etail-colletion Networ Design under Deposit-efund io Wojanowsi, Vedat Verter * and Tamer Boyai Faulty of Management MGill University Montreal, Quebe H3A 1G5, Canada Anowledgements: This researh has been supported in part by a grant from the Soial Sienes and Humanities esearh Counil of Canada (41--75). The omments and suggestions of an anonymous referee were very helpful in improving the paper. This submission was handled by Gilbert Laporte. * Corresponding Author: E-mail: Vedat.Verter@mgill.a, Fa # 514-398-3876.
Abstrat This paper studies the interplay between industrial firms and government onerning the olletion of used produts from households. The fous is on the use of a deposit-refund requirement by the government when the olletion rate voluntarily ahieved by the firms is deemed insuffiient. We present a ontinuous modeling framewor for designing a drop-off faility networ and determining the sales prie that maimize the firm s profit under a given deposit-refund. The ustomers preferenes with regards to purhasing and returning the produt are inorporated via a disrete hoie model with stohasti utilities. Through parametri analyses, we determine the net value that an be reovered from a returned produt as a ey driver for the firm to voluntarily engage in olletion. We show that a minimum deposit-refund requirement would not ahieve high olletion rates for produts with low return value and point out two omplementary poliy tools that an be used by the government. Key words: everse Logistis, Colletion, Deposit-efund, Networ Design, Continuous Model, Disrete Choie Model.
1. Introdution esoure reovery involves diverting used produts from the waste stream and seizing their remaining value via reuse, reyling and/or re-manufaturing. This redues the use of virgin natural resoures, mitigates environmental pollution and eases the burden on limited landfill spae for the waste stream. Providing a means for minimizing the environmental eternalities of the onsumption-oriented eonomies, resoure reovery programs have attrated the attention of many regulatory bodies and governments. The European Parliament, for eample, enated a new Diretive in February 3 that requires the manufaturers to assume finanial responsibility for the reuse and/or reyling of waste eletrial and eletroni equipment (WEEE). Although suh requirements onstitute an additional liability for manufaturers, the value reovered from used produts provides an eonomi opportunity in some ases. For eample, in 1991 Xero Corporation launhed its Asset eyle Management Program that aimed at managing the inreasing volume of produts returned to Xero through ustomer tradeins and lease epirations. The resulting savings in the purhasing osts of new parts and raw materials were reported to be in the order of several hundred million dollars in 1995. In this paper, we fous on the olletion of used produts from households. This is a ommon first phase for many resoure reovery initiatives, and it provides the input for re-manufaturing and reyling proesses. Colletion effetiveness depends on the onsumers willingness to return used produts at the time of disposal. Therefore, it is important to provide the onsumers with onveniene and, if neessary, inentives to partiipate in the olletion program. A ommon eample of onveniene is the pi-up servies offered in the ase of heavy and buly ommodities, suh as used household applianes. When transportation osts assoiated with pi-up are eessive, firms typially establish olletion failities for onsumers to drop-off the used produts. Sine ustomers perform the transport tas in this ase, aessibility of the olletion failities is ruial. Inentives, suh as a ertain rebate at the time of return, an omplement onveniene in inreasing the return rate. In order to study the interplay between aessibility and inentives, we fous on the use of a drop-off poliy for olletion. Note that implementation of pi-up poliies also involves the routing of olletion vehiles 3
(Beullens et al., 3). A detailed aount of the olletion poliies used in the U.S. an be found in MMillen and Sumatz (1). The regulators aspiration with regards to environmental sustainability frequently translates into required rates for resoure reovery. The WEEE Diretive, for eample, establishes target reyling rates for refrigerators and washing mahines at 75%, athode ray tubes used in TV and omputer monitors at 7% and omputer equipment at 55%. When resoure reovery is not eonomially viable for the industry, voluntary olletion programs may not be suffiient to ahieve the target reovery rates. In suh ases, governments an resort to a wide spetrum of poliy tools to failitate ahievement of their targets. Mandatory tae-ba legislation, suh as Germany s paaging reyling law implemented via the well-nown Green Dot program, onstitutes the most radial approah that is typially diffiult to enfore. Prie-based poliies onstitute a less hallenging option in terms of implementation and monitoring. Eamples of suh poliies inlude taes on the use of virgin materials, reyling subsidies, disposal fees and deposit-refund requirements (Fullerton and Wu, 1998). Eonomis literature provides evidene that deposit-refund is the most preferable poliy in terms of the total ost of aomplishing a ertain disposal redution (Palmer et al., 1997; Palmer and Walls, 1997; Sigman, 1995). Motivated by this fat, in this study we represent government s involvement in the olletion ativity via a minimum deposit-refund requirement. A deposit-refund system requires onsumers to pay a ertain deposit at the time of purhase, whih is refunded upon the return of the used produt. Suh systems have been ommonly used in promoting return and reuse of produt paages and ontainers e.g., aluminium ans and glass bottles (OECD, 3). Other eamples of government-initiated deposit-refund systems inlude ar batteries and tires (aymond, 1). In his seminal wor, Bohm (1997) argued that deposit-refund an be used by regulators as an effetive poliy tool in a wide range of industries. Many industry representatives, however, epressed onern over the impat of deposit on retail prie and often lobbied against deposit-refund requirements pointing out a possible redution in sales. In Germany, for eample, the January 3 deposit law is pereived to have aused a to 6 perent drop in sales by an and bottle manufaturers (Bioyle, 3). Although the maro benefits of deposit-refund systems are well studied by eonomists, there is no published 4
