The International Journal of Logistics ManagementA reverse logistics inventory model for plastic bottlesNouri Matar Mohamad Y. Jaber Cory Searcy

Article information:To cite this document:Nouri Matar Mohamad Y. Jaber Cory Searcy , (2014),"A reverse logistics inventory model for plastic bottles",The International Journal of Logistics Management, Vol. 25 Iss 2 pp. 315 - 333Permanent link to this document:http://dx.doi.org/10.1108/IJLM-12-2012-0138

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A reverse logistics inventorymodel for plastic bottles

Nouri Matar, Mohamad Y. Jaber and Cory SearcyDepartment of Mechanical and Industrial Engineering,

Ryerson University, Toronto, Canada

Abstract

Purpose The purpose of this paper is to present an original model for the production-recycling-reuse of plastic beverage bottles.Design/methodology/approach It is assumed that discarded two-liter plastic polyethyleneterephthalate (PET) bottles are collected from the market. The bottles are then sorted into non-contaminatedand contaminated streams. The non-contaminated PET bottles are either remanufactured or used as regrindmixed with virgin PET to produce new bottles to satisfy varying demand. The contaminated bottles areeither sold to industries using low-grade plastic or disposed of in a landfill. Numerical studies are usedto illustrate the behaviour of the model, with an emphasis on exploring the reduction of total system costand the amount of bottles going into a landfill.Findings Numerical analyses conducted on the model found that the amount of bottles collected hadthe largest influence on the outcome of the total system unit time cost. Alternative materials to PET aresurveyed and used to demonstrate a significant reduction in the cost of landfill disposal due to theirmore rapid degradation in the landfill.Research limitations/implications Several areas for future work are highlighted. Potentialmodifications to the model could focus on accommodating bottles made of material other than plastic,incorporating the effects of learning on manual tasks, and on accommodating shortages or excess inventory.Originality/value The model incorporates several unique aspects, including accounting for thecost of land use and associated environmental damage through the calculation of a present value thatis charged to the manufacturer.

Keywords Reverse logistics, Recycling, Production, Inventory management, Waste disposal, EOQ,PET, Biodegradable plastic

Paper type Research paper

1. IntroductionSustainable development has become a well-established goal in governments andorganizations around the world. At its root, sustainable development requires thatthe needs of the current generation are met without compromising the ability offuture generations to meet their own needs (World Commission on Environmentand Development, 1987). This requires that the economic, environmental, and socialimplications of human activity are considered in decision making. However, despitemany advances, a number of challenges remain in meeting sustainable developmentgoals. One of the most prominent challenges of sustainable development is findingways to reduce the huge quantities of waste generated through human activity.

Waste disposal in landfills results in numerous hazards and damage to the naturalenvironment, wildlife, and humans (Tchobanoglous et al., 1993). There are many

The current issue and full text archive of this journal is available atwww.emeraldinsight.com/0957-4093.htm

Received 3 December 2012Revised 12 April 2013Accepted 15 July 2013

The International Journal of LogisticsManagement

Vol. 25 No. 2, 2014pp. 315-333

r Emerald Group Publishing Limited0957-4093

DOI 10.1108/IJLM-12-2012-0138

An earlier version of this paper was presented at the 9th Supply Chain Management Symposiumheld in Toronto, Canada in September 2011. The first and second authors would like to thank theSocial Sciences and Humanities Research Council of Canada (SSHRC)-Canadian EnvironmentalIssues- for providing funding for this research. The third author thanks the Natural Sciences andEngineering Council of Canada (NSERC) for supporting his research.

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factors that may influence the quantity and composition of solid waste generated,including geographic location, season, demographics, population density and size,income levels, purchasing patterns, public attitudes, and legislation; among otherfactors. However, despite increasing attention to these issues, significant amountsof waste continue to be generated. Before recycling, approximately 243 million tons ofmunicipal solid waste was generated in the USA in 2009 (United States EnvironmentalProtection Agency (US EPA), 2010).

In an effort to reduce the amount of material disposed of in landfills, efforts to recycle,remanufacture, or reuse discarded and obsolete products have been steadily growingover the last several decades. Many products now boast recycling rates of over 50 percent, including auto batteries (95.7 per cent), office paper (74.2 per cent), and aluminumcans (50.7 per cent) (US EPA, 2010). However, for other types of products, recycling ratesremain lower. In one prominent example, the recycling rate for polyethylene terephthalate(PET) bottles and jars in the USA is just 28.0 per cent (US EPA, 2010). Given that PETbottles and jars account for 2,570,000 tons of waste generated annually in the USA (USEPA, 2010), efforts to increase the recycling rate for these products are needed.

The disposal of plastic bottles into landfill sites has high environmental and socialcosts as it uses up useful land and disturbs the eco-system. For example, thedecomposition of PET bottles in a landfill leaches harmful chemicals (e.g. BPA orbisphenol A) into the water table. BPA consumption by humans and wildlife disturbscell metabolism (Crisp et al., 1998), creates neurological issues (Palanza et al., 2008), andincreases the risk of cancer in males and females (Prins et al., 2008; Brisken, 2008).Additionally, plastic beverage bottles take approximately 450 years (OceanConservancy, 2005) to fully biodegrade in a landfill. This leads to land use concerns.In response, local government units and municipalities are implementing stringentlaws to restrict the disposal of plastic bottles and encourage the development of moreadvanced technologies and systems for plastic bottle recycling.

To help address these issues, this paper focuses on the remanufacturing of discardedPET plastic beverage bottles and the use of recycled material in the production of newones. The aim of a reuse and recycling system is to reduce the amount of bottles goinginto a landfill. Given the large percentage of PET bottles that are currently disposed of ina landfill, this would represent an important advance towards sustainable development.The supply chain system in this paper has two separate generic entities: collection andmanufacturing. The first entity collects the bottles produced by the manufacturer thatare discarded by the users and sorts them into three streams: non-contaminated wholebottles, non-contaminated damaged bottles and contaminated bottles. The contaminatedbottles are then sorted into two streams. The non-useable badly contaminated bottles aresent to the landfill (e.g. Thompson et al., 2009; Gironi and Piemonte, 2011; Foolmaun andRamjeawon, 2012), while the remaining ones are sold to industries that use low-gradeplastic material (such as the construction industry). The non-contaminated wholeand damaged bottles are then transported to the manufacturing entity. In this systemthe whole bottles are remanufactured through a process where they are de-labelled,cleaned and sanitized, polished and relabelled. The damaged bottles are de-labelled, cleaned,grounded into flakes and processed. The pellets/material produced are then mixed withthe virgin PET pellets (material of origin) to generate new bottles. The remanufacturedbottles plus the newly produced bottles will achieve the demand requirements dictatedby the market.

