Pricing decisions for product recovery facilities in a multi-criteria setting using genetic algorithms

Abstract

Independent and small scale product recovery facilities (PRFs) often struggle to achieve profits when faced with inconsistent inflows of discarded products, varying demand patterns for recovered components, and stringent environmental regulations. Inconsistent inflows coupled with the varying demand cause undue fluctuations in inventory levels and frequently affect costs involved in product recovery operations. An effective pricing strategy can stabilize the fluctuations in demand and consequently can allow PRFs to control inventory levels. This research determines the prices of reusable and recyclable components and acquisition price of discarded products that allow PRFs to simultaneously maximize their financial returns and minimize the product recovery costs. Genetic algorithms and analytic hierarchy process are employed to solve this multi-criteria decision making problem.

Full text

Northeastern University
Department of Mechanical and Industrial
Engineering
January 01, 2006
Pricing decisions for product recovery facilities in a
multi-criteria setting using genetic algorithms
Surendra M. Gupta
Northeastern University
Srikanth Vadde
Northeastern University
Sagar V. Kamarthi
Northeastern University
This work is available open access, hosted by Northeastern University.
Recommended Citation
Gupta, Surendra M.; Vadde, Srikanth; and Kamarthi, Sagar V., "Pricing decisions for product recovery facilities in a multi-criteria
setting using genetic algorithms" (2006). .Paper 94. http://hdl.handle.net/2047/d10009991

Bibliographic Information
Vadde, S., Kamarthi, S. V. and Gupta, S. M., “Pricing Decisions for Product Recovery
Facilities in a Multi-Criteria Setting using Genetic Algorithms”, Proceedings of the SPIE
International Conference on Environmentally Conscious Manufacturing VI,
Boston, Massachusetts, pp. 108-118, October 1-3, 2006.
Copyright Information
Copyright 2006, Society of Photo-Optical Instrumentation Engineers.
This paper was published in Proceedings of SPIE (Volume 6385) and is made available
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or for commercial purposes, or modification of the content of the paper are prohibited.
Contact Information
Dr. Surendra M. Gupta, P.E.
Professor of Mechanical and Industrial Engineering and
Director of Laboratory for Responsible Manufacturing
334 SN, Department of MIE
Northeastern University
360 Huntington Avenue
Boston, MA 02115, U.S.A.
(617)-373-4846 Phone
(617)-373-2921 Fax
gupta@neu.edu e-mail address
http://www.coe.neu.edu/~smgupta/ Home Page
Laboratory for Responsible Manufacturing
LR
m

Pricing Decisions for Product Recovery Facilities in a
Multi-Criteria Setting using Genetic Algorithms
Srikanth Vadde, Sagar V. Kamarthi†and Surendra M. Gupta
Laboratory for Responsible Manufacturing
334 SN, Department of Mechanical and Industrial Engineering
Northeastern University, Boston, MA 02115, USA
ABSTRACT
Independent and small scale product recovery facilities (PRFs) often struggle to achieve profits when faced with
inconsistent inflows of discarded products, varying demand patterns for recovered components, and stringent
environmental regulations. Inconsistent inflows coupled with the varying demand cause undue fluctuations in
inventory levels and frequently affect costs involved in product recovery operations. An effective pricing strategy
can stabilize the fluctuations in demand and consequently can allow PRFs to control inventory levels. This
research determines the prices of reusable and recyclable components and acquisition price of discarded products
that allow PRFs to simultaneously maximize their financial returns and minimize the product recovery costs.
Genetic algorithms and analytic hierarchy process are employed to solve this multi-criteria decision making
problem.
Keywords: Economic models, Second-hand markets, Multi-criteria decision making, Product recovery, Genetic
algorithms.
1. INTRODUCTION AND RELATED WORK
Rising consumer awareness of the environment and the enormously growing quantities of products discarded
by customers have led to legislations that hold the original equipment manufacturers (OEM) responsible for
their products.1234 Products discarded by customers can broadly be classified as obsolete or naturally aged.
Components in the former could be reused whereas those in the later could be recycled for their virgin materials.
In spite of the economic and environmental benefits associated with reuse and recycle of discarded products many
OEMs are apprehensive of the idea of integrating product take back programs in their business models. They
fear that it could affect their new product sales.5Encouraged by this stance from OEMs, third-party firms are
entering the market to exploit the economic potential in discarded products, allowing them to compete against
the OEMs new products. The third-party firms, referred as product recovery facilities (PRFs), collect discarded
products, perform product recovery operations, and sell the recovered components in secondary markets. IBM’s
Global Asset Recovery Services,6AER Worldwide,7NuKote,8and ReCellular9are good examples of PRFs.
Healthy competition between the OEMs and PRFs has an environmentally benign effect: it eases the burden
on landfills, minimizes the consumption of virgin materials, mitigates the energy requirements, and increases
number of product life cycles. Usually PRFs are plagued financially by the costly and labor intense nature of
product recovery operations, competition from OEMs, meagre revenue from sales, and environmental regulations.
Prominent challenges faced by PRFs are: (a) expensive and skilled labor required for product recovery operations;
(b) uncertainty in the timing and quantity of discarded products arriving at the PRFs; (c) fleeting inventory
levels of recovered components ensuing from the unpredictable disposal of products and stochastic demand;
(d) holding costs of surplus inventory; (e) lost sales due to stockouts; (f) disposal cost of leftover and obsolete
inventory; and (e) promotional sales, discounts, and markdowns to clear inventory.
An effective way to address these challenges is to appropriately price components in the inventory. This
strategy has a twofold impact: it facilitates inventory control and enhances the profit margin. Very few studies
†Corresponding author E-mail: sagar@coe.neu.edu, Telephone: 617 373 3070, Fax: 617 373 2921