researh analyzing their impat on the manufaturers operations. A solid understanding of the firm-level impat of deposit-refund requirements, however, is ruial for their overall effetiveness. Our study is motivated by the need for analytial approahes that foster suh an understanding. In this paper, we develop a methodology for designing a drop-off faility networ under deposit-refund requirements. We adopt a ontinuous modeling approah and assume onstant population density over the maret area. Although approimate in nature, ontinuous models allow for the development of losed-form epressions that failitate analytial insights regarding the impat of problem parameters. Daganzo (1999) has devised this approah for the analysis of (forward) logistis systems. Continuous modeling has been used also for determining optimal maret areas (Erlenotter, 1989) and prodution-distribution networ design (Dasi and Verter, 1). eently, Fleishmann (3) presented a ontinuous model for the design of reverse logistis networs. In representing the olletion ativity, he assumed a onstant return rate over the maret area. We etend this approah by inorporating the impat of deposit-refund on both the sales rate and the return rate. Given a deposit-refund requirement, we provide a model to determine the optimal sales prie and olletion area radius so as to maimize the epeted profit of the firm. The variation among onsumers in terms of their response to a ertain deposit-refund is epliitly modeled in estimating the sales and return rates. In terms of inorporating the variability of individuals hoies in the analysis of deposit-refund systems, Kulshreshtha and Sarangi (1) onstitutes the most relevant study in the eonomis literature. The authors, however, are foused on the use of deposit-refund systems as a prie disrimination mehanism rather than the optimal design of olletion faility networs. In ontrast, the earlier researh for reverse logistis networ design is based on mied integer programming formulations, where the variability in the amount of return at eah ustomer loation is ignored (e.g., Barros et al., 1998; Fleishmann et al., 1; Jayaraman et al., 1999; Jayaraman et al., 3). In a reent paper, Guide and Van Wassenhove (1) alled on the industry to adopt a proative approah to used produt aquisition, rather than passively aepting the returns. Deposit-refund onstitutes an effetive means for the firm (as well as the 5
government) to influene the quantity, timing, and possibly the quality of returns. In Setion, we present an analytial framewor that inorporates deposit-refund in the olletion system design deisions of the firm. Setion 3 demonstrates the versatility of the proposed methodology by adapting it to the integrated retail-olletion networ design problem. In Setion 4 we present an illustrative eample to show that the firm an ahieve onsiderable additional profit by optimizing sales prie under deposit-refund rather than simply adding the deposit onto the retail prie. Our parametri analyses also indiate that the net value reovered from a returned produt is a ey driver for the firm to offer voluntary deposit-refund. Setion 5 points out that a minimum deposit-refund requirement would not ahieve high olletion rates for produts with low return value and studies the impat of two additional requirements that an be used by the government. ealizing the inadequay of a prie-based poliy (i.e., deposit-refund), these poliy tools are designed to improve olletion rate by imposing that the firm offers a ertain level of aessibility to its olletion failities. We provide some onluding remars in Setion 6.. Designing a Colletion System with Deposit-efund In this setion, we fous on the design of a olletion system to omplement an eisting retail networ. Most ompanies have a retail networ in plae when they deide to launh a olletion program, either on a voluntary basis or as a result of regulatory requirements. The olletion failities an be loated anywhere in the maret area while the retail networ usually remains unaltered during this proess. The aessibility of retail failities and the retail prie are among the ey fators that determine maret demand for a ommodity. We model the aessibility of retail as well as olletion failities using the ontinuous modeling approah for networ design. The basi premise of the ontinuous approah is to represent the population (or demand) in a maret area by a ontinuous funtion (i.e., density). The underlying assumption is that the density is onstant over the maret area. It is generally aepted that when ustomers bear the travel effort, they hoose the faility that is losest to them. Clearly, under these two assumptions, the maret will be served omprehensively by failities with equal-sized, non-overlapping servie areas. Furthermore, when the maret 6