This paper contributes to the literature by developing a model to manage inventory ina closed-loop supply chain for plastic bottles. The available models in the literature are

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generic and do not specify the type of the product considered (e.g. Richter, 1996; Dobosand Richter, 2004, 2006; El Saadany and Jaber, 2010). They also consider that a productis recovered (e.g. remanufactured) as a whole unit (e.g. El Saadany and Jaber, 2011), whichis an unrealistic assumption. The models in the literature also assume that all unitscan be recovered (e.g. remanufactured, recycled) indefinitely (El Saadany et al., 2013),which is also an unrealistic assumption. The existing studies also ignored the cost ofwaste disposal and social costs in rehabilitating landfill sites. This paper contributesto the inventory management literature on production, remanufacturing and wastedisposal models by: first, assuming that not all items collected for recovery are suitablefor recovery since portions of them are remanufactured, recycled and reused, second,recognizing the disposed items either go to the landfill or are sold as low-grade rawmaterial for use in other processes, e.g. in the construction industry (Siddique et al., 2008;Gaggino, 2012), third, considering the social costs of rehabilitating landfill sites, andfourth, considering the option of using biodegradable material and studying how goinggreen may impact the behaviour of the model developed. These are all uniquecontributions that fill existing gaps in the literature. The importance of the points raisedhere have been argued in Bonney and Jaber (2011), who discussed that there is a direneed to design more environmentally responsible inventory and logistics systems. Thispaper contributes to this call and line of research.

2. Literature surveyThe need to reduce the cradle to grave environmental impacts associated with thedesign, sourcing, production, use, reuse, recycling, and disposal of products has beenwidely recognized in the literature. For example, Ilgin and Gupta (2010) recentlycompleted a review of over 500 articles published on environmentally consciousproduct design, reverse logistics, closed-loop supply chains, remanufacturing, andproduct disassembly. The rapidly growing body of research on life cycle assessment,design for environment, industrial ecology, and sustainable supply chain managementsimilarly underlines the need for more sustainable development of products. Severalstudies that specifically investigate production-recycling systems can be found in theliterature. These studies will be briefly examined and compared to the reverse supplychain inventory model of this paper. Also, articles that demonstrate the use of recycledPET material in different industries and the use of alternative materials that areenvironmental friendly will similarly be discussed and compared.

Dobos and Richter (2004) developed a production-recycling model where themanufacturer serves a stationary product demand and is willing to buyback a portion ofthe used products to recycle and/or to dispose of them. Newly produced and recycleditems were assumed to have indifferent quality. Their production, inventory andrecycling policy shifted between two extremes, either produce or recycle all. In afollow-up paper, Dobos and Richter (2006) extended their earlier model to considerwhether the quality of a collected and returned item is suitable for recycling. Unlike theirearlier finding (Dobos and Richter, 2004), they found that when quality is accounted for amixed policy of production and recycling was found to be economical. Maity et al. (2007)developed a similar model to Dobos and Richter (2004), but with fuzzy holding costs.They assumed that demand is price dependent and that price is dependent on theinventory level. El Saadany and Jaber (2010) investigated a similar model to that of Dobosand Richter (2006) where they assumed that the collection rate is price and qualitydependent. Their results also supported a mixed strategy of production and recovery(recycle, remanufacture) policy. Similar works include, but are not limited to, Li et al.

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(2008), Oh and Hwang (2006), and Maity and Maity (2009). The economic order quantity(EOQ) model (Harris, 1990) has been the basis for these models.

As noted in the introduction, BPA has been proven to have adverse effects on humanbeings and wildlife. Therefore, it is wise that alternative materials be explored for theuse of creating plastic bottles. For example, Kinoshita et al. (2009) developed and testeda green composite made of woodchips, bamboo fibres, and biodegradable adhesivematerial, which is resistant to water. Samarasinghe et al. (2008) created and testeda biodegradable plastic composite made from corn gluten meal (CGM) that can beblended with synthetic biodegradable polyester and wood fibre. This allows thematerial to degrade in soil in a matter of months. Other material was made frombiodegradable composites such as sunflower oil cake (Rouilly et al., 2006), hardwoodsawdust (Schilling et al., 2005), and soy protein-starch (Otaigbe et al., 1999). Therationale is to develop material that does not leach harmful chemical substances intothe soil and water tables and that degrades at a much faster rate than PET in order toincrease the turnover of land.

While the existing literature is abundant and growing, there are many areas in needof further research. For example, Dobos and Richter (2004 and 2006) do not consider thatnewly produced products/items are created from recycled material that is mixed withvirgin material. The models proposed by Li et al. (2008) and Maity and Maity (2009)suffer from a similar deficiency. Furthermore, the models proposed by Dobos and Richterdo not account for the costs of waste disposal related to the use of land and the effects onthe environment due to landfilling of unrecyclable material. In their model, Oh andHwang (2006) assume that all collected materials can be recycled or remanufactured.Non-serviceable items are not considered and their model therefore does not account forwaste disposal costs. None of the existing models consider the possibility of reducing thequantity of bottles disposed of in a landfill by selling contaminated bottles to industriesthat use low-grade plastic material. Given the research demonstrating the use of recycledPET in the production of a wide variety of products such as polymer concrete (Tawfikand Eskander, 2006), moulded automotive carpets (Gurudatt et al., 2005), coating resins(Kawamura et al., 2002), packaging trays (Griffen, 1996), and polyester concrete (Rebeiz,1996), this is an important oversight. Finally, the use of alternative materials in theproduction of the PET plastic bottles in production-recycling-reuse models has not beenwidely explored. The composite materials discussed above all relatively rapidly degradein a landfill and reduce complications associated with BPA.

The model proposed in this paper seeks to address these gaps in the existing literature.The model explicitly considers newly produced products/items that are created fromrecycled material that is mixed with virgin material. The proposed model not only recycleswhole non-contaminated plastic bottles, but also uses non-contaminated damaged bottlesin the production of new bottles. Furthermore, the cost of the long land use by slowdegrading plastics is brought back to the present to be charged to the bottle manufacturer.This cost includes real-estate rental, land rehabilitation and a penalty for damage to theenvironment. Additionally, this paper explores the effects of using biodegradable materialon the inventory system. These unique contributions provide needed insight into thedevelopment of more sustainable production, reuse, and recycling systems.

3. The mathematical modelDisposing plastic bottles into a landfill causes harm to human and wildlife health, aswell as to the natural environment. These harmful effects could be reduced throughincreased recycling of these plastics. In this section, a model will be developed where

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the recycling of two-liter plastic PET bottles is considered. The development of themodel and its assumptions will now be introduced.

3.1 Notations and assumptions3.1.1 Notations.

y the percentage of bottles collected, where 0oyo1a the percentage of non-contaminated bottles that can be used for

remanufacturing via regrinding and using it as raw material, where 0oao1.b the percentage of whole non-contaminated bottles that can be used for

remanufacturing as whole bottles, where 0obo1f the percentage of contaminated bottles that can be sold as low-grade material,

where 0ofo1D the demand rate (unit/unit of time)Knss setup cost for bottle collection ($)Kr setup cost for remanufacturing ($)Krm setup cost for virgin material and regrind mixing ($)KP setup cost for production/manufacturing of new bottles ($)KSc setup cost for contaminated bottle sort ($)KLF Setup cost to prepare the ground for bottle disposal ($)CLs labour cost for sorting bottles ($/unit of time)CCo labour cost for bottle collection ($/unit of time)CLr labour cost for remanufacturing ($/unit of time)CMat material cost for remanufacturing ($/unit of time)Cvm cost for virgin material per cycle ($/unit of time)CLp labour cost for bottle production ($/unit of time)CLSc labour cost for contaminated bottle sort ($/unit of time)CLF labour cost for disposing bottles in the landfill ($/time)Cre the real-estate rental cost per bottle ($/time)Crh the rehabilitation penalty cost per bottle ($/time)hnss carrying cost per bottle from collection and sorting per cycle-period ($/unit/

unit of time)hr carrying cost per remanufactured bottle per cycle-period ($/unit/unit of time)hrm carrying cost per bottle from virgin material and regrind mixing per

cycle-period ($/unit/unit of time)hp carrying cost per newly produced bottle per cycle-period ($/unit/unit of time)hsc carrying cost per contaminated bottle per cycle-period ($/unit/unit of time)lr slope of depleting demand rate for remanufactured bottles ($/unit of time)lrm slope of depleting demand rate for regrind and virgin material mix ($/unit of

time)l the decay rate of PET material (percentage/unit of time)P production rate for producing new bottles (unit)Qr the quantity of bottles remanufactured (unit)Qvm the material needed to be mixed with the regrind in order to produce the

number of bottles required to supplement the number of remanufacturedbottles (units/unit of time)