in the literature address the issue of pricing for PRFs which are usually small scale firms. Most of the studies
focus on OEMs which are usually medium to large scale firms capable of practicing green manufacturing strategies
even at the cost of lower profit margins to abide by environmental regulations and to appear eco-friendly in the
market. Past studies in the literature are listed here.
Guide et al.10 determined the acquisition price of discarded products and the prices of remanufactured
products which are categorized according to their quality level. Pricing in a duopoly was addressed by Majumder
and Groenevelt11 and Ferrer and Swaminathan.12 Savaskan et al.13 evaluated different product take back
configurations in a closed-loop supply chain with the wholesale and retail prices of remanufactured products
as their metric. Ferguson and Toktay5determined the optimal prices for new and remanufactured products
produced by an OEM where remanufactured products can cannibalize the demand for their counterpart new
products. Vorasayan and Ryan14,15 for an OEM, determined the optimal prices of remanufactured products
and the optimal portion of the returned products to be remanufactured when new product sales are affected by
the remanufactured ones. Ray et al.,16 investigated the effect on the sales when trade-in rebates are offered to
customers who are willing to replace their products with new ones. Debo et al.17 determined the optimal price
of remanufactured products and the level of production technology to remanufacture products for a monopolist
firm whose customers distinguish between the new and the remanufactured products. In another work, Debo et
al.18 captured the progressive market penetration of new and remanufactured products of an OEM through a
Bass diffusion model, where the prices of new and remanufactured products and the level of remanufacturability
dictate the diffusion process. Mitra 19 determined the prices of remanufactured and refurbished products where
their demand is dependent on price, quality of products, and availability of discarded products. Bakal and
Akcali20 studied the effect of the component yield from product recovery on the selling and acquisition prices
and profits. Mondal and Mukherjee ,21 investigated the economic factors that impact the product acquisition
decisions and developed an analytical model to determine the optimal time to take back the products in use
to maximize the ensuing economic benefit from remanufacturing. Vadde et al. have developed pricing models
for PRFs when their inventories are vulnerable to gradual and sudden obsolescence,22 under certain inventory
constraints,23 when prices are have to be chosen from a pre-selected set,24 and when the PRFs either passively
accept discarded products or proactively acquire them.25
The present work determines the prices of reusable and recyclable components when the PRF passively
accepts discarded products and proactively acquires them when necessary, in a multi-criteria environment where
the PRF has to simultaneously maximize revenues and minimize various costs. Although Kongar et al.26 27 have
addressed issues in a multi-criteria environment for PRFs, they haven’t considered the pricing aspects in their
study. Addressing this gap is the focal theme of this work and thus makes it unique.
2. PROBLEM DESCRIPTION
Usually in practice the PRFs simultaneously work towards multiple cost and revenue objectives. Pricing decisions
under such a management policy are presented in this section. Some assumptions are made in formulating the
analytical model: (a) PRF is operating in a monopolist environment; (b) price reservation of customers is
inconsequential; (c) inventory is not replenished during selling horizon and excess demand is not backlogged; (d)
demand is deterministic and strictly decreasing with price; (e) PRFs must abide by the local regulations that
impose a fine on quantities exceeding the disposal limit; (f) contents of the discarded products are known to
the PRFs before their disassembly; (g) discarded products contain no missing and upgraded components; (h)
disassembly and sorting process yields are deterministic; (i) material recycling operations are not performed by
the PRF; (j) there is market for all categories of components sold by the PRFs. Prices are posted only after the
component yield is realized as it is a more profitable alternative than the case where price is posted before the
product recovery yield is known.20
PRFs passively accept single type discarded product returns as well as proactively acquire them when neces-
sary. This production control strategy, an integration of both push and pull production systems, can ensure that
the demand is always satisfied without backorders and can stabilize the plans for resources required to perform
product recovery operations, remanufacturing, refurbishing, and processing of recyclable components. PRFs
accept discarded products with no restrictions on their quantity and quality. This research proceeds with the
assumption that the quantity of discarded products and their arrival time at the facility are known beforehand