area is suffiiently large ompared to the servie areas, the design of the networ boils down to speifying the size of eah servie area. From this, it is possible to determine the number of idential failities to install in the maret area. In this paper, we adopt the above desribed approah, with the only additional speifiation that the retail and olletion failities serve irular areas (see Figure 1 for a shemati representation). This assumption failitates mathematial analysis and is also ommon in earlier studies (e.g., Dasi and Verter, 1; Fleishmann 3). Clearly, irular servie areas imply that some segment of the maret would not be served, but when the maret is large ompared to the servie areas, this segment is negligible. As a result, we an represent the retail (olletion) networ in our framewor by simply speifying the radius of the retail (olletion) servie area. Travel distane to the faility Maret area with onstant population density etail or olletion faility with a irular servie area Figure 1: Continuous Model for Networ Design Let r denote retail prie of the ommodity and dr denote radius of the servie area for eah retail faility. In the sequel, we use d r as a proy for retail networ aessibility. We note, however, that dr provides only an aggregate measure of aessibility, sine at the individual level the aessibility depends on the eat distane to the losest retail faility. The firm inurs an annualized ost F r for eah retail faility that inludes the fied establishment and operating osts. Sine the retail faility networ is in plae, F r is a sun ost. We inlude it in the profit epression, however, so that the models in Setion and Setion 3 are omparable. Under a deposit-refund poliy, the ustomer is informed 7
that the retail prie inludes a deposit s, and it will be paid ba upon return of the used produt at a olletion faility. We assume that eah individual deides whether or not to return the used produt at the time of purhase and he/she does not have any other return option than the olletion failities of the firm. Similarly, we let F denote the annualized fied ost of establishing and operating a olletion faility, whih serves an area with radius d. The aessibility of olletion failities and the amount of deposit play a ey role in the ustomer s deision to partiipate in the olletion program. Let w denote the wholesale prie and p denote the net value that an be reovered from the returned produt (i.e., value of the return minus unit reovery osts). With this notation, the firm s profit per unit maret area an be epressed as: F F Π = ( r w) ρ ( p s) ρ π π, (1) r rd, B d dr where ρ B = average number of sales per unit area, and ρ = average number of returns per unit area. Eah term in (1) represents a fator (per unit area) that ontributes to the profit i.e., sales profit, gains/losses from produt reovery, fied olletion ost and fied retail ost, respetively. The firm an maimize its profit by determining the optimal values for r and d. We now turn our attention to deriving losed-form epressions for the average sales and return densities ρ B and ρ. Letφ denote the onstant population density of the maret area. Note that given d r, r and s, the ustomers lielihood of buying and returning the produt varies with the aessibility of olletion failities. There are φπ people at distane from a olletion faility, eah with the same probability P () of buying the produt and partiipating the olletion program. Sine the total number of returns to the faility is ρ d π, d = [ ( ) ] ρ d π φπ P d. () 8
Some of the ustomers who purhase the produt may not partiipate in the olletion program. Let P (N) represent the probability that an item is purhased and not returned by a ustomer at distane from a olletion faility. Naturally, the probability that a ommodity will be sold, whih we denote by P (B), is the sum of P () and P (N). Thus, d d B = = [ ( )] [ [ ( ) ( )]] ρ d π φπ P B d φπ P P N d. (3) P () and P (N) are determined by the ustomers individual preferenes. We use a disrete hoie model with stohasti utilities to represent these probabilities. Disrete hoie models with stohasti utilities are disussed in detail in Anderson et al. (199). Let u denote the minimum utility of onsuming the ommodity that is ommon to all individuals and β represent the additional utility that is different for eah individual. The ommon utility is deterministi and varies with ommodity type. The additional utility of eah individual, however, is not readily observable for the ompany and hene, we model β as a random variable. Thus, the utility attained by an individual via purhasing the ommodity an be represented as u( B) = β u hr dr, 3 (4) where h and are utility oeffiients for prie and travel distane, respetively. Although u(b) is stohasti for the firm, it is deterministi for eah individual; it is the realized value of β that differentiates the individual s purhasing preferene from the others. Note that under onstant population density and irular servie area assumptions, the average distane to a retail faility is /3 d r, 1 so the term /3 d r aptures the impat of the travel effort of the individual to the retail faility. We remar that we are using the average distane and hene an aggregate measure for retail networ aessibility. In reality, ustomers have varying distanes to the nearest retail faility. Unfortunately, inorporating the ustomer s atual distane to both the retail and olletion failities ~ d r ~ ~ φπ d / φπd = d. 3 1 Note that [ ] r r 9