RM the quantity of regrind and virgin material mix in a cycle (units)QP replenishment order quantity in each cycle (units)BLf the amount of bottles that are to be disposed of into a landfill after sorting

during a cycle (units)T cycle time (unit of time) (decision variable)

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3.1.2 Assumptions. Several assumptions have been made in the development of themodel:

(1) The demand for the bottles is assumed to be constant for each cycle but mayvary from one cycle to another.

(2) It is assumed that demand is always met from the newly produced andremanufactured bottles. Therefore, this model assumes neither shortages norexcess inventory of bottles.

(3) In this model if the contaminated bottles are sold to the low-grade plasticindustries, any profit generated goes to the collection company. These bottlesare given to the Bottle Collection Company in exchange for transporting thenon-contaminated bottles to the manufacturing company. This is reasonablegiven that the firm would like to remain sustainable by saving onenvironmental costs related to transportation (Wong, 2010).

The above assumptions are similar to those made in the literature (e.g. Ferrer, 1997;El Saadany and Jaber, 2010, 2011; El Saadany et al., 2013).

3.2 Flow diagram for a plastic bottle recycling systemThe production, remanufacturing, recycling, and waste disposal system for plasticbottles investigated in this paper is depicted in Figure 1. Bottles are collected fromthe market at a rate yD; and then sorted by the Bottle Collection Company intonon-contaminated bottles at a rate ayD and contaminated bottles at a rate (1a)yD.The non-contaminated bottles are sorted furthermore by the Bottles Collection Companyinto whole non-contaminated bottles and damaged non-contaminated bottles. Thenon-contaminated bottles are then transported to the Bottle Manufacturing Company

Process D

Production

Qp Serviceable

V.Material andRegrind Mixing

Recycling/Reuse/RemanufacturingMaterial Mixing Qr

Remanufacturing

Qvm Process C

(0 < < 1)

Process B

(0 < < 1)D

DMarket

D(0 < < 1)

Process ABottle Collection Company

Non-Servicable

Stock

(1 ) DProcess E (0 < < 1)

Low Grade MarketLandfill / disposal

Contaminated bottle sort and Landfill disposal

Process F(1 ) D(1 )

Bottle Manufacturing Company

(1 ) D

(1 ) D D

Figure 1.Flow diagramfor plastic bottlerecycling-reuse system

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where the non-contaminated whole bottles are remanufactured at a rate bayD andthe damaged non-contaminated bottles are used as regrind at a rate (1b)ayD in theproduction of new bottles. The regrind is mixed with virgin material, Qvm, to producethe new bottles. The production of new bottles, Qp, plus the remanufactured bottles, Qr,divided by the cycle time T equals the required demand rate D in one cycle. Thecontaminated bottles are sorted into two streams: badly contaminated bottles which aredisposed of in a landfill at a rate (1f)(1a)yD and bottles that can be sold to industries(such as various industries within construction) that use low-grade plastic material ata rate f(1a)yD. Processes A to F are indicated in Figure 1. The operation costs of theseprocesses will be discussed in detail in 3.3.

3.3 The modelThe model presented in this section is different from those in the literature in that ituniquely considers producing, recycling, and remanufacturing in one model. It is alsounique in its treatment of the disposed items that are classified as either low-gradeitems suitable for a secondary market (e.g. construction industry) or for the landfill.In addition, this paper is also unique in that it accounts for landfill rehabilitationand penalty costs for disposing waste. Unlike the literature in this area (e.g. Dobos andRichter, 2004, 2006; El Saadany and Jaber, 2010, 2011; El Saadany et al., 2013), thispaper explores the benefits of using more environmentally friendly (biodegradable)material. This is an interesting initiative that may pave the way towards morechallenging and interdisciplinary research focused on integrating material science andengineering design into inventory, supply chain and reverse logistics managementdecisions. This is a challenging future research venue that the authors will pursue.

Six processes were considered in the development of the mathematical model. It is tobe noted that the cycle time used in these processes is the same even though the bottlecollection will begin earlier than the production. However, for coordination purposes,the length of the cycle for collection is the same as that for production. This is done inorder to correctly calculate cost allocation. Although a logistics system like the onedescribed in Figure 1 may consist of entities that are independently owned, theliterature reveals that the joint economic lot sizing problem produces a lower systemtotal cost than independently optimising the cost of each entity (e.g. Jaber andZolfaghari, 2008; Glock, 2012). So, this paper considers a centralized lot sizing policywhere the cycle time, T, is common for all processes. A decentralized lot sizing policy issurely worth investigation but is beyond the scope of this paper. A future work thataddresses this limitation is possible. The six processes are described next.

3.3.1 Process a: non-serviceable stock (Bottle Collection Company). The BottleCollection Company collects the bottles produced by the manufacturer and discarded bythe users at a rate yD, where the accumulated quantity during a cycle is yDT. The BottleCollection Company sorts the bottles into three streams: non-contaminated whole bottlesand damaged bottles at a rate ayD and contaminated bottles at a rate (1a)yD. Duringthe sorting process a vision system is used to select the required bottles that are sent tothe bottle manufacturing company. The inventory total cost per unit of time (i.e. the totalprocess cost divided by the cycle time) for process A is given as:

TCUnss KnssT

CLS CCO hnss yDT2

1

Equation (1) is convex since d2=dT2TCUnss 2knss=T3, 8 T40 since Knss40.

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3.3.2 Process B: remanufacturing. The quantity of bottles remanufactured in onecycle is Qr bayDT lrT and it depletes to zero at a rate lr during t2. Prior todepletion, these bottles maybe held for t1 time units prior to being remanufactured,where T t1 t2. The non-contaminated whole bottles are remanufactured by acustomized automated or semi-automated process where they are de-labelled, cleanedand sanitized, polished and relabelled. Elaborating the technology required to performthis process is beyond the scope of this paper. The inventory total cost per unit of timefor process B is given as:

TCUr KrT CLr CMat hr

T

QrQp

D Q

2r

D Q

2r

2lr

2

where QPPT. Equation (2) is convex since d2=dT2TCUr 2Kr=T3 8 T40 sinceKr40.

3.3.3 Process C: regrind and virgin material mix. The quantity of regrind((1b)ayDT) and virgin (QvmT) material mix in one cycle is RM which is depleted fullat a rate lrm over t2. This material may be held for a period t1 prior to mixing, whereT t1 t2. The damaged non-contaminated bottles are recycled where they arede-labelled, cleaned, ground into flakes and processed to produce new and improvedquality PET pelletized material. The inventory total cost per unit of time for process Cis given as:

TCUrm KrmT

CLrm Cvm hrmT

RMQp

D RMQr

D RM

2

2lrm

3

where RM QvmT 1 b ayDT 1 aby DT and Qvm D bayD 1 b ayD 1 ay D with QP and Qr being functions of T as denoted earlier.