Passively
Accepted
Returns
Disassembly
Process
High Grade
Reusable
Components
Scrap Grade
Reusable
Components
Remanufactured
Components
Inventory
Demand for
Remanufactured
Components
High Quality
Recyclable
Components
Scrap Quality
Recyclable
Components
As-Is Reusable
Component
Inventory
Inventory of
Shredded
Components
Disposable
Components Dispose
Demand for As-Is
Reusable Components
Demand for Scrap Grade
Reusable Components
Demand for Scrap Quality
Recyclable Components
Demand for Recyclable
Components
λs
λa
λr
θ γ mrRq
(+
βRp)
rr
Rp
(1 − γ ) mrwrRq
(+
βRp)
r
mdwdRq
(+
βRp)
γr
'mr
'wr
'Rq
(+
βRp)
(1 − γ )
r
'mr
'wr
'Rq
(+
βRp)
λs
'
λr
'
Proactively
Acquired
Returns
Sorting
Process
Scrap
Products
Good
Products
Demand for
Scrap Products
Rq
Rp
(1 − β)
βRp
(1 − θ r)mrRq
(+
βRp)
r
γ
1st Grade
Components
2nd Grade
Components
mrRq
(+
βRp)
r
γ
(1 − γ ) mrwrRq
(+
βRp)λs
_
r
λp
Rp
(1 − β) _λp)
(wp
Figure 1. Production control model of the product recovery facility
to PRFs through forecasting techniques.28 This allows PRFs to plan ahead on the acquisition of discarded prod-
ucts. They can be acquired directly from customers, retailers, and collection agencies if the forecasted returns
are fewer or the on-hand inventory of returns is insufficient to satisfy the demand for recovered components.
The acquisition process should be initiated by PRFs taking into account the time lags in acquiring returns and
the lead times to process the recovered components in order to avoid delays in demand delivery. Obsolescence
could catch up on remanufactured components if acquisition and lead times are long.22 Although PRFs can
advertise their need for discarded products, unless incentives are offered to customers to return their products
the acquisition process could be prolonged. The incentive offered, which depends on the demand for recovered
components and regulated disposal limit, in effect determines the return quantity – more lucrative incentives
yield better returns. PRFs may choose to give incentives only if the products meet certain specifications. This
could enable PRFs to acquire products of specific quality levels which may eliminate the need to sort the good
and damaged products.
3. ANALYTICAL MODEL
The schematic layout of the production control model implemented by the PRF is shown in Figure 1 (subscript
iis dropped for ease of illustration). The passively accepted returns are first sorted and inspected to separate
the good quality products from the scrap quality products which are characterized by inferior quality, blemished
physical appearance, and low reuse and recycle potential. The scrap quality products are preferentially sold for
recyclable material and the rest are disposed of at the end of the selling period. The good quality products and the
proactively acquired products, if any, are fed to the disassembly production system which extracts the constituent
components from the products. These components are segregated by skilled workers on the production line into
various types of reusable, recyclable, and disposable components; if necessary these components are further
tested. The reusable and recyclable components are categorized into four classes described below.