signifiantly ompliates the derivation of the profit funtion (1) and renders subsequent analysis intratable. Sine our primary fous is on olletion, in order to preserve the tratability of our framewor, we model olletion networ aessibility more aurately (see (5) below), by inorporating the ustomer s atual distane to the losest olletion faility. The deision to return is intertwined with the purhase deision sine it affets the net prie under deposit-refund. A purhased item will be returned if the assoiated utility u () is greater than the utility of not returning u(n). Eah individual is onerned about environmental sustainability to a ertain degree. In modeling u (), we inorporate the variation among individuals with respet to the utility they obtain from being part of the olletion program via random variable ε. The utility of (buying and) returning the used produt is ( ) u ( ) = ε h 1 i s u( B) (5) where, represents distane to the losest olletion faility, t represents the average length of time the produt will be used and i denotes the interest rate per unit time period. The third term in (5) represents the utility assoiated with deposit refund at the time of return. Note that (5) is simplified onsiderably by ignoring the variation among individuals in terms of how long they use the produt. Clearly, the utility of refund depreiates while the produt is being used. We also assume that eah individual pereives a ommon utility u assoiated with remaining value of the produt after t time periods. The firm and the ustomer an assoiate different values to the used produt at the time of return i.e., u / h does not have to equal p. Thus, the utility of (buying and) not returning the used produt is t u( N) = u u( B ) (6) The probabilities P () and P (N) an be epressed using the above utility models. The produt will be purhased and returned if u ( ) > u( N ) and u ( ) positive. Thus, ( ) ( ) ( ) is P() = P( u > u N, u > ). Similarly, the produt will be purhased but not returned if u ( N) u ( ) and ( ) ( ) ( ) ( ) u N is positive and onsequently, P(N) = P( u N u, u N > ). Now, we derive the probabilities that mae up 1
P () and P (N). In order to inorporate maimum variability among individuals, we assume ε U [, L] and β U [, M ] the following distane terms: ( 1 ) ( ), where L<M. For the ease of eposition, we define t h i s u A = B C t h i s u hr = 1 d 3 u u hr dr 3 = Using (7) we an epress P () as P ( > A, > B) r (7) ε ε β. This joint probability an be omputed by onditioning on the value of ε. Thus, ( ) P ( ) = P ε β > B ε > A P( ε > A) (8) Using umulative distribution funtion of the uniform distribution we obtain, 1 ( A) < ( A) P( ε > A) = 1 ( A) L L (9) L< ( A) We evaluate (8) for eah range of values in (9). Note that ( ) B ( ) ( ) ( L M ) ( ) P() = for > A L. For A we obtain P ( )= P ( ε β > B) and through onvolution of uniformly distributed random variables ε and β : P( ε β > B) = ( B) 1 ( ) 1 B L LM ( B) L 1 L ( B) M M M B B L M M B L M ( ) 1 LM M M otherwise Now we turn to the values of [ A, A ]. For this range of values, L A (1) 11
( ) P ε β > B ε > A = P( ε β A > B) = P( ε β > A B) where U [, L ] ε and L = L (-A). Sine ε and β are always positive, P( ε β > A B) equals one for A<B. As in (1) we use the onvolution of ε and β to derive P( ε β > A B) for [ A, A ] : L P( ε β > A B) = ( B) 1 A ( A B) 1 ( A B) L LM ( A B) L 1 ( ) L L A B M A A M M ( A B) ( A B) ( ) ( L M ) 1 L ( ) M M A B L M LM M M otherwise (11) In ontrast with (1), the probability epression on ε β is solely determined by the distane terms A and B, whereas the range of ε varies with. Consequently, the intervals over whih piees of P( ε β > A B) are defined depend on as well. Note M that in (11) the first three intervals apply if B > A and the fourth interval applies if M B A. Having derived the building blos of P () over the entire range of, we now turn to P (N). Using (7) we an epress P (N) as P ( A, > C ) ε β. Sine ε and β are independent, the joint probability omprises the multipliation of ( ε ) and P ( β > C ) P A. Note that (9) provides the omplementary distribution for the former term, whereas the latter term an be omputed using the umulative distribution funtion of the uniform distribution as follows: Note that [ εε > A] ~ U [ A, L] 1
1 C < C P( β > C) = 1 C M. (1) M M < C We an now develop losed-form epressions for the average sales and return densities ρ B and ρ. Sine the probability funtions are pieewise, the integrals in () and (3) must be defined over eah interval. The details are provided in Appendi A. This results in a detailed epression for the firm s epeted profit (1), whih we maimize to determine the optimal retail prie r and olletion area radius d. The firm s profit depends on the hoies made by the ustomers with respet to buying and returning the produt. The aggregate impat of these individual hoies is inorporated in (1). Establishment of analytial properties of the proposed model is a formidable tas. Nonetheless, for a given set of parameter values, the model is amenable to solution in a spreadsheet environment. 3. e-designing the etail Networ under Deposit-efund The proposed analytial framewor is quite versatile for studying the olletion faility networ design problem under different strutural assumptions. Note that the model in Setion allows for the loation of olletion failities anywhere in the maret area. When resoure reovery is not a signifiant eonomi opportunity for the firm, establishment of failities dediated to olletion may not be viable. In this ase, firms may agree to offer olletion servies only at their retail failities. Thus, we provide a model for o-loation of retail and olletion failities in this setion. We assume that the integrated retail-olletion failities an be loated at any point in the maret area. Our aim is to identify ideal struture of the integrated faility networ. This provides a benhmar for assessing urrent onfiguration of the firm s failities and indiates the etent of re-struturing required. If the eisting retail failities are the only alternative sites for olletion, then the problem is amenable to solution by a disrete faility loation model. Let d ~ denote radius of the servie area for eah integrated faility. Sine the retail and olletion ativities are o-loated, the distane to a faility affets both the 13