Equation (3) is convex since d2=dT2TCUrm 2Krm=T3 8 T40 since Krm40.3.3.4 Process D: bottle manufacturing. QP units of new bottles are replenished at a

rate P over T, QPPT. New bottles are produced by a two-step moulding processwhich requires two separate machines; one to make the pre-form of the bottle and thesecond to inflate the shape of the bottle by using stretch blow moulding. Thereforeonce the pre-form is made it is transferred to the stretch blow moulding stage to createthe final shape of the bottle. The inventory total cost per unit of time for process D isgiven as:

TCUp KpT CLp hp Qp

24

Similar to Equations (1)-(3), Equation (4) is convex since d2=dT2TCUp 2Kp=T3 8T40 since Kp40.

3.3.5 Process E: contaminated bottle sort (Bottle Collection Company). Thecontaminated bottles are sorted into two streams where a percentage of the bottles willgo to the landfill and the other percentage will be sold to industries that use a lowergrade of plastic material. However, in our case we will only be concerned with the costof the bottles that go to the landfill. Contaminated bottles for disposal are sorted at arate L and the amount of contaminated bottles to be disposed of in the landfill is BLf,

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where L (1f)(1a)y and BLfLDT. The inventory total cost per unit of time forprocess E is given as:

TCUSc KScT CLSc hSc BLf

25

Equation (5) is convex since d2=dT2TCUSc 2KSc=T340 8 T40 since KSc40.3.3.6 Process F: landfill disposal cost. Since the bottles placed into the landfill are

assumed to decay exponentially, a cost equation needs to be developed for each timequantities of bottles are placed into the landfill. Quantities of bottles that are placedinto the landfill take time to decompose to zero (quantity); therefore as the bottlesdecompose in the ground the cost must be captured for the use of the real-estate and forthe admitting of chemicals into the environment. Therefore, the present value is used tobring back the total cost at the end of every cycle (T ).

Since exponential decay can describe the decomposition of material in ecologicalsystems (Kot, 2001) it will be applied in this paper to capture the decay of two-Literplastic bottles when disposed of in a landfill at the end of each cycle. We define N(t) asthe quantity at time t and l is the decay rate, where N t N0elt and N0 is the initialdisposed quantity (i.e. the quantity at time t 0).

The use of the land to dispose bottles until they fully decompose has a real-estaterental cost per bottle which is denoted as Cre and a rehabilitation and penalty cost perbottle which is denoted as Crh. Using the present value approach, the cost for landuse, rehabilitation and environmental damage of disposing bottles into a landfillare brought back at the end of every cycle. Defined as N t N0elt , Cre is thereal-estate rental cost per bottle and Crh is the rehabilitation and penalty cost perbottle. The single amount future-value of Cre Crh N t Cre Crh N0elt .Also, the amount of plastic bottles disposed in the landfill by the end of cycle T is N0,where N t N0el tT ) N T N0el TT N0. So, N t N0el tT ; t 2T;1 is equivalent to N t N0elt; t 2 0;1. The inventory total cost per unit oftime for process F is given as:

TCULF KLFT

CLF Z1

0

Cre Crh N0eiteltdt KLFT

CLF CreN0i l T

CrhN0

i l T 6

where N0 1 f 1 a yDT . Equation (6) is a continuously decreasing functionin T since d=dTTCULF KLF=T2o0 and d2=dT2 2KLF=T340 8T40since KLF40.

3.3.7 Closed form solution. The total system unit time cost is the sum of Equations(1)-(6) and is given as:

TCU TCUnss TCUr TCUrm TCUp TCUSc TCULF Knss

T CLS CCO hnss yDT

2 Kr

T CLr CMat hr

T

QrQp

D Q

2r

D Q

2r

2lr

KrmT

CLrm Cvm hrmT

RMQp

D RMQr

D RM

2

2lrm

Kp

T CLp hp Qp

2

KScT CLSc hSc BLf

2

KLF

T CLF CreN0

i l T CrhN0

i l T

7

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where Qr bayDT UDT lrT , Qp PT 1 U DT , RM 1 aby DT 1 U DT lrmT , BLf N0 1 f 1 a yDT LDT .

Substituting these terms in Equation (7), differentiating Equation (7) w.r.t T, settingthe first derivative equal to zero, and solving for T we get:

T

2K

D hnssy hrU hrm hp 1 U hScL

s

2K

DH

r8

where KKnssKrKrmKpKScKLF . Note that it was shown before thatEquations (1)-(5) are convex in T, with the exception of Equation (6) which is acontinuously decreasing function in T. The sum of convex functions is a convexfunction suggesting that the sum of Equations (1)-(5) is a convex function. Note thata function to be convex is formed by the sum of continuously decreasing andincreasing functions of the decision variable, so adding a continuously decreasingfunction to the sum will not affect convexity. Therefore, Equation (7) is convex forevery T40. It is clear that the cycle time T in Equation (8) increases (decreases) as Kincreases (decreases) and/or D and/or H decreases (increases). This is a typicalbehaviour as Equation (8) is similar in form to the EOQ model. Substituting Equation(8) in Equation (7) along with the necessary terms, Equation (7) can then be written as:

TCU 2KDH

p C Cre Crh LD

i l ; 9

where C CLS CCO CLr CMat CLrm Cvm CLp CLSc CLF . The total costin Equation (9) increases as the following (or any of them) terms: K, D,H, CLS, CCO,CLrm, Cvm, CLp, CLSc, CLF, Cre, and Crh increase (s), or as i and(or) l decrease(s).

4. Numerical resultsThis section provides numerical examples to illustrate the behaviour of themathematical model and discusses the results. Consider a production-recycle-disposalinventory system with D 50,000 bottles/month and the input parameters listedin Table I. Not included in Table I are the unit holding costs for the five processeswhere bottles of different grades are held, which are hnss 0.03 and hr hrmhp hSc 0.02. Using the input parameters listed in Table I, the optimal solutionwas found from Equations (8) and (9) for values of y, a, b, and f of 0.25, 0.5, and 0.75.The results are summarized in Table II.