•High grade reusable components: These components are characterized by their good physical appearance
and quality. They are further classified as first and second grade components on the basis of further tests
on their reusability potential. The first grade components have more economic value when remanufactured
or refurbished (refurbished components are also referred as remanufactured components in the remainder
of the paper) than the second grade ones (referred as high grade as-is reusable) which are sold in as-is
condition with some cosmetic changes. Inventory is carried for both grades of components.
•Scrap grade reusable components: These components are either physically blemished or functionally disabled
but are good candidates for recycling.
•High quality recyclable components: These components can either be directly recycled or require minimal
effort to obtain the actual recyclable components. Before stockpiling in the inventory, the components are
subjected to operations such as shredding and crushing to facilitate processing at the recycling stage.
•Scrap quality recyclable components: These components require more effort and time to separate the actual
recyclable components or have relatively less recycle value.
On the basis of their economic worth the PRF’s prefers to sell, remanufactured, high grade as-is reusable,
high quality recyclable, scrap grade reusable, and scrap quality recyclable components in this order. At the end
of the selling period, the leftover scrap grade reusable and scrap quality recyclable components are disposed of,
whereas the disposable components are disposed of as soon as their yield is realized. According to the disposal
regulation, penalty is imposed if the disposed quantity exceeds the stipulated limit. Inventory is carried to absorb
fluctuations in demand for remanufactured, high grade as-is reusable, and high quality recyclable components.
These inventory levels are expected to be relatively low when returns are acquired and high when the passively
accepted returns are substantial.
In the management policy to simultaneously minimize costs and maximize revenues, the costs include the
acquisition cost of returns, disassembly cost of recovering components, processing and holding costs of the
remanufactured, high grade as-is reusable, and high quality recyclable components, disposal costs of scrap quality
products, scrap grade reusable, and scrap quality recyclable components; and revenues consist of sales from the
four classes of components and scrap quality discarded products. Analytical expressions for revenue and costs
are given below (see appendix for notation used).
Total Revenue:
RT=
nr

i=1
priQri +
n

r

i=1
p

riQ

ri +
nr

i=1
paiAri +
nr

i=1
psiFri +
n

r

i=1
p

siF

ri +ppJ(1)
Total Disposal Costs:
CD=
nr

i=1
(1 −xri)CdiGri +xri[Cdi Dri +Coi(Gri −Dri)] +
n

r

i=1
(1 −x

ri)C

diG

ri +x

ri[C

diD

ri +C

oi(G

ri −D

ri)]
+
nd

i=1
(1 −xdi)Cddimdi wdi(βRp+Rq)+xdi[CddiDddi +Codi(mdi wdi(βRp+Rq)−Dddi)]
+(1 −xp)CdpK+xp[CdpDp+Cop (K−Dp)] (2)
Total Preparation Cos ts:
CP=
nr

i=1
Cpiθri γrimri(βRp+Rq)+
n

r

i=1
C

piγ

rim

riw

ri(βRp+Rq)
+
nr

i=1
Cai(1 −θri)γri mri(βRp+Rq)(3)

Total Holding Costs:
CH=
nr

i=1
Chi(Lri +LAri)+
n

r

i=1
C

hiL

ri (4)
Total Disassembly Costs:
CA=Cr(βRp+Rq)(5)
Total Acquisition Costs:
CQ=CqRq(6)
Total Sorting Costs:
CS=CsRp(7)
Where, Qri =min{λri,θ
riγrimri(βRp+Rq)},Q
ri =min{λ
ri,γ
rim
ri(βRp+Rq)},
Ari =min{λai,(1 −θri)γrimri(βRp+Rq)},LAri =max{0,(1 −θri)γrimri(βRp+Rq)−λai},
Lri =max{0,θ
riγrimri(βRp+Rq)−λri},L
ri =max{0,γ
rim
riw
ri(βRp+Rq)−λ
ri},
Fri =min{λsi,(1 −γri)mri wri(βRp+Rq)},F
ri =min{λ
si,(1 −γ
ri)m
riw
ri(βRp+Rq)},
Gri =max{0,(1 −γri)mriwri(βRp+Rq)−λsi},G
ri =max{0,(1 −γ
ri)m
riw
ri(βRp+Rq)−λ
si},
J=min{λp,(1 −β)wpRp},K=max{0,(1 −β)wpRp−λp}.Thevariable,xri =0,ifGri >D
ri,otherwise
xri = 1; the same description applies to x
ri,xdi,andxp.
The demand for remanufactured and high grade as-is reusable components is in discrete quantities, while that
of scrap grade reusable, high and scrap quality recyclable components is in terms of their weight. The demand
constraints are given by equations 8–13.
λri ≤θriγrimri(βRp+Rq),∀i=1, ..., nr(8)
λ

