, lack
of drug effectiveness (LODE) and/or adverse effects.
These medication errors are assumed to occur with
one period time-lag after prescription of the drug.
Due to these noisy detection principles associated
with counterfeits patients and medical personal might
not always be aware of the causes associated with
medication errors. We will model this situation by
assuming that with some known probability γ, end-
consumers having received a fake product will suffer
from a medication error caused by counterfeit pre-
scription. Each harmed end-consumer that returns
due to fake drug consumption will incur a per patient
cost denoted by R. This cost can represent an increase
in operational health cost associated with medication
errors such as switching to an alternative drug, fur-
ther examinations and/or costs associated to law-sues.
Since this counterfeit related cost only accounts for
the proportion which is internalized by the dispenser,
it is an underestimate of the true social cost. For math-
ematical clarity we additionally assume that individu-
als having received a high quality drug will not suffer
medication errors or, in other words, medication er-
rors arising from non-procurement related causes are
normalized to zero.
The potential number of end-consumers returning due
to medication errors resulting from wholesaler j in
period t is denoted by s
j,t
and the dynamics are de-
fined as follows:
s
j,t+1
=Θ
j
[min{(ξ
j1
i=0
z
i,t
)
+
, z
j,t
}] j W
0
(3)
Where s
j,t+1
represents the potential medication
errors induced by supplier j’th procurement. It is
composed of demand served from wholesaler js
procurement when the inventory from more quality
reliable suppliers was insufficient, adjusted by the
probability or administering fake products. In other
words, the potential number of patients’ suspecting
counterfeit in the next period is determined by the
sales of goods from supplier j’th inventory in period t
ICORES2014-DoctoralConsortium
14
and the random fraction of carrying inferior products.
Further, s
t
represents the total potential medical
errors arising from inferior product procurement
(s
t
=
N1
j=1
s
j,t
).
In addition we assume throughout this study
that fixed costs are negligible, a situation that might
be relaxed in the extension.
Then, the immediate expected costs can be ex-
pressed as:
N1
j=0
c
j
(z
j,t
x
j,t
) + Rγs
t
+
N1
j=0
h
j
E[(z
j,t
(D
j1
i=0
z
i,t
)
+
)
+
]
+ pE[(D z
t
)
+
] (4)
Where the holding cost component is derived from
applying the previously explained depletion rule used
by the dispenser (provide the drugs in decreasing
order of perceived quality reliability).
The cost minimizing dispenser incurs the total
purchasing cost from all available suppliers, cost as-
sociated with suspected medication errors associated
with end-consumers return, holding costs and lost
sales costs.
For mathematical purposes we define g
t
(z
t
, s
t
) as the
immediate expected costs plus the current on hand
inventory before ordering:
g
t
(z
t
, s
t
)
=
N1
j=0
c
j
(z
j,t
) + Rγs
t
+
N1
j=0
h
j
E[(z
j,t
(D
j1
i=0
z
i,t
)
+
)
+
]
+ pE[(D z
t
)
+
] (5)
The dispenser’s objective is to minimize the expected
cost over T periods. Hence, the Bellman equations
for “up” (δ = 0) and “down” (δ = 1) periods are given
by:
V
t
(x, s, 0) = min
z
j,t
jW
g
t
(z
t
, s
t
)
+ E[V
t+1
(x
t+1
, s
t+1
, δ)]
N1
j=0
c
j
x
j,t
(6)
V
t
(x, s, 1) = min
z
j,t
jW
0
g
t
(z
t
, s
t
)
+ E[V
t+1
(x
t+1
, s
t+1
, δ)]
N1
j=0
c
j
x
j,t
(7)
s.t. z
0,t
x
0,t
. . .
z
j,t
x
j,t
. . .
z
N1,t
x
N1,t
For convenience, we assume that in period 0 the gen-
uine manufacturer is available V
0
(x, s, 0) with initial
inventory and potential future medication errors given
by x
0
= 0 and s
0
= 0. Further, the terminal value func-
tion is represented by
V
T+1
(x, s, δ)
= RγE[s
T+1
] = Rγ
N1
j=0
E[Θ
j
min{(D
j1
i=0
z
i,t
)
+
, z
j,t
}]
(8)
That is, we extend the terminal value function
to account for medication errors resulting from con-
sumption of fake products in period T.