The results from Table II show that the percentage of bottles remanufactured, b,does not affect the total system cost per unit of time, TCU, as significantly as thepercentage of bottles collected y, the percentage of non-contaminated bottles a andthe percentage of contaminated bottles sold to industries that use low-grade material f.For example, when y b a 0.25 (Examples 1-3), TCU decreases by about 20per cent (from 17,761 to 14,223) when the percentage of contaminated bottles that canbe sold as low-grade material, f increases from 0.25 to 0.75 of the demand rate. Wheny af0.25 (Examples 4-6), the decrease in TCU is insignificant (from 17,761 to17,715) when b increases from 0.25 to 0.75 of the demand rate. Also, it was observedthat when the percentage of bottles (of all grades) collected, y, has the highestcoefficient it has the most effect on TCU. For example, when b af 0.25 (Examples10-12), TCU increases by about 64 per cent (from 17,761 to 29,070) when y increases

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Parameter Description

Knss All setup costs included are aggregates of three primary costs: preparation, equipmentmaintenance (collection trucks and machinery) and overhead. It is assumed that theprep-process takes 2 hours labour at $20/hr, maintenance $80 per set-up and $180 perset-up for space rental to house the equipment and administration. This gives a total of$300 per set-up

Kr It is assumed the preparation process takes 1 h labour at $20/hr, maintenance $30 perset-up and space rental to house the equipment and administration at $75 per set-up to atotal of $125 per set-up

Krm It is assumed to take 2 hours labour at $20/hr, maintenance $40 per set-up and spacerental to house the equipment and administration at $120 per set-up. Therefore the totalof this set-up is $200

KP It is assumed the preparation process takes 1 h labour at $20/hr, maintenance $30 perset-up and space rental to house the equipment and administration at $75 per cycle.This gives a total of $125 per set-up

KSc It is assumed the prep-process takes 1 h labour at $20/hr, maintenance $20 per set-upand space rental to house the equipment and administration at $60 per set-up to a totalof $100 per set-up

KLF This setup cost includes machine rental and their operators. It is assumed the labour is3 hours at $40 per set-up; and machine rental $80 per set-up. Therefore, this total cost is$200 per set-up

CLs This labour cost includes loading collected items on a conveyor belt and collection of thesorted bottles and the operation of the vision system. It is assumed in one hour 15,000units can be loaded on a conveyor belt and only 10% are manufacturers bottles. Thismeans in one hour 1,500 bottles are collected. Since this operation requires 2 operators,one at the loading and one at the receiving end, the labour cost is (2$10)/1,500 $0.013per bottle and the cost for the vision system is $0.002 per bottle. This gives a total of$0.015 per bottle; when multiplied by yD this gives the labour cost for sorting bottlesafter collection per cycle

CCo This labour cost includes a truck and two labourers. It is assumed the cost of the truckand two labourers are $60 per hour and the truck collects 60,000 items in an hour inwhich 10% are the required brand of bottles, this cost would be $0.01 per bottle; whenmultiplied by yD this the gives labour cost for bottle collection per cycle

CLr Here it is assumed that 2 labour hours at $10 dollars per hour are required to clean,sanitize and pack 200 bottles per hour. Therefore the labour cost is $0.1 dollars perbottle. Add to this cost $0.03 per bottle for the cost to run the machinery. This gives arunning cost of $0.13/bottle; when multiplied by bayD which equals lr this gives thelabour cost for remanufacturing per cycle

CMat This process involves cleaning agent/solvent, clear coat polish and labels. It is assumed$2 is required for the solvent and clear coat for 200 bottles and the label is $0.01 perbottle. Therefore, the material cost is $0.02 per bottle; when multiplied by bayD thisgives the material cost for remanufacturing per cycle

CLrm This process involves de-labelling the bottles, cleaning and grinding the material intoflakes and processing it through a Recycling line- recoSTAR PET machine whichproduces new and improved quality PET pelletized material due to solid statepolycondensation. Consider 1.5 labour hours at 10 dollars per hour required to process1000 bottles; and 5 dollars per hour for the cost to run the machinery for the 1000 bottlesper hour. Then the total cost is $0.02 per bottle; when multiplied by [Qvm (1b)ayD]which equals lrm. This gives the labour cost for regrind and mixing per cycle

Cvm This is a variable amount and is based on the demand. However, the material requiredfor supplementing the re-grind material to produce new bottles is considered to be $0.03/bottle. For the cycle this cost is obtained from $0.03 multiplied by Qvm

(continued)

Table I.Input parameters for

numerical example

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from 0.25 to 0.75 of the demand rate. The systems best performance occurred wheny and b af 0.75 where TCU 12,672 (Examples 34).

Upon further analysis of Table II, it is also evident that the cost of landfilldisposal (TCULF) can have a significant effect on the total system unit time cost(TCU). As the amount of bottles placed in the landfill increases the cost of landfilldisposal increases. By examining the process unit time cost equation of landfilldisposal (Equation 6), an increase in the decay rate l causes a decrease in TCULF.The current material being used to produce plastic beverage bottles is PET whichyields a very low value for the decay rate l which is 0.000256/month. Therefore, inorder to increase the decay rate and reduce the process unit time cost of landfilldisposal (TCULF), alternative materials must be used which take less time tobiodegrade in a landfill. As previously noted, Samarasinghe et al. (2008) created andtested biodegradable plastic composites from CGM while Otaigbe et al. (1999)experimentally developed and tested a biodegradable soy protein-starch plastic(SPSP). Both of these alternative plastic materials represent intriguing possibilitieseven though further testing would be required for applicable use in the production of

Parameter Description

CLp This involves a two-step moulding process which requires two separate machines; oneto make the pre-form of the bottle and the second to inflate the shape of the bottle byusing stretch blow moulding. Each machine is operated by a skilled operator at $15.00per hour. Assuming this process can produce 240 bottles per hour which gives $0.125/bottle, plus $0.025/bottle for the cost to run the machines and labelling. Then the totalcost is $0.15 per bottle; when multiplied by [Qvm (1b)ayD] this gives the labour costfor bottle production/manufacturing

CLSc This process requires more labour work than the prior sorting process because itrequires more time to determine if a bottle is badly contaminated and will be disposed inthe landfill or if a bottle is contaminated but can be sold to industries that require a lowergrade of material. Although this process does not require a vision system, its longerinspection time justifies charging the same as the other sorting process i.e. $0.015 perbottle; when multiplied by (1f)(1a)yD this gives the labour cost for contaminatedbottle sort

CLF This process involves an operator placing these contaminated bottles together withother disposables of different unrelated processes into a landfill. Although the number ofbadly contaminated bottles to be disposed of in the landfill is determined, it is difficult toestimate how many bottles will be part of each process. Therefore a flat fee of only $25dollars is charged per disposal

Cre It is assumed that a square foot of rural land can be rented for $0.5. It is also estimatedthat four bottles occupy approximately one cubic foot and if bottles are piled on theaverage 10 feet high, then one square foot of land carries 400 bottles. Therefore thereal-estate rental cost is $0.00125/bottle/month

Crh The cost of the rehabilitation of the land per bottle will be similar to the real-estate rentalcost per bottle. However, a penalty for the effect on the environment is added andassumed to be three times the cost of rehabilitation. Therefore the cost of rehabilitationand the penalty will be $0.005 bottle/month. It is to be noted that a good approximationof the cost of the effect of disposing bottles in a landfill on the environment is extremelydifficult to evaluate therefore we have assumed three times the cost of rehabilitation(1 for cleaning the water, 1 for cleaning soil, 1 for protecting wildlife)

l It is estimated that it takes approximately 450 years for plastic beverage bottles to fullybiodegrade in a landfill. Using the exponential decay half life where l ln(2)/t, the decayrate (l) is found to be 0.0256% per monthTable I.

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beverage bottles because they can be injection moulded. These materials have hightensile strength, high elongation at break and high water resistance. Also, sincethese plastic materials are biodegradable, and mostly consist of natural substances,they can degrade in a landfill in an environmentally benign manner within months(Samarasinghe et al., 2008). By taking this into account, the decay rate willdramatically increase, and the penalty can be eliminated from the rehabilitationpenalty cost per bottle. Now, the value for Crh is $0.00125/bottle/month whichrepresents a rehabilitation cost per bottle. This will result in a decrease of TCULF,hence, decreasing the total system unit time cost (TCU) as seen in Table III.

