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Development of a cost model and its application in determining optimal size of a diesel engine remanufacturing facility
CIRP Annals - Manufacturing Technology 59 (2010) 49–52
Contents lists available at ScienceDirect
CIRP Annals - Manufacturing Technology jou rnal homep age : ht t p: // ees .e lse vi er. com/ci rp/ def a ult . asp
Development of a cost model and its application in determining optimal size of a diesel engine remanufacturing facility J.W. Sutherland (2)a, T.L. Jenkins b, K.R. Haapala c,* a
Division of Environmental and Ecological Engineering, Purdue University, West Lafayette, IN 47907, United States Department of Mechanical Engineering-Engineering Mechanics, Sustainable Futures Institute, Michigan Technological, University, Houghton, MI 49931, United States c School of Mechanical, Industrial, and Manufacturing Engineering, Oregon State University, 204 Rogers Hall, Corvallis, OR 97331, United States b
A R T I C L E I N F O
A B S T R A C T
Keywords: Sustainable development Optimization Remanufacturing
Remanufacturing represents a business opportunity and a means to promote environmental sustainability. In planning remanufacturing operations for a specific product in a particular market, determining the facility size is a critical decision. A large centralized facility offers economies of scale advantages, but has greater transportation costs relative to a set of smaller distributed facilities. A remanufacturing facility cost model is developed and applied for diesel engine remanufacturing that includes product, operation, inventory, and transportation-related costs. The effects of product yield, remanufacturing efficiency, transportation cost rate, and product mass on remanufactured product unit cost and remanufacturing facility size are examined. ß 2010 CIRP.
1. Introduction Sustainability is recognized as embracing the environmental, economic, and social needs of current and future generations [1]. A range of strategies can be pursued to reduce environmental impacts across the product life cycle, e.g., dematerialization, modular design, cleaner production, and end-of-life value recovery. Increasingly, value recovery, often in the form of product remanufacturing and material recycling, is seen as a means of improving the sustainability of products and production systems [2]. Value recovery has proven to be profitable in several industries, e.g., engines and metal goods, but is not attractive in some others due to technical challenges and prohibitive costs. Recovery of some products has been mandated within the European Union, and takeback legislation continues to be adopted globally. Due to market competition, incentives, and policy pressures, manufacturing companies are increasingly redesigning their processes, products, and systems in ways that are amenable to product takeback and remanufacturing. A financially successful value recovery operation requires careful consideration of collection, remanufacturing, and redistribution costs. While remanufacturing processes have been investigated for profitability and environmental performance previously [3–5], the research presented in this paper develops a model for evaluating system-scale costs associated with diesel engine remanufacturing facilities. The size and number of facilities, and their respective locations in a market area, are key in determining product unit costs [6]. Facility (e.g., construction and operation) and transportation costs
* Corresponding author. 0007-8506/$ – see front matter ß 2010 CIRP. doi:10.1016/j.cirp.2010.03.050
are major contributors to product unit costs. When transportation costs are low, a few large facilities are favored for a given market. These centralized facilities require more travel for recovery and redistribution, but benefit from economies of scale in facility costs. Conversely, a decentralized network with many smaller facilities serving smaller service areas has lower transportation costs, but higher facility-related costs [7]. Products to be remanufactured must be collected from across a service region at the end of their use. This recovery activity involves more complex logistics than new product or material distribution [7]. Collection of used products that are highly diffused across a region represents a cost to the remanufacturer or recycler, when not borne by the final user. Thus, the upstream flow, reverse logistics, of used goods and materials, is driven by end-consumer supply, or the amount of used products reaching end-of-life. Uncertainties about the quantities and quality of endof-use products pose a challenge for production and financial planning. Given this background, a diesel engine remanufacturing facility cost model that accounts for various system level costs is developed and applied to a representative case. 2. Model development The model assumes the total annual cost of operation, Ctot, is dependent upon the cost of used products, or cores, CM, the cost of recovering the products, CR, the amortized annual cost of constructing the remanufacturing facility, CC, the annual costs of facility operation, CO, the cost of distributing remanufactured products, CT, and the cost associated with selling the remanufactured products, CS. Thus, the total annual cost is C tot ¼ C M þ C R þ C C þ C O þ C T þ C S ;
(1)
50
J.W. Sutherland et al. / CIRP Annals - Manufacturing Technology 59 (2010) 49–52