5.1.1 Model with Track-and-Trace System in
Place
Opposed to the before-hand mentioned post-
consumption counterfeit revealing method we now
focus on the optimal periodic replenishment and
allocation strategy when a track-and-trace system is
in place. That is, instead of suspecting counterfeit
post-consumption, the dispenser now is capable of
filtering out quantities from doubtful origins prior
to circulating the products to end-consumer. Since
the pharmaceutical supply chain is scattered, with
most suppliers and wholesalers trading medications
worldwide, product liabilities is rarely enforceable
in todays inconsistent legal systems. Even if supply
chain members and/or government authorities are
able to locate the counterfeit source it is unlikely that
SourcingDecisionsforGoodswithPotentiallyImperfectQualityunderthePresenceofSupplyDisruption
15
members involved reimburse downstream members.
We will hence assume that track-and-trace systems
will be implemented without wholesalers being held
liable for selling inferior products. We define Ξ
j
as
the random fraction of goods procured from supplier
j which were genuine with probability distribution
h
j
(·): Further we approximate the effect of this new
technology implementation by assuming that the
dispenser will perform full-inspections of incoming
goods and in case a suspicious good is found it will
be subsequently discarded. The immediate cost
function for such a system can be written as:
˜g
t
(y
t
, x
t
) =
N1
j=0
c
j
(y
j,t
)
+
N1
j=0
h
j
E
D,Ξ
j
[(x
j,t
+ Ξ
j
y
j,t
(D
j1
i=0
x
i,t
+ Ξ
i
y
i,t
)
+
)
+
]
+ pE
D,Ξ
j
[(D
N1
j=0
x
j,t
+ Ξ
j
y
j,t
)
+
] (9)
The dispenser will pay the procurement cost to each
wholesaler j, perform a check of the source and in-
cur holding cost for the random fraction Ξ of those
units which are not detected as (and, therefore, are
not) inferior. Then the dispensers’ cost minimization
problem is given by:
˜
V
t
(x, 0) = min
y
j,t
0 jW
˜g
t
(y
t
, x
t
) + E[
˜
V
t+1
(x
t+1
, δ)]
(10)
˜
V
t
(x, 1) = min
y
j,t
0 jW
0
˜g
t
(z
t
, x
t
) + E[
˜
V
t+1
(x
t+1
, δ)]
(11)
With terminal cost function
˜
V
T+1
(x, δ) = 0 (12)
6 EXPECTED OUTCOME
Recurrent shortages of essential drugs by themselves
undermine the effective delivery of medicines due
to steep price increases that persist when demand
exceeds supply. Counterfeiters using such supply-
constrained environments to infiltrate their drugs ag-
gravate this situation even more.
This Ph.D. project aims to capture the intricate issues
affecting the decision of medicine dispensers when
facing observable and perceived uncertainties origi-
nated from supply disruptions, demand variability and
product quality. The problem is mathematically rich
and, at the same time, can provide important insights
on how to approach the implementation of quality de-
tection mechanisms such as track-and-trace systems,
which in turn can have substantial impact on the ef-
fective delivery of public health.
Upon completion of this project, we expect to have
achieved the following:
Develop a dynamic programming model for the
dispenser’s problem considering the existence of
uncertainties from three different sources, ex-
tending the literature stream on stochastic multi-
sourcing/multi-period models.
Implement the model within a decision support
tool that can be of use to pharmaceutical supply
chain stakeholders in assessing their optimal risk
mitigation strategies.
Generate insights for public health officials and
pharmaceutical manufacturers about the incen-
tives of supply chain partners for adopting new
technologies to increase visibility and combat
against counterfeits, as well as the role of supplier
unavailability in inducing the procurement of po-
tentially inferior-quality drugs.
At the current stage of this work, and using the mod-
els described in the previous sections, we are starting
to gain some insights and develop some conjectures
on how these trade-offs develop for pharmaceutical
dispensers. Specifically, regarding the procurementof
inferior quality products, we believe that at least when
costs form the perception of inferior quality procure-
ment (e.g. c
1
> c
2
> . . . > c
N1
) a global optimal
sourcing and allocation strategy can be found. This
allocation may depend on the marginal differences of
procurement costs, holding costs, perceived inferior
quality and the return costs.
Second, our results seem to indicate that the less
likely patients and medical personnel raise suspicion
(γ 0), the more these inferior products will go un-
noticed and become used as perfect substitutes, re-
ducing the impact of improving visibility. Also, the
value of the track-and-trace system is given by the dif-
ference of random yield and circulation; however, if
γ is small then such a track-and-trace system would
make the pharmacy worse off than before, in addi-
tion to the implementation and administration costs.
If this holds true, it becomes critical for public au-
thorities and manufacturers to develop proper incen-
tive schemes and legal frameworks to reduce the fi-
nancial burden for dispensers in participating in the
ever-growing fight against counterfeiting.
ICORES2014-DoctoralConsortium
16
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SourcingDecisionsforGoodswithPotentiallyImperfectQualityunderthePresenceofSupplyDisruption
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