purhase and the return deisions in this ase. In ontrast with (4), a onsumer s utility of purhasing the ommodity an be represented as u ' ( B) = β u hr. (13) t Consequently, u' ( ) = h( 1 i ) s u' ( B) ε and u' ( N ) = u u' ( B). Note that P( u' ( ) > u' ( N )) = P( u ( ) u( N )) hene (9) remains as a building blo > for the model in this setion. In deriving the probabilities that ' ( ) and ( N ) positive, however, we need to define new distane terms: ( 1 ) t h i s u hr B ' = u u hr C ' = In this ase, P () an be epressed as P ( > A, > B) a logi similar to the previous Setion, for values of < A ( > ' > ) = ( > ') u u ' are (14) ε ε β. Using P ε β B ε A P ε β B. Thus, through onvolution of random variables ε and β we obtain, P( ε β > B') = ( ') B ( ') ( ') ( ) 1 ( B') < 1 ( B') L LM ( B' ) L (15) 1 L ( B') M A M M B B L M 1 L M M ( B') L M LM LM LM otherwise For [ A, A ]: L ( ) P ε β > B ' ε > A = P( ε β A > B ') = P( ε β > A B) It is important that not only the range of ε but also the probability epression on ε β vary with in this model. Thus, onvolution provides: 14
P( ε β > A B') = ( ') A B ( ') ( ') ( ') ( ) 1 ( A B') < LM LM LM 1 ( A B') L LM A B L L 1 L ( A B') M A A M M A B A B L M 1 L M M ( A B') L M otherwise (16) that ( N ) u Note that (15) and (16) show strutural similarity to (1) and (11). The probability ' is positive, however, is quite different than the model in Setion. 1 C ' < C ' P( ε C) = 1 C ' M M. (17) M < C' It is important that (17) is a funtion of, whereas (1) is not distane dependent. The epeted sales and return densities ρ ' and ' B ρ an be modeled via epressions analogous to () and (3), respetively, where d ~ is replaed by d. Appendi B provides the details of integration. The firm s epeted profit per unit maret area is F Fr Π =, ( r w) ρ' B ( p s) ρ' rd. (18) d π The third term in (18) assumes that the eonomies of sale assoiated with o-loating retail and olletion failities is insignifiant. Interestingly, (18) redues to a retail networ design model (without olletion) for s = and u L. For this speial ase, we observe from (9) that P A P( u ( ) u( N) ) ( ε > ) = > =, and hene there are no returns. Having developed a methodology to represent the impat of deposit-refund on the firm s profit, we are now in a position to ondut omputational analyses to develop an understanding of voluntary and government-initiated olletion programs. 15
as 4. Firm-Initiated Deposit-efund: An Illustrative Eample We have done etensive numerial studies with the models proposed in Setions and 3. Our objetive for the remainder of this paper is to highlight the main insights we gained through these analyses. This setion illustrates the firm s perspetive on depositrefund systems via a set of hypothetial eamples. We first analyze a firm that has an eisting retail faility networ and optimizes its olletion faility networ design while simply adding the deposit onto the retail prie. We ompare the profit resulting from this base senario with that of an improved senario, whih involves optimization of retail prie as well as olletion area radius. This highlights the benefits that an be ahieved via the analytial framewor outlined in Setion. We then analyze a third senario to demonstrate the impat of return produt value on the firm s olletion and priing deisions. The model is implemented in an Eel spreadsheet. The base set of model parameters are depited in Table 1. In order to fous on a produt the firm is ompelled to ollet, the return produt value p is $1 in both base and improved senarios. We assume that the firm s eisting retail areas are optimal. Sine u = L in our parameter set, we set the deposit s= and use (18) to determine the optimal value for d = d r 7m. Utility Parameters Other Parameters L 1, F $5, M, F r $4, 3 /m w $4 h 1 /$ φ 1 people/m u,5 i. u 1, d r 7 m Table 1: Model parameters Let r denote the optimal retail prie when there is no deposit-refund. Setting s=, we use (1) to determine the firm s maimum profit as $5.3 per square-m attained at r = $467.8. There are no returns at this point and the average number of sales per square- 16
m is 3.4 units. To study the base senario, we fi r = r s and determine d maimize profit in (1). r,π d ~ so as to 7 6 5 4 3 1 r s Π* r ~ d * 1 8 6 4 1 8 6 4 ρ ρb ρ 5 1 15 5 3 s Figure : The impat of deposit-refund when it is added on retail prie r Figure shows the impat of refleting the inrease in deposit-refund diretly onto retail prie r while optimizing the olletion area radius d. Note that all the sold items are returned when s $68. Naturally, return density ρ inreases with s until s = $68. The ustomers who buy and not return the produt inur higher net retail pries as deposit-refund inreases (i.e., prie disrimination), whih eplains the sharp derease in sales density ρ B for values of s $68. One 1% olletion is ahieved the net retail prie remains the same for all ustomers who purhase the produt. The sales density ρ, however, ontinues to derease in s due to inreasing opportunity ost of the deposit (sine i =.). We assume the ustomer returns the produt after one time period i.e., t=1. Figure shows that the deposit-refund that maimizes the firm s profit is $ per unit, whih results in only 1% olletion. When s $, the net value aptured from B 17