where each of the terms on the right-hand-side of the equation is dependent upon the annual output of the remanufacturing facility, PS (products/year), a measure of facility size. The number of products, or units, processed by the remanufacturing facility is (PS/ hR), where hR is the remanufacturing efficiency, i.e., the fraction of products entering the facility that are ultimately remanufactured. It should be noted that new make-up parts may need to be acquired to complete the remanufacture of a product if elements of the used product are so badly damaged that they cannot be repaired or refurbished. This cost is not considered in the model. Attention now turns to examining each of the cost components in detail. The annual cost of product recovery, CM, includes the purchase cost of all used products, CAP, transaction costs, COR, and holding (i.e., handling and storage) costs, C M ¼ C AP þ C OR þ C H :
(2)
The purchase cost of all products collected and holding costs depend on the number of units required annually: PS PS (3) and C H ¼ hS hP C P ; C AP ¼ C P
hR
hR
where CP is the price paid to purchase the end-of-use product. The holding costs, or annual inventory costs, CH, are based on the fraction, hS, of annual production volume held in inventory and are scaled by a cost factor, hPCP (hP was assumed to be 0.15), i.e., hPCP is 15% of the purchase price for recovered products. Gunter and Sutherland [8] developed a model of demanufacturing inventory costs for multiple component products to determine the optimal selling quantity (analogous to economic order quantity). In the study herein, it is assumed the remanufacturer will hold about 30% of its annual output in inventory (hS = 0.3). Taking into account the used product value (purchase price), transaction costs, and holding costs, annual expenditures on recovered products are PS ð1 þ hS hP Þ þ C OR : (4) CM ¼ CP
hR
The annual cost, CR, of delivering recovered products to the remanufacturing facility is CR ¼ CDd
PS
hR c
(5)
;
where CD is the transportation cost rate ($/tonne/km), c is the number of products per tonne (metric ton), and d is the delivery distance. To find d, it is assumed that the remanufacturing facility is centered in a circular service area with a radius, R. Transportation costs are based on the distance from the source to the facility. Assuming a uniform distribution of used products to be remanufactured within this service area, the average delivery distance is d = (2/3)R. The size of the service region depends on the capacity or annual production rate of the remanufacturing facility, PS, and the remanufacturing efficiency, hR. Thus, the radius, R, can be determined using sffiffiffiffiffiffiffiffiffiffiffiffiffi PS PS =hR 2 ; (6) r pR ¼ or R ¼
hR
pr
where the product yield within the service area is r (products/ km2), which is a measure of end-of-use product availability. Thus, the average delivery distance is sffiffiffiffiffiffiffiffiffiffiffiffi 2 PS d¼ (7) 3 phR r and the annual product recovery transportation costs are CR ¼
2 PS P S 1=2 CD 3 hR c phR r
(8)
Annualized construction costs, CC, are influenced by facility life, L, and an economies of scale factor, a, which has typical values
between 0.6 and 0.8 [9]. With this in mind, CC ¼
C C;base P S =hR a ; L PS;base
(9)
where a baseline facility with a capacity of PS,base has a construction cost of CC,base. In this paper a = 0.7 and a ten year life (L = 10) are assumed. Likewise, the annual operation cost, CO, is influenced by economies of scale, and is given by C O ¼ C O;base
PS =hR b P S;base
(10)
where CO,base is the annual operating cost of the baseline facility. It should be noted that operating cost considers production-related costs in aggregate, and includes all functions associated with a given product remanufacturing process (e.g., disassembly, sorting, cleaning, and inspection). For operation costs, the scale factor, b, is typically between 0.5 and 1; b = 0.8 was used in this study [9]. The transportation cost, CT, associated with redistributing remanufactured products to customers or retailers assumes the same service area from which the used products are collected, as CT ¼
2 PS PS 1=2 CD : 3 c phR r
(11)
The same delivery distance, d, and cost rate, CD, are used as in calculating CR. The number of newly remanufactured products that must be redelivered is reduced based on the remanufacturing efficiency, hR. The cost incurred to sell remanufactured products, CS = SCPS, is specific to a given product, where SC is the cost associated with selling each product. Substituting the expressions above for the cost components in Eq. (1) produces the following equation for total annual costs: 1=2 PS 2 PS PS C tot ¼ C P ð1 þ hS hP Þ þ C OR þ C D 3 h hR c phR r R C C;base P S =hR a P S =hR b þ þ C O;base L P S;base PS;base 1=2 2 PS PS þ CD þ SC P S 3 c phR r
(12)
The cost model displayed in Eq. (12) can be used to estimate the total annual cost associated with remanufacturing operations, however, in order to perform a comparative cost evaluation on a per unit basis, the total annual cost must be divided by the number of products remanufactured each year, PS. Thus, the product cost per unit of product remanufactured, Cu, is 0:5 C OR 2 C D PS 1 þ 1þ hR PS 3 c phR r hR C C;base PS a1 C O;base P S b1 þ þ þSC hR PS;base a L hR PS;base b C u ¼ ð1 þ hS hP Þ
CP
þ
(13)
3. Application of the model The model considers a representative facility that remanufactures large shipments of several sizes of diesel engines [5]. Diesel engines consist of hundreds of components and many subassemblies. As described above, this system-level model does not account for the variability among individual processes for each component and assembly, but considers aggregate remanufacturing operations. Fig. 1 shows how the transportation cost rate and facility size, measured as annual output, affect remanufacturing unit cost (Table 1 shows the values for the model coefficients for this base case). As expected, unit costs decrease with transportation cost rate; however, for small facility sizes, this effect appears minor. More importantly, the graph indicates that a minimum unit cost exists as a function of plant size. This optimal facility size increases as transportation costs are reduced.
