A cost model for optimizing the take back phase of used product recovery
© Ghoreishi et al; licensee Springer. 2011
Received: 17 November 2010
Accepted: 5 July 2011
Published: 5 July 2011
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.
KeywordsTake Back Product Acquisition Remanufacturing Modeling Cost Benefit Analysis
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 . 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. This way, 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 . 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 . Proper advertisement and providing a convenient method for the customers to return the E.O.L product can increase the return rate as well .
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  or as a linear function (with a threshold) of the financial incentive . We developed a 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.
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 a would be a transfer 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.
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, for purchasing new products.
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).
where A is the average price of the new products to which the discount can be applied.
where t is 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 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, we only determine the aspects of advertisement 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, cost of running the ad. (e.g. posting, publishing, distributing or broadcasting). We may refer to W 2 as the advertisement expenditure.
W sc and Ω ss are characteristic parameters of advertisement method; they are different for different advertisement options. The Ω function 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 , Lanchester model , or empirical models  may be used as well.
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.
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 incentive strategy differs substantially from the cost model of discount incentive strategies. In the following, different cost models were derived for different incentive strategies.
Cash incentive strategy
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 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 revenue to the company as a consequence of the take 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.
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 Λ as 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).
Therefore, to include the effect of discount in the net profit, we need to estimate Λ, the proportion of new customers and η 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 η 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, Λ may be 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, is replaced by the discount 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 α is 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.
Parameters of the model
Average value of returned product at the recovery site
Amount of cash incentive
Amount of discount incentive (fixed value discount)
Percentage of discount incentive
Number of returned products
Cash equivalent of discount
Ratio of cash to discount incentive
average price of the new products to which the discount can be applied
Convenience factor of transportation
Transportation cost per returned product
Fixed cost of transportation
Onetime cost of advertisement (Preparing the ad.)
Advertisement expenditure (e.g. posting, publishing, distributing, broadcasting)
Total number of customers holding the used product
Fraction of (total) customers that are informed about take back
Fraction of (informed) customers that return the used product
Parameter of advertisement method
Parameter of advertisement method
Number of coupons used for new product j.
Number of coupons that have never been used
Number that are reached by advertisement
Maximum that can be reached by advertisement
Motivation effectiveness of advertisement
Reduction in motivation effectiveness caused by transportation method
Inconvenience of transportation
Fixed cost of take back
Total number of discountable products
Number of discount coupons used for the new product j
Change in number of sale of the new product j
Sale profit of new product j
Proportion of the sale of new products without the take back procedure
Proportion of discounts used for new product j
Proportion of new customers due to discount
Number of the coupons that are not used
Proportion of the coupons that are not used
Profit of take back with cash incentive
Profit of take back with fixed value discount incentive
Profit of take back with percentage discount incentive
Sale price of new product j
The model developed in previous sections provides a 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 . 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.
Three transportation options have been considered:
1- Pick up from the customers convenient location (residential or business location).
2- Providing the customers with the postage paid envelopes.
3- Asking the customers to hand deliver their handsets at particular locations.
Parameters of transportation options
Option 1: Pick Up
Option 2: Postages Paid Mail
Option 3: Collecting at Branches
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
Parameters of different advertisement options
Option 1: TV ad.
Option 2: Radio ad.
Option 3. Internet ad.
Option 4. Local Newspaper
Option 5. Retail Store ad.
Specifications of new discountable products
Parameters of η j functions
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, or p), 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 x and 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.
Determining the number of returns and its variation with respect to different parameters of the take back procedure is required in a cost benefit analysis of a take back problem. Number of returns depends on many parameters and in general should be measured or estimated for all combinations of these parameters (i.e. in a multidimensional domain of variables), which is not practical. In a simple model, the number of returns may be considered simply as a function of one variable [4, 9] usually termed the financial incentive or more generally the take back cost per returned product. Such a simple model, although provides overall theoretical insights about he take back process, but is not sufficient for many practical applications. It is not clear how the number of returns, which is a function of several variables, can be calibrated in terms of one variable. For example, increasing either the transportation cost or the financial incentive by $5, increases the take back cost by $5, but the resultant change in the number of returns can be significantly different. To overcome this limitation of the simple models, we first determined a set of factors that can significantly affect the number of returns like the transportation method, advertisement expenditure, and type and amount of financial incentives. Based on a solely theoretical analysis of the take back process, we derived a more detailed model for take back process that present several aspects of take back process. We tried to keep the model as simple as possible by imposing some reasonable assumptions. This model provided a general framework for different aspects of take back process and determined what empirical data is required for model calibration/validation.