returned produts (i.e., p-s) and the revenue through prie disrimination offset the loss of sales revenue due to inreased retail prie. Hene the firm will offer a voluntary deposit of $ in this ase. The profit delines as s further inreases and when s > $7 the firm inurs a loss due to the olletion ativity i.e., profit drops below that of s =. Note that by pulling out of olletion the firm would inrease the net retail prie to r s for all ustomers. Thus, the firm ontinues offering olletion until profit drops to zero in order to avoid a muh severe derease in sales. Now, we turn to the improved senario, where the firm optimizes both r and d. For inreasing values of s, Figure depits the optimal retail prie and olletion faility radius that maimize profit in (1). r,π d ~ 7 6 5 r s subsidy r* deposit r 1 8 4 3 ~ d * Π* 6 4 1 1 8 6 4 ρ ρ B ρ 5 1 15 5 3 s Figure 3: The impat of deposit-refund when the firm optimizes r and d The maimum profit is 185% of that of the base senario and it is attained at a deposit-refund of $94 per unit. In fat, a omparison of Figures and 3 shows that the 18
firm maes higher profit (and sales) for all deposit-refund values when both r and d are optimized. Note that the optimal retail prie is less than r when s $86. In this range, s an be interpreted as a tae-ba inentive provided by the firm to the ustomers who buy and return the produt. This omplements the lower retail prie in inreasing sales. Interestingly, the firm always subsidizes a portion of the deposit s in determining retail prie, sine returned produts have high value (i.e., p=$1). Figure also depits the part of deposit that is subsidized by the firm in determining the retail prie i.e., r s r. When s $1, however, the epeted number of returns would be too small to justify the fied ost F of establishing a olletion faility. This prompts the firm to withdraw from the olletion ativity by maing its failities inaessible to the ustomers (i.e., d taes a large value in the optimal solution of (1)). Consequently, ρ = for s $1 depited in Figure. It is important that the olletion rate at the voluntary deposit-refund of $94 per unit is 81%, notably higher than that of the base senario. The value of returned produts plays a ey role in determining the impat of deposit-refund on the firm s profit. To illustrate this, we fous on a third senario that involves another produt with onsiderably lower return value i.e., p=$6. The other model parameters are as in Table 1. Using (1), we find that offering olletion is eonomially viable for the firm only when $13 s $85, a muh narrower range of deposit values than the improved senario. The net value that an be aptured through olletion is redued due to the 5% derease in p. Thus, the number of returns required to justify F is higher in this senario. The redution in p also lowers the firm s inentive to subsidize s in determining the retail prie, whih auses a drop in sales. For values of deposit-refund higher than $85, the epeted profit falls below the level that an be attained when there is no deposit (s=). Therefore, the firm avoids suh a loss by withdrawing from the olletion ativity for s>$85. That is, d taes a large value in the optimal solution of (1) for s>$85, maing olletion failities inaessible to ustomers so as to push returns down to zero. In ontrast with the base ase, the ability to optimize retail prie enables the firm to avoid olletion when it is not profitable without inurring a sharp deline in sales. Note that the redution in profit as s inreases beyond a threshold as 19
is also prevalent in Figure. Sine p is higher in the improved senario, however, the firm offers olletion for a wider range of deposit-refund values. 5. Government-Initiated Deposit-efund In the previous Setion, we showed that the proposed methodology an be used for identifying the deposit-refund that maimizes the firm s profit. It is safe to assume that the firm will offer this deposit-refund voluntarily. Our analysis also identified returned produt value p as a ey fator in profitability of the olletion ativity. In order to approah the problem from the government s perspetive, this Setion presents a parametri analysis of the voluntary deposit-refund with respet to p (while the remaining model parameters are fied as in Table 1). This enables us to identify the potential inadequay of deposit-refund requirements when imposed single-handedly to improve olletion rate. Therefore, we also disuss two additional requirements that an be used by the government to omplement a minimum deposit-refund requirement. In Figure, the solid urve s * depits the voluntary deposit-refund as a funtion of returned produt value. The assoiated profit, sales and return densities are also shown in Figure via solid urves. The voluntary deposit-refund does not ahieve high olletion rates when the returned produts have low value for the firm i.e., ρ / ρ dereases as p dereases and reahes zero at a threshold p value. In this illustrative eample, olletion is not eonomially viable for the firm when p $6 (sine ρ = in Figure 4). This shows that the olletion rate voluntarily ahieved by the firm may not be suffiient for the government, partiularly for produts with low return value. In suh ases, a ommon pratie among governments is to impose a minimum deposit-refund that the firm must offer. Suh a deposit-refund requirement, however, an ause profit to drop below that of s=, in whih ase the firm will avoid olleting returned produts as disussed in the previous setion. Thus, the dashed urve above s * in Figure depits the maimum deposit-refund that an be imposed by the government without pushing the firm out of the olletion ativity (i.e., the resulting profit is equal to that of s = for all p values). The assoiated sales and return densities are also shown via dashed urves in Figure 4. As epeted, the return density shows a sharp inrease under the maimum governmentinitiated deposit that is aeptable to the firm. It is important that any deposit between the B