J.W. Sutherland et al. / CIRP Annals - Manufacturing Technology 59 (2010) 49–52
51
Table 2 Variable ranges investigated for each factor. Variable name
Value
Variable name
Value
Yield (units/km2), r Product mass (kg) Products per tonne, c Reman. efficiency, hR Inventory factor, hS Holding cost factor, hP Construction factor, a Operating factor, b
0.0335 1,250 0.800 0.750 0.300 0.150 0.700 0.800
Ordering cost ($), COR Product cost ($/unit), CP Sales cost ($/unit), SC Trans. cost rt. ($/t/km), CD PS,base (Prod thousands) CC,base ($ million) CO,base ($ million) Facility life (years), L
20,000 1000 1000 20.55 10.011 13.125 2.625 10
Fig. 1. Unit cost versus plant size for various transportation cost rates.
Fig. 3. Unit cost ($/product) as a function of product yield and transportation cost rate.
Fig. 2. Optimal plant size (annual output) as a function of product yield and transportation cost rate.
As noted above, a minimum remanufacturing unit cost exists as a function of facility size. To obtain this minimum, the derivative of the unit cost with respect to facility size is taken as pffiffiffiffiffiffiffiffiffi dC u C OR 0:5ð2=3Þð 1=pÞð1 þ 1=hR ÞC D ¼ þ dPS PS2 hR rcðPS =hR rÞ0:5 þ
ða 1ÞC C;base PS a2 ðb 1ÞC O;base P S b2 : þ ðhR PS;base Þa L ðhR PS;base Þb
plant size. These factors were investigated for their influence on facility size and unit cost, with value ranges as shown in Table 2. Unless otherwise stated, all other variables were set at the levels indicated in Table 1. The behavior of optimal facility size as a function of product yield, essentially the density of end-of-use products within a service area, and transportation cost rate are shown with a contour plot in Fig. 2. The figure shows that the optimal facility size is increasingly sensitive to transportation costs as the yield increases. The optimal facility size is highly sensitive to changes in product yield when the transportation cost rate is low. Fig. 3 displays unit cost contours for the same conditions as Fig. 2. The unit cost
(14)
The minimum unit cost can then be determined by equating Eq. (14) to zero and solving for PS. In this case, a closed form expression for optimal remanufacturing facility size cannot be determined, but the facility size can be solved for numerically. It is evident from Eqs. (13) and (14) that the unit purchase price, CP, the holding cost factor, hP, and the cost associated with reselling the product, SC, are independent of annual output and do not influence optimal facility size when minimizing unit cost. However, product yield, r, product mass, 1/c, remanufacturing efficiency, hR, and transportation cost rate, CD, do affect the optimal
Table 1 Model coefficient values for engine remanufacturing base case. Variable
Range
Variable
Range
r
0.005–0.100 0.100–0.500
hR c
0.500–0.900 0.500–1.330
CD
Fig. 4. Optimal plant size (annual output) as a function of product yield and remanufacturing efficiency.
52
J.W. Sutherland et al. / CIRP Annals - Manufacturing Technology 59 (2010) 49–52
(1) For high product yields, a high density of end-of-use products, the optimal facility size is very sensitive to the transportation cost rate. Higher yields lead to larger optimal facility size, and higher transportation cost rates reduce the facility size. (2) Larger facility sizes produce lower remanufacturing unit costs, and small facility sizes result in large unit costs. (3) The holding cost and costs of product recovery affect the remanufacturing unit cost; however, they do not influence the optimal size of the remanufacturing facility. (4) Remanufacturing efficiency and product mass both influence facility size. In general, as remanufacturing efficiency increases or the mass of the product decreases, the optimal facility size increases.
