A cost model for optimizing the take back phase of used product recovery

Ghoreishi, Niloufar; Jakiela, Mark J.; Nekouzadeh, Ali Article A cost model for optimizing the take back phase of used product recovery Journal of Remanufacturing Provided in Cooperation with: Springer Nature Suggested Citation: Ghoreishi, Niloufar; Jakiela, Mark J.; Nekouzadeh, Ali (2011) : A cost model for optimizing the take back phase of used product recovery, Journal of Remanufacturing, ISSN 2210-4690, Springer, Heidelberg, Vol. 1, pp. 1-15, https://doi.org/10.1186/2210-4690-1-1 This Version is available at: https://hdl.handle.net/10419/108882 Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen. 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If the documents have been made available under an Open Content Licence (especially Creative Commons Licences), you may exercise further usage rights as specified in the indicated licence. http://creativecommons.org/licenses/by/2.0/ RESEARCH Open Access A cost model for optimizing the take back phase of used product recovery Niloufar Ghoreishi 1* , Mark J Jakiela 1 and Ali Nekouzadeh 2 Abstract Taking back the end-of-life products from customers can be made profitable by optimizing the combination of advertising, financial benefits for the customer, and ease of delivery (product transport). In this paper we present a detailed modeling framework developed for the cost benefit analysis of the take back process. This model includes many aspects that have not been modeled before, including financial incentives in the form of discounts, as well as transportation and advertisement costs. In this model customers are motivated to return their used products with financial incentives in the forms of cash and discounts for the purchase of new products. Cost and revenue allocation between take back and new product sale is discussed and modeled. The frequency, method and cost of advertisement are also addressed. The convenience of transportation method and the transportation costs are included in the model as well. The effects of the type and amount of financial incentives, frequency and method of advertisement, and method of transportation on the product return rate and the net profit of take back were formulated and studied. The application of the model for determining the optimum strategies (operational levels) and predicting the maximum net profit of the take back process was demonstrated through a practical, but hypothetical, example. Keywords: Take Back, Product Acquisition, Remanufacturing, Modeling, Cost Benefit Analysis Introduction Taking back used products is the first step in most of the end of life (E.O.L) recovery options which include remanufacturing, refurbishment, reuse, and recycling. “Take back”includes all the activities involved in transferring the used product from the customers’possession to the recovery site. In general optimizing of the take back (also called product acquisition) has received limited attention in research and operations. Guide and Van Wassenhove categorized take back processes into two groups: waste stream and market driven [1]. In a waste stream process, the collecting firm cannot control the quality and quantity of the used products: all the E. O.L. products will be collected and transferred. In a market driven process, customers are motivated to return the end of life product by some type of financial incentive.Thisway,the(re)manufacturer can control the quantity and quality of the returned products through the amount and type of incentives and increase its profit [2-4]. In general the taking-back firm can control the process by setting strategies regarding financial incentives, advertisement, and collection/transportation methods [2,3,5-8]. Usually, offering higher incentives (in the form of cash or discounts toward purchasing new products) will increase the return rate and lead to acquisition of higher quality used products. Higher incentives sometimes can encourage the customers to replace their old products with a new one earlier [9]. Another way to control the quality of the used product is to have a system for grading the returned products based on their condition and age and paying the financial incentives accordingly [4]. Proper advertisement and providing a convenient method for the customers to return the E.O. L product can increase the return rate as well [9]. In the existing models of the take back process all the involved costs are bundled together as the take back cost and the return rate is modeled as a linear function of the take back cost [9] or as a linear function (with a threshold) of the financial incentive [4]. We developed a * Correspondence: [email protected]du 1 Mechanical Engineering and Materials Science Department, Washington University in St. Louis, 1 Brooking Dr., St. Louis Missouri 63130, USA Full list of author information is available at the end of the article Ghoreishi et al.Journal of Remanufacturing 2011, 1:1 http://www.journalofremanufacturing.com/content/1/1/1 © 2011 Ghoreishi et al; licensee Springer. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. market driven model of a take back process by considering different aspects of take back including financial incentives, transportation methods, and advertisement separately to provide more theoretical insights about the process. Three different types of financial incentives (cash, fixed value, and percentage discount) were modeled. This includes considering the effect of discount incentives on the sale of new (or remanufactured) products and allocating the relevant costs and revenues among the take back process and the sale process of the new products. The relation between the incentives and return rate is considered as a market property reflecting consumers’willingness to return products. This should be measured or estimated. The model enables operational level decisions over a broader choice of variables and options compared to existing approaches. A practical example is used to show how this modeling framework can determine the optimum options and values of the take back process and provide significant insights for analyzing and also managing the take back process. Model We consider three important aspects of take back in our model: the financial incentives, the transportation and the advertisement. Each of these aspects incurs a cost to the process, and in return, can increase the revenue by increasing the number and average quality of returned products. Some of the take back costs are associated with each individual product and so are scaled with the number of returned products and some are fixed costs associated with the whole take back process. The value of a returned product at the recovery site is termed a.a is the price that the recovery firm is willing to pay for the used product at the site. If the take back is performed by the recovery firm then awouldbeatransfer price [10,11] which separates the cost benefit analysis of the take back from the rest of the recovery process. We modeled the net profit of take back during a certain period of time. If the take back process is intended for a period of time, this period could be the entire time of the take back process, and if it is intended to be a long lasting process, this period is a time window large enough to average out the stochastic fluctuations in the return rate. Financial incentives Three strategies were considered for motivating the customers to return their used products: 1- Paying a cash value $c. 2- Offering a discount of value $d, for purchasing new products (usually of similar type). 3- Offering a percentage discount of %p,forpurchasing new products. These incentives affect the total cost, the number of return, and the average quality of the returned products. Increasing these incentives may increases the net profit by increasing the number of returned products and their average quality, or may decrease the net profit by increasing the cost of take back. Therefore, it is an optimization problem to find the type and amount of incentive to maximize the net profit. It is reasonable to expect the number of returns, N R , varies by the amount of incentives and also varies differently for different types of incentives: NR=NRc(c)=NRd(d)=NR p (p ) (1) However, we may assume that N R is a function of a more general variable called motivation effectiveness, whichisconsideredasthe amount of motivation induced in the customers by a motivation strategy. The magnitude of motivation effectiveness, mte, is defined as the equivalent amount of cash that generates the same level of motivation in the customers to return the used product. Therefore, we may simply write: NR=NR ( mte ) (2) Different customers respond differently to the same amount of mte. A customer returns the used product if the motivation effectiveness of the incentive (mte)is higher than his or her threshold motivation effectiveness for returning the used product. Therefore, N R (mte) represents the number of customers that their threshold motivation effectiveness is less than mte (the cumulative density function for the threshold motivation effectiveness among the customers). The attractiveness of the discount is less than or equal to the same amount of cash, because the discount can be used only to buy specific products [12-16]. We define c d as the cash equivalent of discount d;thenumberof customers that return the used product with discount incentive dis equal to the number of customers that return the used product with cash incentive c d . Then we define a, the ratio of cash to discount incentive, via: cd=dα ( d ) (3) The value of adepends on the new products that the discount is applicable to and varies between 0 and 1. Generally, if customer X has a higher cash incentive threshold than customer Y to return the used product, he has most likely a higher discount incentive threshold aswell.Therefore,itisreasonabletoassumealinear regression between the dand c d and replace a(d) by its average value simply termed a. Therefore mte for three different motivation strategies is modeled by: mte =c,mte =αd,ormte =αA p (4) Ghoreishi et al.Journal of Remanufacturing 2011, 1:1 http://www.journalofremanufacturing.com/content/1/1/1 Page 2 of 15 where Ais the average price of the new products to which the discount can be applied. Transportation Once a customer is motivated to return the used product, the product must be transported to the recovery site. Gathering the used product from the customers can be very costly. In many situations, it may be possible to reduce the transportation cost by asking the customer to contribute partially or fully to the transportation of their products. This usually comes at the cost of reducing the motivation effectiveness of the financial incentives because it requires the customers to spend time and energy to return the used product. Therefore, the motivation effectiveness depends on the convenience of the transportation in addition to the financial incentives. To quantify the convenience of the transportation, we introduce the parameter f, termed the convenience factor of transportation method. In general mte is assumed as a function of fin our modeling framework: mte =mte ( f,c ) ,mte =mte ( f,αd ) ,ormte =mte ( f,αAp ) (5) Transportation imposes a cost termed TC to the take back process. Transportation cost is a function of the number of returns. A linear relation [17] between the transportation cost and the number of returns is the simplest method for modeling this cost [18]: TC =NRt+t g (6) where tis the transportation cost per returned item (slope of the variable cost) and tg is the fixed cost of transportation (does not scale with the number of returns). Advertisement Advertisement includes any action for informing the customers about the take back policy. Optimum advertisement strategy depends on many social and psychological factors which are beyond the scope of this paper.Here,weonlydeterminetheaspectsofadvertisement that are important for cost benefit analysis of the take back procedure. Advertisement cost is categorized into two groups: W 1 , the one-time cost of advertisement associated with preparing and designing the ad., including its content and its presentation (e.g. posters, audio clips or video clips), and W 2 ,costof running the ad. (e.g. posting, publishing, distributing or broadcasting). We may refer to W 2 as the advertisement expenditure. Among all the customers that possess the used product, only the ones that are aware of the take back procedure may return the used product (if they are motivated enough). Therefore, we may rewrite the number of returns as: NR ( mte,W2 ) =N ( W2 )  ( mte ) (7) Where Nis the total number of customers holding the used product, Ωis the fraction of total customers that are informed by the advertisement and Γis the fraction of informed customers that return the used product in response to motivation effectiveness of the take back procedure. Ωdepends on the frequency of running the advertisement and therefore, is a function of W 2 .Equation (7) implicitly assumes that the demography of the informed customers and consequently how they respond to the motivation effectiveness is independent of the number of informed customers. The following expression was derived as an estimate for the Ωfunction (see Appendix): ( W2 ) =Ωss ( 1−e W 2 Wsc ) (8) W sc and Ω ss are characteristic parameters of advertisement method; they are different for different advertisement options. The Ωfunction presented in equation (8) is derived analytically for a general advertisement method. More accurate functions may be derived by fitting the empirical data (if available) for each specific advertisement method. Other advertisement models like Vidale-Wolfe model [19], Lanchester model [20], or empirical models [21] may be used as well. Advertisement, if designed accordingly, can have a motivating effect by informing the customers about the environmental and global benefits of their product return effort including reducing waste and reducing the consumption of energy and natural recourses. To quantify the motivation effect of advertisement, we introduce the parameter g. Therefore, mte can be written in general as a function of financial incentive, the convenience factor of transportation and the motivation effect of advertisement. mte =mte ( f,c,g ) ,mte =mte ( f,αd,g ) ,ormte =mte ( f,αAp,g ) (9) A suggested model for motivation effectiveness mte should be determined for all the possible combinations of the financial incentive, the convenience factor of transportation and the motivation effect of advertisement, for the three financial incentive strategy. However, this requires extensive amount of data points and makes the calibration procedure very expensive and even impractical. In this section we rationalize a simple model for mte without further empirical validation. Alternative models may be used based on empirical data. Ghoreishi et al.Journal of Remanufacturing 2011, 1:1 http://www.journalofremanufacturing.com/content/1/1/1 Page 3 of 15 In equation (4) we modeled the motivation effect of the three financial incentives by estimating the cash equivalent of a discount incentive. In order to quantify the convenience of the transportation, we should first determine its effect on the motivation effectiveness. If a customer participates partially in transporting the used product, he or she has to spend some time and energy which reduces the effective value of the financial incentive. Defining mte t as the reduction in motivation effectiveness associated with the transportation method we may write: mte =c-mte t ,mte =αd-mte t ,ormte =αA p -mte t (10) The energy and time that a customer has to spend on transportation is almost the same for different customers, but different customers value their time and energy differently. Usually the customers that return their used product at higher financial incentives are busier or less interested in returning their product and so are more sensitive to the convenience of transportation. Therefore a correlation between mte t and mte is expected. Assuming a linear relation between mte t and mte: mtet=βc,mtet=βαd,ormtet=βαA p (11) we may rewrite equation (10) as: mte = ( 1−β ) c,mte = ( 1−β ) αd,ormte = ( 1−β ) αA p (12) where brepresents the inconvenience of transportation and varies between 0 and 1; it is zero if the take back firm undergoes all the transportation activities. The convenience factor of transportation, f, may be quatified as: f= ( 1-β ) (13) And consequently the equation (12) can be rewritten as: mte = f c,mte = f αd,ormte = f αA p (14) In contrast, there is no reason to believe a significant correlation between the motivation effect of the advertisement and the motivation effect or the type of the financial incentive. Therefore, we may assume that g represents the average increase in the motivation effectiveness associated with the advertisement. Therefore, equation (14) can be rewritten as: mte = f c+ g ,mte = f αd+ g ,ormte = f αA p + g (15) In general gdepends on the quality of the ad and providing a more effective ad usually costs more. Therefore, the motivation effect of advertisement may be considered as a function of W 1 : g =g ( W1 ) (16) Cost model In the discount incentive strategies the cost benefit analysis of take back and the sale of new products are coupled together. Therefore, the cost model of the cash incentivestrategydifferssubstantiallyfromthecost model of discount incentive strategies. In the following, different cost models were derived for different incentive strategies. Cash incentive strategy The cost that is scaled with the number of returns (cost per returned item) consists of the amount of cash incentive, c, and the transportation cost, t. The revenue which is generated by the value of returned product, a,also scales with the number of returns. Advertisement costs, W 1 and W 2 andthefixedcostoftransportation,tg,do not scale with the number of returns. Therefore, the net profit of take back, Ψ c , can be modeled as: ψc=NR. [ a−c−t ] −W1−W2−t g −t b (17) Where tb is the implementation cost of take back, modeled as a fixed cost. A variable term may be considered for the implementation cost as well; for example larger number of returns usually corresponds to larger capacity of the take back process and consequently higher implementation cost. In this model ais the average value of taken back products. Taken back products are expected to have better quality (in average) at higher incentives [4]. To include this effect, we considered aas afunctionofmte in the model. Note that the decision of customers for returning their used product depends on the all the incentives which are included in the motivation effectiveness, mte. Substituting for number of returns from equation (7) and for mte from equation (15) the net profit in a cash incentive strategy is: ψc=N. (f c+g ) . ( W2 ) .