The use of biodegradable plastic materials has immense benefits because they canfully degrade in a landfill within months and they are environmentally safe. In turn, thisprovides tremendous cost savings because it lowers the landfill disposal cost (TCULF)which ultimately lowers the total system unit time cost (TCU ), as shown in Table III.

Example y a b f T TCUnss TCUr TCUrm TCUP TCUSc TCULF TCU

1 0.25 0.25 0.25 0.25 0.917 812 261 3,060 7,970 279 5,379 17,7612 0.25 0.25 0.25 0.5 0.925 810 260 3,062 7,973 222 3,665 15,9923 0.25 0.25 0.25 0.75 0.934 809 258 3,065 7,976 164 1,951 14,2234 0.25 0.25 0.25 0.25 0.917 812 261 3,060 7,970 279 5,379 17,7615 0.25 0.25 0.5 0.25 0.919 811 385 3,038 7,847 279 5,379 17,7386 0.25 0.25 0.75 0.25 0.922 811 509 3,016 7,724 279 5,378 17,7157 0.25 0.25 0.25 0.25 0.917 812 261 3,060 7,970 279 5,379 17,7618 0.25 0.5 0.25 0.25 0.928 810 384 2,946 7,850 222 3,665 15,8769 0.25 0.75 0.25 0.25 0.940 808 507 2,833 7,729 164 1,950 13,990

10 0.25 0.25 0.25 0.25 0.917 812 261 3,060 7,970 279 5,379 17,76111 0.5 0.25 0.25 0.25 0.837 1,297 397 2,926 7,820 448 10,536 23,42512 0.75 0.25 0.25 0.25 0.775 1,761 531 2,799 7,679 609 15,692 29,07013 0.5 0.5 0.5 0.25 0.864 1,296 1,136 2,609 7,085 337 7,105 19,56914 0.5 0.5 0.5 0.5 0.874 1,296 1,135 2,611 7,088 263 4,819 17,21215 0.5 0.5 0.5 0.75 0.884 1,296 1,134 2,613 7,091 188 2,534 14,85516 0.5 0.5 0.25 0.5 0.864 1,296 640 2,699 7,581 263 4,822 17,30217 0.5 0.5 0.5 0.5 0.874 1,296 1,135 2,611 7,088 263 4,819 17,21218 0.5 0.5 0.75 0.5 0.884 1,296 1,631 2,523 6,594 262 4,817 17,12219 0.5 0.25 0.5 0.5 0.855 1,297 642 2,885 7,578 338 7,107 19,84620 0.5 0.5 0.5 0.5 0.874 1,296 1,135 2,611 7,088 263 4,819 17,21221 0.5 0.75 0.5 0.5 0.894 1,296 1,630 2,337 6,597 187 2,531 14,57822 0.25 0.5 0.5 0.5 0.940 808 631 2,903 7,605 183 2,520 14,65023 0.5 0.5 0.5 0.5 0.874 1,296 1,135 2,611 7,088 263 4,819 17,21224 0.75 0.5 0.5 0.5 0.820 1,765 1,636 2,327 6,579 339 7,117 19,76325 0.75 0.75 0.75 0.25 0.859 1,770 3,491 1,716 4,730 282 5,394 17,38226 0.75 0.75 0.75 0.5 0.867 1,771 3,491 1,716 4,731 226 3,680 15,61527 0.75 0.75 0.75 0.75 0.874 1,772 3,491 1,716 4,732 170 1,966 13,84728 0.75 0.75 0.25 0.75 0.832 1,766 1,263 2,114 6,953 175 1,977 14,24829 0.75 0.75 0.5 0.75 0.852 1,769 2,376 1,916 5,844 172 1,972 14,04930 0.75 0.75 0.75 0.75 0.874 1,772 3,491 1,716 4,732 170 1,966 13,84731 0.75 0.25 0.75 0.75 0.820 1,765 1,265 2,674 6,950 285 5,405 18,34432 0.75 0.5 0.75 0.75 0.846 1,768 2,376 2,197 5,842 228 3,686 16,09733 0.75 0.75 0.75 0.75 0.874 1,772 3,491 1,716 4,732 170 1,966 13,84734 0.25 0.75 0.75 0.75 0.966 804 1,252 2,700 6,990 123 803 12,67235 0.5 0.75 0.75 0.75 0.917 1,296 2,375 2,204 5,856 147 1,385 13,26236 0.75 0.75 0.75 0.75 0.874 1,772 3,491 1,716 4,732 170 1,966 13,847

Table II.Optimal production-

recycling-disposalpolicies for differentnumerical examples

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Therefore, the uses of these types of plastic materials are advantageous when comparedto PET plastic material which takes an enormous amount of time to decay in a landfilland upon degradation admits dangerous chemicals such as BPA (bisphenol A) into theenvironmental water table. Table III illustrates how using biodegradable material reducesboth landfilling and rehabilitation costs. Other social and environmental costs couldalso be considered to further emphasize the benefits of using biodegradable material.For example, emission costs from transportation activities, costs of contaminating watertables and soil, and additional health costs could all potentially be considered. Thesecosts, however, are beyond the scope of this paper.

5. ConclusionIn this paper, a recycling-reuse model that remanufactures non-contaminated PETplastic bottles and uses regrind from damaged non-contaminated PET bottles mixedwith virgin PET material in the production of new bottles was developed and analysedin order to reduce the amount of plastic PET bottles that are disposed of in landfills.The model is assumed to have no shortages and the different percentages regarding theclasses of bottles are taken to be deterministic. In this model, a present value cost ischarged for landfill disposal. This cost included the use of real-estate, cost of landrehabilitation, and a penalty for contaminating the water and harming wildlife and theenvironment. In the analyses conducted on this recycling model, it was found thatthe percentage of bottles collected from the market y, had the largest influence onthe outcome of the total system unit time cost (TCU). This is because an increasein y caused the process unit time costs of bottle collection and sorting (TCUnss),remanufacturing bottles (TCUr), contaminated bottle sorting (TCUSc), and landfilldisposal of bottles (TCULF) to increase. This supersedes the decreasing process unittime costs of regrind and virgin material mixing (TCUrm) and the production of newbottles (TCUp). The use of alternative biodegradable plastics in place of PET was alsoexamined. It was shown that the use of biodegradable plastic materials made fromnatural contents such as CGM or soy protein-starch (SPS) are good candidates asalternative materials to PET. They degrade in a landfill in a significantly much shorterperiod of time and are made from environmentally safe substances that degrade in abenign manner. This in turn provides cost savings because the process unit time costfor landfill disposal (TCULF) decreases due to an increase in the decay rate (l) and theelimination of a penalty from the rehabilitation penalty cost per bottle (Crh). This inturn decreases the total system unit time cost (TCU ).