Number of returns is modeled in terms of two functions; it is equal to the number of customers that are informed about the take back policy times the proportion of informed customers that return their used product. Number of informed customers depends on the method and volume of advertisement and is modeled as the Ω function. Proportion of informed customers that would return their used product depends on financial incentives and transportation method in addition to the method of advertisement; it is modeled as the Γ function. Γ function is a market characteristic of the take back process and should be determined using function approximation methods and the data obtained through surveys or pilot implementations. A general form of the Ω function was derived based on a basic analysis of advertisement. It should be mentioned that a detailed analysis of the advertisement is out of the scope of this paper; we only identified a set of parameters that are associated with advertisement and affect the number of returns through Ω or Γ functions. To determine Γ function, we first introduced the concept of motivation effectiveness, mte, and modeled Γ as a function of mte and then quantified and modeled the effect of different parameters of the take back (e.g. convenience of transportation and type of financial incentives) in terms of how they change the motivation effect of financial incentive. For example we assumed that offering financial incentive in the form of discount scales down the motivation effect of financial incentive (compared to equal amount of cash) by an average factor termed α. This enabled estimating Γ as a simplified single variable function while effects of other significant factors are included. Depending on the nature of the take back problem this model can be modified for the specific conditions of the problem. For example assume that the recovery firm requires the number of used products to be between N min and N max . This means that the number of taken back products should be larger than N min and the taken back products beyond N max does not generate any revenue. Therefore, in equations (10), (16) and (21) the value of used product, a should be multiplied by the minimum of N R and N max and in determining the maximum profit at each combination of reward strategy, advertisement method, and transportation method the domain of advertisement cost (W 2 ) and financial incentive (c, d or p) should be limited to the regions where N R is greater than N min .
Although as pointed out by Guide et al. , offering multiple incentives based on the condition of product can potentially increase the profit, it may not be the optimum strategy in all take back problems. In many practical cases customers may not be able to determine the condition of their used product and make their own decision about the return without knowing what they get in exchange. This usually affects the return rate adversely and may reduce the profit. However, most likely, the average quality of the returned products increases by increasing the incentive. This effect is included in the model by assuming the average value of returned products is a function of motivation effectiveness.
In this modeling framework the mutual effect between take back procedure and new product sale in discount strategies has been dissected and included in determining the net profit of take back. We allocated the total amount of discount as a cost to the take back procedure. We also allocated the increase in the profit of new product sale (because of discount) as revenue to the take back procedure. In doing this it is implicitly assumed that the take back and recovery procedures are performed by different segments of the same firm. However, even if the take back is offered by a different firm, the discount strategy can be considered as a financial incentive. Generally the take back firm should be able to purchase the new products from the new product manufacturer below their retail value at a wholesale price and resell them to the take back customers at a discounted price. The cost model is applicable to this case as well; the value of Λ should be set to one and the sale profits are the difference between the retail price of new product and the wholesale price minus any handling fee associated with the resell.
The amounts and types of advertisement and transportation can significantly affect the net profit of take back. The type and amount of financial incentive is similarly influential. The developed modeling framework enables the determination of the optimum strategies for advertisement and transportation. It also compares cash and discount incentives, and determines if the extra sale of new product associated with the discounts can generate sufficient revenue to compensate for the reduced motivation of discount incentives (compared to cash). For the take back process studied in this paper, the model predicts that the maximum profit of the discount incentive strategy is about 70% higher than the cash incentive strategy, even though it requires a higher amount of financial incentives. The model also provides insights about the take back process and can be used for sensitivity analysis and feasibility study. For example, for the take back problem presented, the model predicts that the return rate and consequently the net profit are initially more sensitive to the frequency of advertisement (or advertisement cost W 2 ) than the amount of financial incentive (Figure 2). Therefore, if the system parameters and consequently the optimum advertisement cost are unspecified, it would be a wise operational decision to implement the take back process initially with a higher advertisement frequency, until more accurate data is acquired.
An estimate can be found for the number of customers that are exposed to the advertisement (Ω function) based on available information about the statistics of advertisement method. Assume N ad is the number of customers (or in general people) that are exposed to the advertisement at least one time. Not all customers can be reached by a specific advertisement method. For example, the customers who do not read the newspaper containing the ad, or do not watch or hear the TV or radio program that broadcasts the ad, will not be exposed to the ad independent of the number of the times the ad posts or broadcasts. The maximum number of customers that are potentially exposed to the ad over frequent postings or broadcasts is defined as N ss . Also the average fraction of customers that are exposed to the ad in one run is defined by λ*. Both N ss and λ* are statistical parameters of the advertisement method and are assumed to be known.
where Ω ss is the maximum fraction of customers that can be informed by this method of advertisement. Ω ss and W sc are the two parameters that are different for different advertisement methods.
Authors are thankful to Dr. Garry Brandenburger and Dr. Guy Genin for their insightful comments.
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