[a (f c+g ) −t−c]−W1−W2−tg −t b (18) Discount incentive strategies If the take back is performed by the OEM (Original Equipment Manufacturer) firm, the financial incentives may be offered in the form of discount (fixed value of percentage) toward buying a new product. The discount incentive reduces the net profit of the new products by selling a fraction of them at the discounted price. On the other hand, the discounted price makes the product affordable for some additional customers and may increase the net profit by increasing the number of sales or redistributing the sale profile toward more profitable products. As both changes in the net profit of new Ghoreishi et al.Journal of Remanufacturing 2011, 1:1 http://www.journalofremanufacturing.com/content/1/1/1 Page 4 of 15 products are caused by the take back procedure, the reduction of profit, associated with reduced price, is considered as a take back cost and the extra revenue associated with the increased amount of sales is considered as take back revenue. To model the effect of discount coupons on the sale profile of new products we first categorize the customers who would return their used product into the following groups: 1- Current customers who planned to buy a certain product (with or without the discount). These customers simply use the coupon to pay less for the new product they would have bought anyway. 2- New customers who have been motivated by the discount incentive to return their used product and buy a new product at discounted price. Their choice of new product may or may not depend on the amount of discount incentive. 3- Customers who returned their used product but for any reason do not buy any new product to redeem their coupon. Customers of group 1 are the less favorable customers for the take back procedure and do not bring any extra revenuetothecompanyasaconsequenceofthetake back strategy. Customers of group 2 are new customers that are motivated by the discount and so any generated revenue associated with their purchase can be attributed to the take back procedure. Finally customers of group 3 do not impose any motivation cost on the take back procedure. The motivation cost, MC, in this method can be assumed as the total value of redeemed coupons minus the extra generated revenue in the sale of new products caused by discount motivation: MC = M  j =1 m j d− M  j =1 n j s j (19) where Mis the total number of discountable products referred by index j;s j is the sale profit of new product j; n j is the change in number of sale of the new product j, caused by discount incentive; m j is the number of discount coupons used for the new product j. Including the motivation cost, the net profit of discount incentive strategy is: ψd=N.(mte).(W2).[a(mte)−t] −d M  j =1 mj+ M  j =1 njsj−W1−W2−tg −t b (20) The customers’decision regarding returning the used product depends on the motivation effectiveness, but, once the customers returned the product their decisions for choosing the new product depend only on the amount of discount. We define h i as the proportion of the discount coupons that are used for the new product j. Therefore: m j =NRη j =NΓ(mte)Ω(W2)η j (d ) (21) Assuming that h o and m o show the proportion and the number of coupons that are not used (customers of group 3), respectively: η0+ M  j=1 ηj=1 m0+ M  j =1 mj=N R (22) Note that the number of issued coupons is the same as the number of returned products, NR. We also define ξ j as the proportion of the sale of each new product without the take back procedure. Usually, the discount incentives of the take back procedure increase the sale of new product and we define Λas the ratio of the new customers (estimated by the increased in the number of sale) to the total customers who buy a new product with coupon. Therefore, number of new customers (who buy a new product because of discount) is (N R -m o )Λ and the number of customers that would have bought a new product without the discount is (N R -m o )(1-Λ). n j and m j are related to each other for each new product j. For each new product j,n j is m j minus the number of customers that would have bought a new product without discount. These customers were distributed proportional to ξ j before discount incentive, so: n j =m j −ξ j (N R −m o )(1 −Λ)=N R [η j −ξ j (1 −η o )(1 −Λ) ] (23) Substituting equations (15), (21), (22) and (23) in equation (20), the net profit in discount incentive strategy can be rewritten as: ψd=N.(α f d+g).(W2). ⎛ ⎝a(αfd +g)−t−d(1 −ηo(d)) + M  j=1 [ηj.