Fig. 5. Optimal plant size (annual output) as a function of product yield and number of products per tonne.
contours appear to have a similar shape to the facility size contours, with larger facility sizes corresponding to smaller unit costs. The unit cost is most sensitive to changes in product yield for higher transportation cost rates, and the unit cost is most sensitive to changes in transportation cost rate when the product yield is large. Fig. 4 shows the behavior of optimal plant size as a function of product yield and remanufacturing efficiency. Product yield appears to have a stronger effect on plant size than remanufacturing efficiency; and optimal plant size increases with both factors. For higher yields, the role of efficiency appears to be stronger. The number of products per tonne, c, was varied in Fig. 5, along with varying the product yield. The effect of c is nearly comparable to that of product yield, with the effect of c being larger at higher yields. At higher values for c, the plant size is highly sensitive to product yield. 4. Summary and conclusions Product value recovery through remanufacturing represents an excellent opportunity to improve sustainability. A financially successful remanufacturing operation, however, requires careful consideration of all costs. With this in mind, a model was developed that considers facility, transportation, and other costs to identify the optimal size for a diesel engine remanufacturing facility. From the work described herein, the following conclusions may be drawn:
The results of this work suggest that care is needed during facility planning for remanufacturing operations. Special attention must be given to such issues as product yield, transportation costs, remanufacturing efficiency, and product mass. As is evident, selecting an appropriate size for a remanufacturing facility promotes both environmental and economic sustainability of a business. Acknowledgements Support from the National Science Foundation is gratefully acknowledged (under CBET-0524872). Discussions with A.R. Clarke-Sather during the early phases of this work were very helpful. Special thanks to Joseph Allen of Caterpillar for providing background information.
References [1] WECD. (1987) Our Common Future, World Commission on Environment and Development. Oxford University Press, New York, NY. [2] Kumar V, Shirodkar PS, Camelio JA, Sutherland JW (2007) Value Flow Characterization During Product Lifecycle to Assist in Recovery Decisions. International Journal of Production Research 45(18):4555–4572. [3] Sutherland JW, Gunter KL (2002) A Model for Improving Economic Performance of a Demanufacturing System for Reduced Product End-of-Life Environmental Impact. CIRP Annals 51(1):45–48. [4] Seliger G, Franke C, Ciupek M, Basdere B (2004) Process and Facility Planning for Mobile Phone Remanufacturing. CIRP Annals 53(1):9–12. [5] Sutherland JW, Adler DP, Haapala KR, Kumar V (2008) A Comparison of Manufacturing and Remanufacturing Energy Intensities with Application to Diesel Engine Production. CIRP Annals 57(1):5–8. [6] Erlenkotter D (1989) The General Optimal Market Model. Annals of Operations Research 18:45–70. [7] Fleischmann M, Krikke HR, Dekker R, Flapper SDP (2000) A Characterisation of Logistics Networks for Product Recovery. Omega 28(6):653–666. [8] Gunter KL, Sutherland JW (2004) Analytical Models for Economic Demanufacturing Inventory Management. Proceedings of IMECE, Paper IMECE2004-61446, 8. [9] Haldi J, Whitcomb D (1967) Economies of Scale in Industrial Plants. Journal of Political Economy 75(4):373–385.
Contents lists available at ScienceDirect
CIRP Annals - Manufacturing Technology jou rnal homep age : ht t p: // ees .e lse vi er. com/ci rp/ def a ult . asp
Development of a cost model and its application in determining optimal size of a diesel engine remanufacturing facility J.W. Sutherland (2)a, T.L. Jenkins b, K.R. Haapala c,* a
Division of Environmental and Ecological Engineering, Purdue University, West Lafayette, IN 47907, United States Department of Mechanical Engineering-Engineering Mechanics, Sustainable Futures Institute, Michigan Technological, University, Houghton, MI 49931, United States c School of Mechanical, Industrial, and Manufacturing Engineering, Oregon State University, 204 Rogers Hall, Corvallis, OR 97331, United States b
A R T I C L E I N F O
A B S T R A C T
Keywords: Sustainable development Optimization Remanufacturing
Remanufacturing represents a business opportunity and a means to promote environmental sustainability. In planning remanufacturing operations for a specific product in a particular market, determining the facility size is a critical decision. A large centralized facility offers economies of scale advantages, but has greater transportation costs relative to a set of smaller distributed facilities. A remanufacturing facility cost model is developed and applied for diesel engine remanufacturing that includes product, operation, inventory, and transportation-related costs. The effects of product yield, remanufacturing efficiency, transportation cost rate, and product mass on remanufactured product unit cost and remanufacturing facility size are examined. ß 2010 CIRP.