voluntary and maimum levels onstitutes a win-win senario for the firm and the government, beause the firm still maes a profit higher than the no-deposit ase while the olletion rate is improved. r,π,s 7 6 5 4 3 1 Π* s* 6 5 4 3 1 ρ ρ B ρ 4 6 8 1 1 14 16 p Figure 4: The impat of return value of voluntary and maimum deposit-refund It is apparent from the above disussion that a deposit-refund requirement may not be suffiient to ahieve high olletion rates for produts with low return value. More importantly, the firm is an simply avoid olletion under suh a prie-based poliy when it is not eonomially viable (e.g., ρ = in Figure 4 when p $6). In suh ases, the government an improve the olletion rate by the use of additional poliies. One suh poliy is to require a minimum level of aessibility for olletion failities (i.e., an upper bound on d ) as well as a minimum deposit-refund. To illustrate this, we fous on a produt with p=$3 and eep the remainder of model parameters as in Table 1. Assuming the government would lie to ensure that olletion failities are at least as 1
aessible as retail failities, we analyze the impat of imposing d d = 7m. A parametri analysis with respet to s under this requirement is depited in Figure. r,π d ~ r 7 1 6 5 4 3 ~ d * r* 1 8 6 1 Π* 4 1 8 6 4 ρ ρb ρ 5 1 15 5 3 s Figure 5: The impat of deposit-refund when d is bounded Using (1), we find that the firm voluntarily offers olletion only for $ s $37 when there is no upper bound on d. This is the range of s values for whih the * d urve in Figure 5 first falls below 7m. Notie that under the additional requirement of d 7m, the firm is obliged to offer olletion for all values of s despite inurring a profit loss. Naturally, this leads to an inrease in the olletion rate. More interestingly, the additional requirement prompts the firm to offer better aessibility to olletion failities for s $15 so as to avoid further redution in sales. An alternative poliy for the government to improve olletion rate is to require that the firm offers olletion at its retail failities. This ouples the sales and olletion ativities, whih would entie the firm to offer olletion under less favorable onditions. We assume that the firm is willing to re-design its faility networ to aommodate the
government s requirement. Thus, we used (18) in arrying out a parametri analysis with respet to s, whih is depited in Figure. r,π d ~ 7 6 5 4 3 r* ~ d* 1 1 8 6 1 Π* 4 1 8 6 4 ρ ρb ρ 5 1 15 5 3 s Figure 6: The impat of deposit-refund when the firm optimizes r and d In the above analysis, we set p=$3 so that Figure 6 is omparable to Figure 5. The remaining parameters are as in Table 1. Note that the fied ost of establishing and operating an integrated retail-olletion faility is $45,. The range of s values for whih olletion is profitable is shown via the thier portion of the * d urve in Figure 6. The additional requirement ahieves reasonable olletion rates for higher deposit levels. For s=$7, for eample, Figure 6 shows that the firm ollets 5% of the sold items when it is required to offer olletion at retail failities. Without this additional restrition, however, the firm would not offer olletion under a minimum deposit refund requirement of $7. When s is not in the eonomially viable range, the firm inreases d ~ to mitigate returns and benefit from prie disrimination. This beomes less effetive as olletion rate approahes 1%, whih then auses d ~ to derease. Interestingly, a 3
omparison of Figures 5 and 6 reveals that the profit and prie urves under the two alternative poliies are struturally similar. Although these poliies are effetive in supplementing a deposit-refund requirement to enable the government to ahieve its olletion targets, it is important that the firm inurs a profit loss (ompared to the nodeposit ase) under both poliies. 6. Conluding emars In this paper, we present an analytial framewor that inorporates deposit-refund in the firm s olletion faility networ design and priing deisions. We use the proposed methodology for modeling the launh of a olletion program as well as the establishment of integrated retail-olletion failities. Our omputational analyses on an illustrative eample show that the returned produt value is a ey fator that determines the nature of olletion in an industry. For produts with high return value, the depositrefund voluntarily offered by the firms an be suffiient to ahieve high olletion rates. Even if the olletion rate is below the government s target, a minimum deposit-refund requirement higher than the voluntary level would improve olletion rate for suh produts. This is not true, however, for produts with low return value beause of the firms tendeny to avoid the profit loss due to olletion. A minimum deposit-refund requirement by the government is not suffiient for improving olletion rate in suh ases. Our analyses show that the use of additional aessibility-based requirements is neessary to ahieve the government s olletion targets. The proposed methodology etends the literature on deposit-refund systems by providing a better understanding of their impat at the firm level. For eample, Bohm (1997) suggested that the government an improve olletion rate of a used produt by taing on the responsibility of operating its deposit-refund system (i.e., the deposit will be ept by the government until the produt is returned). Our analysis shows that it is suboptimal for the firm to simply add the deposit onto its retail prie. The firm subsidizes a portion of the deposit in determining the optimal retail prie, whereas the level of subsidy varies with the value of the returned produt. Bohm s proposal onstitutes taing away this priing fleibility from the firm, whih will learly redue the firm s eonomi inentive to engage in the olletion ativity. 4