(d)−ξj(1 −ηo(d))(1 −)]sj ⎞ ⎠ −W1−W2−tg −tb (24) Therefore, to include the effect of discount in the net profit,weneedtoestimateΛ, the proportion of new customers and h i , the distribution of discount coupons among the new products. These parameters are measurable once the take back procedure is implemented. However, in order to use the model for feasibility analysis of the take back procedure, accurate estimates of Λ and h i is required. In equation (24) it is implicitly assumed that the number of new customers increases proportionally by the number of returns, and consequently the fraction of new customers is modeled with a constant number. For a more accurate model, Λmay be Ghoreishi et al.Journal of Remanufacturing 2011, 1:1 http://www.journalofremanufacturing.com/content/1/1/1 Page 5 of 15 considered as a function of mte. However, this accuracy comes at the cost of more complex model calibration. Comparing equation (24) with equation (17) helps to understand how changing the financial incentive from cash to discount affects the net profit of the take back. First the cash incentive cost, c,isreplacedbythediscount incentive cost. The discount incentive, d,is reduced by a constant factor to account for the unused coupons. As discussed before, changing the incentive from cash to discount decreases the profit by reducing the motivation of customers to return the used product and increases the net profit by increasing the sale of new products. Scaling down the discount incentive by parameter ais how the first effect appeared in the cost model. It reduces the number of returns and consequently the net profit of take back. The second effect appeared as a summation term in the right side of equation (24). The term inside the square brackets is difference between the sale (for each new product) of new products with and without the coupon. The number of sale without the coupon is the number of customers that would have purchased the product without the coupon, (1-Λ), distributed among the new products. The net profit of take back for the percentage discount strategy, ψ p , can be derived using a similar approach as for the fixed discount strategy. With a percentage discount, the amount of discount is not fixed and depends on the sale price of new products. The motivation cost, MC, is: MC = M  j =1 m j v j p− M  j =1 n j s j (25) where v j is the sale price of new product jand pis the percentage of discount. Therefore, the net profit of take back with a percentage discount is: ψp=N.(mte).(W2).[a(mte)−t] −p M  j =1 mjvj+ M  j =1 njsj−W1−W2−tg −t b (26) Similar to a fixed value discount, m j can be modeled as: m j =N R η j =NΓ(mte)Ω(W 2 )η j (p ) (27) The average price of discountable products, A,canbe determined as: A= M j=1 m j v j  M j =1 m j = M j=1 η j (p)v j  M j =1 η j (p) (28) We used A previously to estimate the motivation effectiveness of a percentage discount. In the percentage discount strategy, buying more expensive products is more motivated compared to the fixed value discount strategy as the amount of discount increases by the priceofproduct.Therefore,theh j functions and Λare differentfromthefixedvaluediscountandneedtobe estimated or measured separately. The relationship between m j and n j is the same as in the fixed value discount strategy. The net profit of a percentage discount strategy can be rewritten using equations (23) and (28) as: ψp=N.(αfAp +g).(W2). ⎛ ⎝a(αfAp +g)−t−Ap(1 −ηo(p)) + M  j=1 [ηj(p)−ξj(1 −ηo(p))(1 −)]sj ⎞ ⎠ −W1−W2−tg −tb (29) Note that in general Ais a function of p. A list of all model variables is provided in Table 1. This list also includes intermediate variables that do not appear in the final equations of the net profit. Results Themodeldevelopedinprevioussectionsprovidesa general framework to optimize the take back procedure by determining the type and amount of financial incentives, optimum options of transportation and advertisement, and the optimum spending on advertisement. In this section we present a hypothetical real world take back problem that is characterized in this general framework. The model will be used to estimate the net profit of the take back and determine optimum values and choices of parameters. Take back problem and its characteristic parameters Cellular phones are among the products considered suitable for multiple life cycles [22]. Our goal is to outline a take back procedure for collecting a particular type of used hand set from the market for a recovery firm. The optimum recovery option and marketing the recovered product (or material) is out of the scope of this problem. In the following we explain the parameters and options we considered. Although, the parameter values are hypothetical and are not measured for a specific case, they represent a set of possible options and values. It is assumed that the recovery firm is willing to pay from $30 to $50 for each used handset at the recovery site based on the average condition. The average value of returned product, a, is modeled as: a=  30 + 1.5mte mte <2 0 50 mte >2 0 (30) Three transportation options have been considered: 1- Pick up from the customers convenient location (residential or business location). Ghoreishi et al.Journal of Remanufacturing 2011, 1:1 http://www.journalofremanufacturing.com/content/1/1/1 Page 6 of 15 2- Providing the customers with the postage paid envelopes. 