5.1 ContributionsThe model proposed in this paper makes several contributions to the literature.The most prominent original contribution of the model is that it charges a present

Material Time l TCULF TCU

PET 450 years 0.000256/month 4,819 17,212CGM or SPS 5 months 0.277/month 391 12,784CGM or SPS 4 months 0.347/month 364 12,757CGM or SPS 3 months 0.462/month 337 12,730CGM or SPS 2 months 0.693/month 310 12,703

Note: When y a bf 0.5

Table III.Decay rate comparisonof PET versus CGMor SPS material

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value cost for land use, land rehabilitation, and a penalty for contamination of theenvironment. This cost is unique to this model and underlines the importance ofexplicitly considering the costs of material being placed in a landfill. These costs havenot been systematically considered in the existing literature. In the paper, this cost wasarrived at by considering exponential decay and continuous compounding of interest.Other original contributions include the models ability to accommodate productsthat are created from a mix of recycled and virgin material, the potential sale ofcontaminated PET plastic bottles to industries that use low-grade plastic materials,and the possible effects of using biodegradable alternative materials. The existingmodels in the literature do not address these considerations. The paper thus contributesto the inventory management literature through its recognition that all recovered bottlesmay not be suitable for recovery, its emphasis on the environmental and social costs oflandfilling items, and underlining the importance of considering the impact of differentmaterials in plastic bottles.

5.2 Managerial implicationsThe paper has several important implications for managers of production, reuse,and recycling systems. At a fundamental level, the paper further underlines the needfor life cycle thinking with respect to the economic, environmental, and socialimpacts associated with PET plastic bottles. It highlights the need for improvedcoordination between bottle collection, production, and disposal systems. The paperalso provides insight into a number of policy changes that are required to drive moresustainable development. For example, the model indicates that there is a clear needto accommodate the use of alternative materials to PET in the production ofbeverage bottles. The use of alternative materials has the potential to substantiallyreduce the life cycle impacts of beverage bottles. In particular, in cases wherethe bottles are disposed, the alternative materials possess the benefits of rapiddegradation and reduced complications associated with BPA. There is also aneed to better account for the true costs of disposing PET bottles in landfills.Current models do not reflect the costs associated with land use, environmentalcontamination, and rehabilitation. Given the large percentage of PET bottles that arecurrently disposed of in the landfill, these costs are substantial. Implementingpolicies that take into account the true costs of disposal could serve as a furtherincentive in the reuse and recycling of beverage bottles. Moreover, the notion ofimproved accounting for the true costs of landfill disposal may have implicationsfor the disposal of other products.

5.3 Limitations and future workThe model is subject to several limitations that provide opportunities for additionalresearch. The model is explicitly focused on the recycling-reuse of PET plastic bottlesand it does not apply to metal bottles, metal cans, glass bottles, or bottles made ofother plastic materials. To accommodate the recycling-reuse of different typesof bottles, modifications to the model would be required. These modifications, suchas changes to the collection and production systems, exploring the use of alternativematerials in those contexts, or centralised vs decentralized lot sizing decisions, couldbe the subject of future research. The model also assumes that all six processesconsidered are under the control of a single decision maker. In practice, it is possiblethat the bottle manufacture, collection, and disposal will be handled by independententities. In such cases, it will be challenging to coordinate decision making so as to

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minimize the total system cost. However, the model underlines that a holisticperspective will lead to the most beneficial outcomes. An additional area of futureresearch could be the application of the learning curve effect to the model in order toreduce the different processing costs over time. Maity and Maity (2009) consideredlearning effects in their production-recycling model, with an emphasis on the impactof learning on setup costs and recycling cycles. Incorporating learning effects in themanual aspects of the plastic bottle recycling system explored in this paper couldprovide a basis for extending the model. Further research could also be carried out inprocesses of bottle sorting with the aim of reducing cost. For example, sorting carriedout in Process A and Process E could be combined to produce four streams: wholenon-contaminated bottles, damaged non-contaminated bottles, contaminatedbottles to be sold to industries that use low-grade plastic PET material and badlycontaminated bottles to be disposed of in a landfill. Future research could focus oncost savings from the combination of these two processes. Additional research on thefeasibility of employing alternative materials, such as CGM or SPS, in the productionof bottles on a large scale is also needed. It is important to acknowledge that the costsof replacing bottles made from PET material with alternative biodegradablematerials could be substantial. Therefore, future research should focus not only onthe production of these bottles on a large scale but also their production at a low cost.Modifications to the assumptions made in the paper, including varying demandwithin a cycle, accommodating varying cycle times, and accommodating shortagesor excess inventory, provide a further basis for additional research. Finally, like othermodels in the literature, the model developed in this paper still needs to be put intopractice. Access to empirical data remains the major obstacle in operationalizingsuch mathematical models. Unless academicians and practitioners collaborate toovercome this obstacle, mathematical models will largely function as theoreticalexercises.

References

Bonney, M. and Jaber, M.Y. (2011), Environmentally responsible inventory models: non-classicalmodels for a non-classical era, International Journal of Production Economics, Vol. 133No. 1, pp. 43-53.

Brisken, C. (2008), Endocrine disruptors and breast cancer, CHIMIA International Journal forChemistry, Vol. 62 No. 5, pp. 406-409.

Crisp, T.M., Clegg, E.D., Cooper, R.L., Wood, W.P., Anderson, D.G., Baetcke, K.P., Hoffmann, J.L.,Morrow, M.S., Rodier, D.J., Schaeffer, J.E., Touart, L.W., Zeeman, M.G. and Patel, Y.M.(1998), Environmental endocrine disruption: an effects assessment and analysis,Environmental Health Perspectives, Vol. 106 No. 1, pp. 11-56.

Dobos, I. and Richter, K. (2004), An extended production/recycling model with stationarydemand and return rates, International Journal of Production Economics, Vol. 90 No. 3,pp. 311-323.

Dobos, I. and Richter, K. (2006), A production/recycling model with quality consideration,International Journal of Production Economics, Vol. 104 No. 2, pp. 571-579.

El Saadany, A.M.A. and Jaber, M.Y. (2010), A production/remanufacturing inventory model withprice and quality dependant return rate, Computers & Industrial Engineering, Vol. 58No. 3, pp. 352-362.

El Saadany, A.M.A. and Jaber, M.Y. (2011), Production/remanufacture EOQ model with returnsof subassemblies managed differently, International Journal of Production Economics,Vol. 133 No. 1, pp. 119-126.

330

IJLM25,2

Dow

nloa

ded

by IQ

RA U

NIVE

RSIT

Y At

05:28

28 Se

ptemb

er 20

14 (P

T)

El Saadany, A.M.A., Jaber, M.Y. and Bonney, M. (2013), How many times to remanufacture?,International Journal of Production Economics, Vol. 143 No. 2, pp. 378-384.

Ferrer, G. (1997), The economics of tire remanufacturing, Resources, Conservation andRecycling, Vol. 19 No. 4, pp. 221-255.

Foolmaun, R.K. and Ramjeawon, T. (2012), Disposal of post-consumer polyethyleneterephthalate (PET) bottles: comparison of five disposal alternatives in the small islandstate of Mauritius using a life cycle assessment tool, Environmental Technology, Vol. 33No. 5, pp. 563-572.

Gaggino, R. (2012), Water-resistant panels made from recycled plastics and resin, Constructionand Building Materials, Vol. 35 No. 1, pp. 468-482.

Gironi, F. and Piemonte, V. (2011), Life cycle assessment of polylactic acid and polyethyleneterephthalate bottles for drinking water, Environmental Progress & Sustainable Energy,Vol. 30 No. 3, pp. 459-468.

Glock, C.H. (2012), The joint economic lot size problem: a review, International Journal ofProduction Economics, Vol. 135 No. 2, pp. 671-686.

Griffen, J.C. (1996), Evaluation of PET and recycled PET as replacements for a PETG packagingtray, Journal of Plastic Film & Sheeting, Vol. 12 No. 2, pp. 139-148.