ri ≤γ

rim

riw

ri(βRp+Rq),∀i=1, ..., n

r(9)
λai ≤(1 −θri)γrimri(βRp+Rq),∀i=1, ..., nr(10)
λsi ≤(1 −γri)mriwri(βRp+Rq),∀i=1, ..., nr(11)
λ

si ≤(1 −γ

ri)m

riw

ri(βRp+Rq),∀i=1, ..., n

r(12)
λp≤(1 −β)wpRp(13)
The management wishes to determine the optimal acquisition price of discarded products and the optimal
prices of remanufactured, high grade as-is reusable, high quality recyclable, scrap grade reusable, and scrap
quality recyclable components which maximize the total revenue (eq. 1), minimize the total disposal cost (eq. 2),
total preparation cost (eq. 3), total holding cost (eq. 4), total disassembly cost (eq. 5), total acquisition cost
(eq. 6), and total sorting cost (eq. 7), under the demand constraints (eqs. 8–13). This multi-criteria decision
making problem is solved using genetic algorithms in the next section.
4. GENETIC ALGORITHMS
Genetic algorithm is a heuristic search technique whose principles are rooted in the theory of evolution29 3031 .
In a nutshell, a genetic algorithm starts with a population of individuals which are left to evolve under certain
rules until the objective function (or fitness value) of the problem is optimized.
A multi-criteria based genetic algorithm is employed to solve the optimization problem presented in the
previous section. A weighted sum approach is employed to obtain a single scalar objective function which is then
maximized.32 The contribution of each criteria to the overall objective function (net profit), PN,isgivenby
their respective weights, wi,i=1,2, ..., 7. The function, PN(eq. 14), is used as the fitness value in the genetic
algorithm. The weighted sum technique is appropriate if the decision maker is knowledgable of the contribution