3- Asking the customers to hand deliver their handsets at particular locations. The transportation costs, tand tg and the convenience factor, f, of each method is summarized in Table 2. Five options have been considered for advertisement: 1- Broadcasting a video clip on a T.V. channel 2- Broadcasting a vocal clip on a radio channel 3- Internet advertisement 4- Advertising in local newspapers 5- Announcing (by LCD panels or posters) in related retail stores Characteristic parameters of each method of advertisement are given in Table 3. The values of the advertisement parameters are roughly estimated based on the available data on costs (e.g. air time rates) and estimates of the number of people that will be impacted by the ad. N, the total number of customers that posses the used handset is assumed to be 70,000 and the Γfunction is modeled as: (mte)= mte3+20 1 . 2 mte 3+1 0mte 2+1 000 (31) ThisfunctionisdrawninFigure1.Thisestimateof the Γfunction is based on the following assumptions: 1-with no financial incentive still a small fraction of customers (~2%) who are motivated by the overall environmental aspects of take back would return their hand sets. 2-incentives up to $4 would have no significant motivation effect and the return rate would start to increase for incentives of $5 or more. 3-return rate increases almost linearly in the beginning and then yields toward a saturation value. 4-$25 motivation effectiveness is a fair exchange value and about half of the customers would return their handsets at this price. For discount strategies it is assumed that the customer can buy 3 new handsets (Table 4) with their discount. The h j proportions are assumed to vary linearly (after an initial threshold, x ts ) with the amount of discount: Table 1 Parameters of the model aAverage value of returned product at the recovery site cAmount of cash incentive dAmount of discount incentive (fixed value discount) pPercentage of discount incentive N R Number of returned products mte Motivation effectiveness c d Cash equivalent of discount aRatio of cash to discount incentive Aaverage price of the new products to which the discount can be applied fConvenience factor of transportation tTransportation cost per returned product tg Fixed cost of transportation W 1 Onetime cost of advertisement (Preparing the ad.) W 2 Advertisement expenditure (e.g. posting, publishing, distributing, broadcasting) NTotal number of customers holding the used product ΩFraction of (total) customers that are informed about take back ΓFraction of (informed) customers that return the used product Ω ss Parameter of advertisement method W sc Parameter of advertisement method m j Number of coupons used for new product j. m o Number of coupons that have never been used N ad Number that are reached by advertisement N ss Maximum that can be reached by advertisement gMotivation effectiveness of advertisement mte t Reduction in motivation effectiveness caused by transportation method bInconvenience of transportation tb Fixed cost of take back MTotal number of discountable products m j Number of discount coupons used for the new product j n j Change in number of sale of the new product j s j Sale profit of new product j ξ j Proportion of the sale of new products without the take back procedure h j Proportion of discounts used for new product j ΛProportion of new customers due to discount m o Number of the coupons that are not used h o Proportion of the coupons that are not used ψ c Profit of take back with cash incentive ψ d Profit of take back with fixed value discount incentive ψ p Profit of take back with percentage discount incentive v j Sale price of new product j Table 2 Parameters of transportation options Transportation Options ttg f Option 1: Pick Up 15 5000 1 Option 2: Postages Paid Mail 4 2000 0.85 Option 3: Collecting at Branches 2 500 0.6 Table 3 Parameters of different advertisement options W 1 gΩ ss W sc Option 1: TV ad. 8000 7 0.9 400000 Option 2: Radio ad. 1000 5 0.5 40000 Option 3. Internet ad. 400 5 0.35 30000 Option 4. Local Newspaper 500 3 0.3 8000 Option 5. Retail Store ad. 700 4 0.4 25000 Ghoreishi et al.Journal of Remanufacturing 2011, 1:1 http://www.journalofremanufacturing.com/content/1/1/1 Page 7 of 15 ηj(x)=  ξj(1 −ηo(x)) x<xts ξj(1 −ηo(x)) + λj(x−xts)x>xts j=1,2, 3 (32) where xis the amount of discount (dor p). When the discount is small it does not affect the customers’decision for selecting the new product and the discounts are distributed among the new products proportional to their global sale distribution, ξ j . The proportion of customers who have returned the used product without using their discount coupon is assumed to decline exponentially: ηo=ρ 1 +ρ 2 exp(−x/xsc ) (33) Parameters of the h j functions are provided in Table 5. Finally the fraction of new