There are a number of assumptions of our stylized framewor that are worth revisiting. One partiular assumption is the onstant population density. We antiipate that our results and main insights would remain valid even when the density φ is slowly varying. The results of Dasi and Verter (1) provide some support for this laim. However, when the population density hanges onsiderably in the maret area, our representation of the olletion and retail networs would not be very aurate, sine the firm would most liely be better off by installing failities with unequal servie sizes. Another assumption is the use of average distane to a retail faility to model a ustomer s travel effort to purhase a produt. We ran a series of simulation tests to ompare the purhase probabilities that arise under our approimation to those under an aurate representation of the effort to purhase. This preliminary study indiates that our aggregate representation onstitutes a good approimation. Nonetheless, a definite assessment of the validity of our ey results and insights requires a omplete (simulationbased) model of the system and a omprehensive eperimental study. We believe this is a study of its own, whih ould be eplored as an etension in the future. Our study opens a number of other avenues for future researh. From the firm s perspetive, the proposed models provide a means to estimate return density based on the olletion faility networ struture. It would be desirable to integrate these estimates in a mied integer programming formulation for designing the entire reverse logistis networ of the ompany. From the government s perspetive, our methodology an be used to assess the profit loss inurred by the ompany in meeting the olletion targets. One way to mitigate the firms resistane to omply with the government s requirements is the development of an analytial framewor to failitate loss-sharing between the two parties. Finally, the firm-level impat of other poliy tools, suh as reyling subsidies, disposal fees and taes on the use of virgin materials, need to be eamined in detail so as to improve our understanding of the government s overall ability to influene the olletion proess. Another worthwhile researh diretion is to epliitly model the ompetition for sales and/or olletion in the industry, and investigate the ritial role ompetition an play in this environment. 5
APPENDIX A To ompute ρ, the integral in () must be arried over seven possible intervals i.e., four L for A in (1) and three for [ A, A ] in (11). We now define the endpoints of these seven intervals, whih depend on the values of distane oeffiients A and B. Let A = ma(, A) and B = ma (, B). For A the endpoints are _1= min (, L, ) B A d, _= min B, A, d, M L M _3= min B, A, d, _4= min,, B A d Using (1) we derive ρ, for A as _4 ( _4) ( ( ') ) = φ P u > d / d _1 _ ρ ( ) B = [ ] 1 φd φ d _1 LM _3 ( B) L φ 1 d _ M M _4 ( B) ( B) L M φ 1 ( L M ) d _3 LM LM LM The range where (11) is valid starts at _4. Either the first three piees or the fourth piee of (11) is valid depending on the value of B M. For M B > A : L L L _5= min B, A, d, _6= min, A d Using these endpoints we derive ρ for M > A and B > A as / d 6
ρ M _6 1 B A ( _ 4 _6) 1 ( ( ') ) ( ( ) ( )) = > > / φ P u M P u u N d d B A _4 M _5 B A ( ) A B A φ M B A _4 ( ) L A M L 1 = 1 1 1 d _6 ( A B) ( ) φ L A 1 A 1 d / d _5 M M L ρ _ 4 _6 onsiders ases where B > A. For B M A the upper Note, that ( ) L M L bound is restrited by B A. Thus, L M _7= min B, d We derive ρ, for M > A and B A as ρ M _7 1 B A ( _ 4 _7) = 1 φ P( u( ' ) ) P( u( ) u( N) ) d / d M > > B A _4 M _7 1 B A 1 A 1 1 ( A B) = φ M B A L _4 ( L A) M ( A B)( L A M ) ( L A) M d / d ( L A) M ( L A) M Finally, we an ompute the density ρ as ( _4 ) ( _4 _6 ) ( _4 _7) ρ = ρ ρ ρ. Either the seond or the third term taes the value zero in the above epression depending on the value of B M. The resulting value of ρ an be used in (1) to alulate the profit. 7
To ompute ρ B through the integral in (3) we first derive ρn i.e., the density of individuals who buy and not return the produt. We define the following endpoints to address the relevant intervals: N_ 1= min( A,d ) L N_ = min A,d N_ 3 = d Using (9) and (1) we an now write the integral to derive ρ N as d ρ = φp( u( N) > ) P u( N) > u ( ) d / d ( ) N N _ C A = φ 1 d M L N _1 N _3 C φ 1 d / d N _ M Aording to (3) we an add the densities unit area i.e., ρb = ρ ρ N. ρ and ρ N to obtain the number of sales per 8
APPENDIX B Following the same logi as in Appendi A, we first define the following integral endpoints: 1 1 L '_1 = min A, d, B', '_ = min A, B', d 1 M 1 L M '_ 3 = min A, B', d, '_ 4 = min A, B', d L '_ 5 = min ( A, d), '_ 6 = min A, ma ( B' A, A ), d L 1 L L '_ 7 = min A, ma B', A, d, L M L '_ 8 = min A, ma B' A, A, d M M L N'_ = min C', A, d, N'_1 = min ',,, ma ', C A d C A ( ) M M L N'_ = min C', d,ma ( C', A ), N'_ 3 = min C', A, d M N'_ 4 = min C', d Then, we use the above in deriving the sales and return densities as follows: 9
'_ 4 ρ' ( '_4) '( ' ( ) ) ( ( ) ( )) = φ P u > P u > u N d / d '_1 '_ '_ 3 ( ') B ( B ') L = [ ] 1 1 φ d φ d '_1 φ d LM '_ M M '_ 4 ( B ') ( B ') L M φ 1 ( L M ) d / d LM LM '_ 3 LM '_ 8 ρ' ( '_4 '_8) = φ P' ( u' ( ) > ) P( u( ) > u( N) ) d / d '_ 4 '_ 5 '_ 6 A ( A B ') = φ 1 d 1 d L φ '_ 4 '_ 5 ( L A) M '_ 7 '_ 8 ( A B ') ( L A) A ( A B) φ 1 1 d 1 M M '_ 6 L φ '_ 7 ( L A) M ( A B) ( L A) M A ( L A M) 1 d / d ( L A) M ( L A) M L ( ) ( ) ρ ' = ρ' '_ 4 ρ ' _ ' 4 _ ' 8 ρ d ' '( ' ( ) ) ( ( ) ( )) N = φp u N > P u N > u d / d N'_1 N_ N_3 A C ' A = φ d [ φ] d φ 1 d '_ L _1 _1 M L N N N N '_ 4 C ' φ 1 d / d N '_ 3 M ρ' B = ρ' ρ' N 3
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