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

Wagner L. and Gürbüz M..

Sourcing Decisions for Goods with Potentially Imperfect Quality under the Presence of Supply Disruption.

 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

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

, x

, . . . , x

) denote a vec-

tor and x =

∑

i=0

refers to the sum of its

components, unless otherwise indicated. x

−i

, x

, . . . , x

i−1

, x

i+1

, . . . , x

) 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

(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

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

∈ [0, 1] of the procurement

quantity will be of inferior quality with mean β

for

all j ∈ W. The probability distribution g

(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

, β

, . . . β

, . . . , β

N−1

) 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) such that β

< β

, < β

< . . . , < β

N−1

The procurement cost of each source is denoted by

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

∀ 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

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

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

> c

> . . . > c

N−1

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

= (x

0,t

, x

1,t

, . . . , x

N−1,t

) with x

j,t

representing the

amount of products in stock from supplier j. We fur-

ther denote with x

the total on-hand inventory in pe-

riod t before the receipt of current orders. Likewise,

let y

= (y

0,t

, y

1,t

, . . . , y

N−1,t

) represent the vector of

orderings in period t and let z

= (z

0,t

, z

1,t

, . . . , z

N−1,t

)

account for the amount of inventory after ordering be-

fore demand realizes.

The total on-hand inventory after ordering, z

, in pe-

riod t is given by:

= x

+ y

N−1

∑

j=0

j,t

N−1

∑

j=0

j,t

(1)

SourcingDecisionsforGoodswithPotentiallyImperfectQualityunderthePresenceofSupplyDisruption

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:

0,t+1

=(z

0,t

− D)

j,t+1

=(z

j,t

− (D−

j−1

∑

i=0

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

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:

j,t+1

=Θ

[min{(ξ−

j−1

∑

i=0

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 j’s

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

and the random fraction of carrying inferior products.

Further, s

represents the total potential medical

errors arising from inferior product procurement

N−1

∑

j=1

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:

N−1

∑

j=0

j,t

− x

j,t

) + Rγs

N−1

∑

j=0

E[(z

j,t

− (D−

j−1

∑

i=0

i,t

)

]

+ pE[(D− z

)

] (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

, s

) as the

immediate expected costs plus the current on hand

inventory before ordering:

, s

)

N−1

∑

j=0

j,t

) + Rγs

N−1

∑

j=0

E[(z

j,t

− (D−

j−1

∑

i=0

i,t

)

]

+ pE[(D− z

)

] (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:

(x, s, 0) = min

j,t

∀ j∈W



, s

)

+ E[V

t+1

, s

t+1

, δ)]



−

N−1

∑

j=0

j,t

(6)

(x, s, 1) = min

j,t

∀ j∈W

−0



, s

)

+ E[V

t+1

, s

t+1

, δ)]



−

N−1

∑

j=0

j,t

(7)

s.t. z

0,t

≥ x

0,t

. . .

j,t

≥ x

j,t

. . .

N−1,t

≥ x

N−1,t

For convenience, we assume that in period 0 the gen-

uine manufacturer is available V

(x, s, 0) with initial

inventory and potential future medication errors given

by x

= 0 and s

= 0. Further, the terminal value func-

tion is represented by

T+1

(x, s, δ)

= RγE[s

T+1

] = Rγ

N−1

∑

j=0

E[Θ

min{(D−

j−1

∑

i=0

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

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

the random fraction of goods procured from supplier

j which were genuine with probability distribution

(·): 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

, x

) =

N−1

∑

j=0

j,t

)

N−1

∑

j=0

D,Ξ

[(x

j,t

+ Ξ

j,t

− (D−

j−1

∑

i=0

i,t

+ Ξ

i,t

)

]

+ pE

D,Ξ

[(D−

N−1

∑

j=0

j,t

+ Ξ

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:

(x, 0) = min

j,t

≥0∀ j∈W



˜g

, x

) + E[

t+1

, δ)]



(10)

(x, 1) = min

j,t

≥0∀ j∈W

−0



˜g

, x

) + E[

t+1

, δ)]



(11)

With terminal cost function

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

> c

> . . . > c

N−1

) 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

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SourcingDecisionsforGoodswithPotentiallyImperfectQualityunderthePresenceofSupplyDisruption