Gurudatt, K., De, P., Rakshit, A.K. and Bardhan, M.K. (2005), Dope-dyed polyester fibers fromrecycled PETwastes for use in moulded automotive carpets, Journal of Industrial Textiles,Vol. 34 No. 3, pp. 167-179.

Harris, F.W. (1990), How many parts to make at once?, Operations Research, Vol. 38 No. 6,pp. 947-950, The Magazine of Management, Vol. 10 No. 2, pp. 136-152.

Ilgin, M.A. and Gupta, S.M. (2010), Environmentally conscious manufacturing and productrecovery (ECMPRO): a review of the state of the art, Journal of EnvironmentalManagement, Vol. 91 No. 3, pp. 563-591.

Jaber, M.Y. and Zolfaghari, S. (2008), Quantitative models for centralised supply chaincoordination, in Kordic, V., (Ed.), Supply Chains: Theory and Applications, I-TechEducation and Publishing, Vienna, pp. 307-337.

Kawamura, C., Ito, K., Nishida, R., Yoshihara, I. and Numa, N. (2002), Coating resinssynthesized from recycled PET, Progress in Organic Coatings, Vol. 45 Nos 2-3,pp. 185-199.

Kinoshita, H., Kaizu, K., Fukuda, M., Tokunga, H., Koga, K. and Ikeda, K. (2009), Development ofgreen composite consists of woodchips, bamboo fibers and biodegradable adhesive,Composites: Part B: Engineering, Vol. 40 No. 7, pp. 607-612.

Kot, M. (2001), Elements of Mathematical Ecology, Cambridge University Press, Cambridge.

Li, C., Yang, X. and Zhang, Z. (2008), An extended EOQ model in production-recycling system,The 4th International Conference on Wireless Communications, Networking and MobileComputing (WiCOM 08), pp. 1-5.

Maity, A.K. and Maity, K. (2009), A production-recycling inventory model with learning effect,Optimization and Engineering, Vol. 10 No. 3, pp. 427-438.

Maity, A.K., Maity, K. and Maiti, M. (2007), A production-recycling-inventory systemwith imprecise holding cost, Applied Mathematical Modelling, Vol. 32 No. 11,pp. 2241-2253.

Ocean Conservancy (2005), Pocket Guide to Marine Debris, The Ocean Conservancy,Washington, DC.

Oh, Y.H. and Hwang, H. (2006), Deterministic inventory model for recycling, Journal ofIntelligent Manufacturing, Vol. 17 No. 4, pp. 423-428.

331

Reverse logisticsinventory model

Dow

nloa

ded

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Otaigbe, J.U., Goel, H., Babcock, T. and Jane, J. (1999), Processability and properties ofbiodegradable plastics made from agricultural biopolymers, Journal of Elastomers andPlastics, Vol. 31 No. 1, pp. 56-71.

Palanza, P., Gioiosa, L., Vom Saal, F.S. and Parmigiani, S. (2008), Effects of developmentalexposure to bisphenol A on brain and behavior in mice, Environmental Research, Vol. 108No. 2, pp. 150-157.

Prins, G., Tang, W., Belmonte, J. and Ho., S. (2008), Developmental exposure to bisphenol Aincreases prostate cancer susceptibility in adult rats: epigenetic mode of action isimplicated, Fertility and Sterility, Vol. 89 No. 2, pp. E41-E41.

Rebeiz, K.S. (1996), Strength and durability properties of polyester concrete using PET and flyash wastes, Advanced Performance Materials, Vol. 3 No. 2, pp. 205-214.

Richter, K. (1996) The extended EOQ repair and waste disposal model, International Journal ofProduction Economics, Vol. 45 No. 1, pp. 443-447.

Rouilly, A., Orliac, O., Silvestre, F. and Rigal, L. (2006), New natural injection-mouldablecomposite material from sunflower oil cake, Bioresource Technology, Vol. 97 No. 4,pp. 553-361.

Samarasinghe, S., Easteal, A.J. and Edmonds, N.R. (2008), Biodegradable plastic compositesfrom corn gluten meal, Polymer International, Vol. 57 No. 2, pp. 359-364.

Schilling, C.H., Tomasik, P., Karpovich, D.S., Hart, B., Garcha, J. and Boettcher, P.T. (2005),Preliminary studies on converting agriculture waste into biodegradable plastics Part III: sawdust, Journal of Polymers and Environment, Vol. 13 No. 2, pp. 177-183.

Siddique, R., Khatib, J. and Kaur, I. (2008), Use of recycled plastic in concrete: a review, WasteManagement, Vol. 28 No. 10, pp. 1835-1852.

Tawfik, M.E. and Eskander, S.B. (2006), Polymer concrete from marble wastes andrecycled poly(ethylene terephthalate), Journal of Elastomers and Plastics, Vol. 38 No. 1,pp. 65-79.

Tchobanoglous, G., Theisen, H. and Vigil, S. (1993), Integrated Solid Waste Management:Engineering Principles and Management Issues, McGraw-Hill, Boston, MA.

Thompson, R.C., Moore, C.J., vom Saal, F.S. and Swan, S.H. (2009), Plastics, the environment andhuman health: current consensus and future trends, Philosophical Transactions of theRoyal Society-B, Vol. 364 No. 1526, pp. 2153-2166.

United States Environmental Protection Agency (US EPA) (2010), Municipal Waste in the UnitedStates: 2009 Facts and Figures, US EPA, Washington, DC, available at: www.epa.gov/osw/nonhaz/municipal/pubs/msw2009rpt.pdf (accessed 6 October 2011).

Wong, C. (2010), A Study of Plastic Recycling Supply Chain, The chartered institute of logisticsand transport, University of hull business school and logistics institute, available at:www.ciltuk.org.uk/portals/0/documents/pd/seedcornwong.pdf (accessed 12 April 2013).

World Commission on Environment and Development (1987), Our Common Future, OxfordUniversity Press, Oxford.

About the authors

Nouri Matar holds a BEng and MASc in Industrial Engineering from the Ryerson University.He has worked as a Design and Manufacturing Engineer for companies in the USA and Canada.

Mohamad Y. Jaber is a Professor of Industrial Engineering at the Ryerson University.He obtained his PhD from the University of Nottingham. His research interests include modelinglearning and forgetting processes and their applications, inventory management in supplychains and reverse logistics, and thermodynamic analysis of production and inventory systems.He has published more than 100 articles in internationally reputable journals and conference

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proceedings. He is the editor of the book Inventory Management: Non-Classical Views and theforthcoming one Learning Curves: Theory and Modern Applications, both with CRC Press.He is an Area Editor for Computers & Industrial Engineering. His industrial experience is inconstruction management and he is a member of several professional societies. ProfessorMohamad Y. Jaber is the corresponding author and can be contacted at: mjaber@ryerson.ca

Cory Searcy is an Associate Professor and the Director of the Industrial Engineering Programat the Ryerson University. He is also an Associate with the International Institute for SustainableDevelopment (IISD). His current research focuses on sustainability indicators, sustainabilityreporting, and sustainable supply chain management. He has published in a number ofinternational journals, including the Journal of Cleaner Production, the International Journal ofProduction Economics, and the Journal of Business Ethics.

To purchase reprints of this article please e-mail: reprints@emeraldinsight.comOr visit our web site for further details: www.emeraldinsight.com/reprints

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