1. Introduction Sustainability is recognized as embracing the environmental, economic, and social needs of current and future generations [1]. A range of strategies can be pursued to reduce environmental impacts across the product life cycle, e.g., dematerialization, modular design, cleaner production, and end-of-life value recovery. Increasingly, value recovery, often in the form of product remanufacturing and material recycling, is seen as a means of improving the sustainability of products and production systems [2]. Value recovery has proven to be profitable in several industries, e.g., engines and metal goods, but is not attractive in some others due to technical challenges and prohibitive costs. Recovery of some products has been mandated within the European Union, and takeback legislation continues to be adopted globally. Due to market competition, incentives, and policy pressures, manufacturing companies are increasingly redesigning their processes, products, and systems in ways that are amenable to product takeback and remanufacturing. A financially successful value recovery operation requires careful consideration of collection, remanufacturing, and redistribution costs. While remanufacturing processes have been investigated for profitability and environmental performance previously [3–5], the research presented in this paper develops a model for evaluating system-scale costs associated with diesel engine remanufacturing facilities. The size and number of facilities, and their respective locations in a market area, are key in determining product unit costs [6]. Facility (e.g., construction and operation) and transportation costs
* Corresponding author. 0007-8506/$ – see front matter ß 2010 CIRP. doi:10.1016/j.cirp.2010.03.050
are major contributors to product unit costs. When transportation costs are low, a few large facilities are favored for a given market. These centralized facilities require more travel for recovery and redistribution, but benefit from economies of scale in facility costs. Conversely, a decentralized network with many smaller facilities serving smaller service areas has lower transportation costs, but higher facility-related costs [7]. Products to be remanufactured must be collected from across a service region at the end of their use. This recovery activity involves more complex logistics than new product or material distribution [7]. Collection of used products that are highly diffused across a region represents a cost to the remanufacturer or recycler, when not borne by the final user. Thus, the upstream flow, reverse logistics, of used goods and materials, is driven by end-consumer supply, or the amount of used products reaching end-of-life. Uncertainties about the quantities and quality of endof-use products pose a challenge for production and financial planning. Given this background, a diesel engine remanufacturing facility cost model that accounts for various system level costs is developed and applied to a representative case. 2. Model development The model assumes the total annual cost of operation, Ctot, is dependent upon the cost of used products, or cores, CM, the cost of recovering the products, CR, the amortized annual cost of constructing the remanufacturing facility, CC, the annual costs of facility operation, CO, the cost of distributing remanufactured products, CT, and the cost associated with selling the remanufactured products, CS. Thus, the total annual cost is C tot ¼ C M þ C R þ C C þ C O þ C T þ C S ;
(1)
50
J.W. Sutherland et al. / CIRP Annals - Manufacturing Technology 59 (2010) 49–52
where each of the terms on the right-hand-side of the equation is dependent upon the annual output of the remanufacturing facility, PS (products/year), a measure of facility size. The number of products, or units, processed by the remanufacturing facility is (PS/ hR), where hR is the remanufacturing efficiency, i.e., the fraction of products entering the facility that are ultimately remanufactured. It should be noted that new make-up parts may need to be acquired to complete the remanufacture of a product if elements of the used product are so badly damaged that they cannot be repaired or refurbished. This cost is not considered in the model. Attention now turns to examining each of the cost components in detail. The annual cost of product recovery, CM, includes the purchase cost of all used products, CAP, transaction costs, COR, and holding (i.e., handling and storage) costs, C M ¼ C AP þ C OR þ C H :
(2)
The purchase cost of all products collected and holding costs depend on the number of units required annually: PS PS (3) and C H ¼ hS hP C P ; C AP ¼ C P
hR
hR