customers, Λ,isassumed to be 0.5 and the ratio of cash to discount incentive, a, is assumed to be 0.8. Model prediction for the optimum strategy and net profit Finding the optimum strategy in this problem involves determining the type of financial incentive (cash, fixed value or percentage discount), the amount of financial incentive, the optimum transportation method, the optimum advertisement method and the optimum volume of advertisement (W 2 ) to maximize the profit. The advertisement cost, W 2 , and the amount of incentives, x (c,d,orp), are continuous parameters. Therefore, for each combination of incentive strategy, transportation method, and advertisement method, we calculated the profit of take back, ψ, as a 2D function of xand W 2 and determined the maximum amount of net profit, ψ,and its associated W 2 and x. These maximum profits were compared to find the maximum net profit of the take back and its associated incentive strategy, transportation and advertisement methods. Figure 2 shows the net profit of take back, ψ,andthe number of returns, N R , as a function of advertisement cost, W 2 and percentage of discount, p, for a percentage discount incentive, method 2 of advertisement (radio advertisement) and method 2 of transportation (postage paid mailing). Increasing the amount of advertisement (W 2 ) and percentage of discount incentive, initially increases the profit because of increasing the amount of returns, and after a maximum point, decreases the profit because of increased costs of motivation or advertisement. It has a maximum shown by the black circle over the 2D domain of its two variables. The number of returns increases monotonically (as expected) by increasing the amount of advertisement and incentive and approaches a maximum value. The net profit of take back of all 15 combinations of advertisement method and transportation method is shown in Figure 3 for cash, fixed value discount, and percentage discount incentives in panels A, B and C respectively. Quantitative comparison of these net profits concludes that a percentage discount incentive, method 2 of advertisement, and method 2 of transportation generates the maximum net profit of about $685,000 in a year (time duration of modeling) based on the estimated values we chose for the parameters of this problem. The maximum net profit of fixed value discount and percentage discount strategies are close to each other (panels B and C) which means that the type of discount does not have a significant effect on the net profit. The maximum net profit of cash incentive strategy is significantly lower than the discount strategies. This means that a significant portion of the profit in discount strategies is resulted from the sale of new products, particularly to the new customers. The maximum net profit in cash incentives is about $404,000 associated with method 2 of advertisement and method 2 of transportation. For each combination of incentive strategy, advertisement method, and transportation method, the maximum net Figure 1 Proportion of the customers that return their used product, Γ, as a function of motivation effectiveness, mte, estimated for the practical example of this paper. The analytical expression of this function is given by equation (31). Table 4 Specifications of new discountable products New Handsets v j s j ξ j HS1 90 30 0.3 HS2 110 35 0.45 HS3 150 55 0.25 Table 5 Parameters of h j functions x ts l 1 l 2 l 3 r 1 r 2 x sc d5 -0.005 0.003 0.002 0.03 0.17 10 p0.05 -0.4 0.1 0.3 0.02 0.18 0.2 Ghoreishi et al.Journal of Remanufacturing 2011, 1:1 http://www.journalofremanufacturing.com/content/1/1/1 Page 8 of 15 20. Erickson GM: Dynamics Models of Advertising Competition: open- and closedloop extensions Norwell, Massachusetts: Kluwer Academic Publishers; 1991. 21. Cowling K, Cable J, Kelly M, McGuinness T: Advertising and Economic Behaviour London, UK: The McMillan Press LTD; 1975. 22. Kerr W: Remanufacturing and eco-efficiency: A case study of photocopier remanufacturing at Fuji Xerox Australia. Book Remanufacturing and ecoefficiency: A case study of photocopier remanufacturing at Fuji Xerox Australia (Editor ed.^eds.) City: IIIEE Communications; 2000, 2005. doi:10.1186/2210-4690-1-1 Cite this article as: Ghoreishi et al.: A cost model for optimizing the take back phase of used product recovery. Journal of Remanufacturing 2011, 1:1. Submit your manuscript to a journal and benefi t from: 7 Convenient online submission 7 Rigorous peer review 7 Immediate publication on acceptance 7 Open access: articles freely available online 7 High visibility within the fi eld 7 Retaining the copyright to your article Submit your next manuscript at 7 springeropen.com Ghoreishi et al.Journal of Remanufacturing 2011, 1:1 http://www.journalofremanufacturing.com/content/1/1/1 Page 15 of 15