of each criteria to the overall objective function, the same is assumed in this work. A judicious method of
choosing the weights with the decision maker’s knowledge is discussed in section 4.1.
PN=w1RT−w2CD−w3CP−w4CH−w5CA−w6CQ−w7CS(14)
The structure of the algorithm is briefly described here. Initially, each problem variable is encoded into a
gene (for the problem at-hand encoding is not necessary) and a set of genes is called a chromosome which is a
point in the problem’s search space and a signature of an individual in the population. For the current problem,
the acquisition price of products and prices of all components and scrap products compose a chromosome. The
algorithm starts of by randomly choosing a set of chromosomes from the search space. Individuals (or parents)
are chosen by some selection criteria which then are allowed to mate to produce offsprings. The rank based
roulette wheel weighting technique is used in selecting the parents and the single point crossover method is
used to obtain the offspring from a pair of parents during mating.30 The current set of parents and offsprings
constitutes a generation. At this stage, a certain percentage (mutation rate) of the population is allowed to
mutate. Mutations which alter the composition of the chromosomes are necessary to explore the search region
and avoid convergence at local optima. The algorithm is terminated if the desired fitness value is reached or
a pre-specified number of generations have elapsed. Before starting the next generation, the chromosomes are
sorted in the descending order of their fitness value and a certain percentage (selection rate) of the population
is preserved to generate new offsprings.
4.1. Determination of criteria weights using the analytic hierarchy process
The analytic hierarchy process (AHP) is a decision making tool which exploits the decision maker’s knowledge
about the various criteria influencing a decision.33 First, the various criteria are hierarchically arranged consid-
ering their interdependencies and the decision maker’s perception of the relative importance of a criterion with
respect to the other is captured on a quantitative scale between 1-10; the values 1, 3, 5, 7, and 9 respectively
represent if a criterion is of equal, moderate, strong, very strong, and extreme importance with respect to other
criterion, whereas the values 2, 4, 6, and 8 quantify the intermediary perceptions, and the reciprocals of these
values represent the converse perceptions. After each criterion is weighted against the remaining criterion, a
pairwise comparison matrix is generated. The weights of the criteria are obtained by employing techniques such
as eigenvalue, mean transformation or row geometric mean to the pairwise comparison matrix. To determine
the bias in the decision maker’s perception of a criterion’s relative importance, an index called the consistency
ratio is computed. Usually the consistency ratio values less than 0.1 are acceptable otherwise a revision of the
pairwise comparison matrix is undertaken.
5. NUMERICAL EXAMPLE
Assume that the PRF processes PCs with configuration shown in Table 1 and the associated data for its com-
ponents listed in Table 2. Let the data for the PC be, wp=5.95 lb, β=0.8, Cs= $9, Cr= $15, Cdp = $15,
Cop = $12, Dp= 300 lb, Rp= 20, Rq=7Cq,λp=30−2.4pp. Linear demand functions are assumed for the
case example: λr1= 125 −1.2pr1,λr2= 120 −2.4pr2,λa1=70−2.5pa1,λa2=65−3.2pa2,λs1=18−5.2ps1,
λs2=19−4.1ps2,λ
r1=80−4.6p
r1,λ
r2=90−2.1p
r2,λ
r3= 125−5.3p
r3,λ
r4= 110−8.5p
r4,λ
r5= 105−3.5p
r5,
λ
s1=18−2.2p
s1,λ
s2=12−1.9p
s2,λ
s3=19−3.7p
s3,λ
s4=11−4.5p
s4,λ
s5=17−3.5p
s5,λp=30−2.5pp.
The pairwise comparison matrix to compute the weights for each criteria using the AHP technique is shown
in Table 3. The consistency ratio for the pairwise comparison matrix is found to be less than 0.093, which is
clearly less than 0.1. The genetic algorithm is executed with number of generations = 400, mutation rate = 20%
, selection rate = 50%, and population size = 12 chromosomes.
The following results are obtained from executing the genetic algorithm: price to acquire a PC (Cq)=$3.58,
number of returns to acquire (Rq)=25.09 units, and the overall is profit $1086.89; other parameters obtained
are listed in Table 4.

Table 1. Product configuration
Index (i)Component Multiplicity We i ght Yield Yield Disposal
(Recycle) (γr/γ
r) (θr)Limit (lb)
1LCD 12.1”11.10 0.85 n/a 26
2Chassis 10.68 0.95 n/a 38
3128 MB RAM 10.05 0.70 n/a 25
464 MB RAM 10.02 0.80 n/a 20
51.44 MB FD 10.68 0.75 n/a 19
(Reuse)
124x CD-ROM 10.90 0.90 0.50 50
210 GB HD 21.30 0.70 0.60 90
(Dispose)
1150 MHz Processor 10.40 n/a n/a 120
Table 2. Cost data
Costs
Index (i)Component Preparation As-Is Holding Disposal Disposal
(Recycle) Penalty
1LCD 12.1”7n/a 1.02 8 9
2Chassis 9n/a 1.01 9 6
3128 MB RAM 8n/a 0.95 7 4
464 MB RAM 9n/a 1.03 7 6
51.44 MB FD 8n/a 1.04 7 7
(Reuse)
124x CD-ROM 12 31.05 6 8
210 GB HD 8 5 1.04 9 6
(Dispose)
1150 MHz Processor n/a n/a n/a 10 14
Table 3. Pairwise comparison matrix
RTCDCACPCHCQCSWei ghts ( wi)
RT1 1 5 4 5 4 8 0.3034
CD1 1 4 4 6 5 7 0.3009
CA1/5 1/4 1 1 3 5 7 0.1276
CP1/4 1/4 1 1 3 4 6 0.1201
CH1/5 1/6 1/3 1/3 1 4 6 0.0812
CQ1/4 1/5 1/5 1/4 1/4 1 1 0.0389
CS1/8 1/7 1/7 1/6 1/6 1 1 0.0279

Table 4. Results obtained from executing the genetic algorithm
Price Inventory
Component High grade/ Scrap grade/ As-Is High grade/ As-Is Disposed
quality quality ($/lb) ($) quality (units) (lb)
LCD 12.1”9.38 ($/lb) 5.39 n/a 1.58 (lb) n/a 0.66
Chassis 30.43 ($/lb) 5.74 n/a 0.45 n/a 0.31
128 MB RAM 23.33 ($/lb) 5.07 n/a 0.08 n/a 0.38
64 MB RAM 12.91 ($/lb) 2.42 n/a 0.42 n/a 0.09
1.44 MB FD 24.02 ($/lb) 3.77 n/a 0.05 n/a 3.21
24x CD-ROM 88.93 ($/unit) 2.75 20.60 0.22 (units) 00.05
10 GB HD 36.49 ($/unit) 0.26 13.57 2.11 (units) 1.43 14.13
150 MHz Pro n/a n/a n/a n/a n/a 16.43
Computer n/a 2.64 n/a n/a n/a 0.14
6. CONCLUSIONS AND FURTHER RESEARCH
The disparity between the return flow of discarded products and the demand for reusable and recyclable compo-
nents creates undue inventory level variations and affects the product recovery costs. In this work, PRFs passively
accept discarded products normally but proactively acquire them when required to reduce the mismatch between
product returns and component demand. Prices of reusable and recyclable components of various grades and
acquisition price of discarded products are determined in a multi-criteria setting where the PRF has to maximize
its financial returns while minimizing various product recovery costs such as, disposal cost, disassembly cost,
preparation cost, holding cost, acquisition cost, and sorting cost. The multi-criteria problem is solved using ge-
netic algorithms and AHP techniques. Further research is planned to extend the analytical model to multi-type
products and a multi-period case. It would be interesting to study the impact of disassembly yield, product
recovery costs, and disposal regulations on the sale and acquisition prices.
Appendix
Notation:
RTTotal revenue.
CDTotaldisposalcost.
CPTotal preparation cost.
CHTotal holding cost.
CATotal disassembly cost.
CQTotal acquisition cost.
CSTotal sorting cost.
PNNet profit.
nrNumber of unique reusable components in a discarded product.
n
rNumber of unique recyclable components in a discarded product.
ndNumber of unique disposable components in a discarded product.
mri Multiplicity of reusable component i.
m
ri Multiplicity of recyclable component i.

mdi Multiplicity of disposable component i.
wri Weight of reusable component i.
w
ri Weight of recyclable component i.
wdi Weight of disposable component i.
wpWeight of discarded product.
pri Selling price of remanufactured component i($/unit).
p
ri Selling price of high quality recyclable component i($/lb).
pai Selling price of high grade as-is reusable component i($/unit).
psi Price of scrap grade reusable component i($/lb).
p
si Price of scrap quality recyclable component i($/lb).
ppPrice of discarded product ($/lb).
λri Demand for remanufactured component i.
λ
ri Demand for high quality recyclable component i.
λai Demand for high grade as-is reusable component i.
λsi Demand for scrap grade reusable component i.
λ
si Demand for scrap quality recyclable component i.
λpDemand for damaged discarded products.
βYield of sorting process.
γri Yield of high grade reusable component i.
γ
ri Yield of high quality recyclable component i.
θri Yield of remanufacturable quality reusable component i.
RqQuantity of proactively acquired returns.
RpQuantity of passively accepted returns.
CsCost to sort a discarded product.
CrCost to disassemble a product.
CqCost to acquire a discarded product (acquisition price) ($/unit).
Cpi Cost to remanufacture high grade reusable component i.
C
pi Cost to prepare (such as crushing) high quality recyclable component i.
Cai Cost to prepare high grade reusable component ifor as-is sale.
Chi Holding cost for high grade reusable component i.
C
hi Holding cost for high quality recyclable component i.
Cdi Cost to dispose reusable component i.

C
di Cost to dispose recyclable component i.
Cddi Cost to dispose the disposable component i.
Cdp Cost to dispose the discarded product.
Coi Penalty cost to dispose reusable component i.
C
oi Penalty cost to dispose recyclable component i.
Codi Penalty cost to dispose the disposable component i.
Cop Penalty cost to dispose the discarded product.
Dri Disposal limit for reusable component i.
D
ri Disposal limit for recyclable component i.
Ddi Disposal limit for disposable component i.
DpDisposal limit for damaged discarded products.
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