where CP is the price paid to purchase the end-of-use product. The holding costs, or annual inventory costs, CH, are based on the fraction, hS, of annual production volume held in inventory and are scaled by a cost factor, hPCP (hP was assumed to be 0.15), i.e., hPCP is 15% of the purchase price for recovered products. Gunter and Sutherland [8] developed a model of demanufacturing inventory costs for multiple component products to determine the optimal selling quantity (analogous to economic order quantity). In the study herein, it is assumed the remanufacturer will hold about 30% of its annual output in inventory (hS = 0.3). Taking into account the used product value (purchase price), transaction costs, and holding costs, annual expenditures on recovered products are PS ð1 þ hS hP Þ þ C OR : (4) CM ¼ CP
hR
The annual cost, CR, of delivering recovered products to the remanufacturing facility is CR ¼ CDd
PS
hR c
(5)
;
where CD is the transportation cost rate ($/tonne/km), c is the number of products per tonne (metric ton), and d is the delivery distance. To find d, it is assumed that the remanufacturing facility is centered in a circular service area with a radius, R. Transportation costs are based on the distance from the source to the facility. Assuming a uniform distribution of used products to be remanufactured within this service area, the average delivery distance is d = (2/3)R. The size of the service region depends on the capacity or annual production rate of the remanufacturing facility, PS, and the remanufacturing efficiency, hR. Thus, the radius, R, can be determined using sffiffiffiffiffiffiffiffiffiffiffiffiffi PS PS =hR 2 ; (6) r pR ¼ or R ¼
hR
pr
where the product yield within the service area is r (products/ km2), which is a measure of end-of-use product availability. Thus, the average delivery distance is sffiffiffiffiffiffiffiffiffiffiffiffi 2 PS d¼ (7) 3 phR r and the annual product recovery transportation costs are CR ¼
2 PS P S 1=2 CD 3 hR c phR r
(8)
Annualized construction costs, CC, are influenced by facility life, L, and an economies of scale factor, a, which has typical values
between 0.6 and 0.8 [9]. With this in mind, CC ¼
C C;base P S =hR a ; L PS;base
(9)
where a baseline facility with a capacity of PS,base has a construction cost of CC,base. In this paper a = 0.7 and a ten year life (L = 10) are assumed. Likewise, the annual operation cost, CO, is influenced by economies of scale, and is given by C O ¼ C O;base
PS =hR b P S;base
(10)
where CO,base is the annual operating cost of the baseline facility. It should be noted that operating cost considers production-related costs in aggregate, and includes all functions associated with a given product remanufacturing process (e.g., disassembly, sorting, cleaning, and inspection). For operation costs, the scale factor, b, is typically between 0.5 and 1; b = 0.8 was used in this study [9]. The transportation cost, CT, associated with redistributing remanufactured products to customers or retailers assumes the same service area from which the used products are collected, as CT ¼
2 PS PS 1=2 CD : 3 c phR r
(11)
The same delivery distance, d, and cost rate, CD, are used as in calculating CR. The number of newly remanufactured products that must be redelivered is reduced based on the remanufacturing efficiency, hR. The cost incurred to sell remanufactured products, CS = SCPS, is specific to a given product, where SC is the cost associated with selling each product. Substituting the expressions above for the cost components in Eq. (1) produces the following equation for total annual costs: 1=2 PS 2 PS PS C tot ¼ C P ð1 þ hS hP Þ þ C OR þ C D 3 h hR c phR r R C C;base P S =hR a P S =hR b þ þ C O;base L P S;base PS;base 1=2 2 PS PS þ CD þ SC P S 3 c phR r
(12)
The cost model displayed in Eq. (12) can be used to estimate the total annual cost associated with remanufacturing operations, however, in order to perform a comparative cost evaluation on a per unit basis, the total annual cost must be divided by the number of products remanufactured each year, PS. Thus, the product cost per unit of product remanufactured, Cu, is 0:5 C OR 2 C D PS 1 þ 1þ hR PS 3 c phR r hR C C;base PS a1 C O;base P S b1 þ þ þSC hR PS;base a L hR PS;base b C u ¼ ð1 þ hS hP Þ
CP
þ
(13)
3. Application of the model The model considers a representative facility that remanufactures large shipments of several sizes of diesel engines [5]. Diesel engines consist of hundreds of components and many subassemblies. As described above, this system-level model does not account for the variability among individual processes for each component and assembly, but considers aggregate remanufacturing operations. Fig. 1 shows how the transportation cost rate and facility size, measured as annual output, affect remanufacturing unit cost (Table 1 shows the values for the model coefficients for this base case). As expected, unit costs decrease with transportation cost rate; however, for small facility sizes, this effect appears minor. More importantly, the graph indicates that a minimum unit cost exists as a function of plant size. This optimal facility size increases as transportation costs are reduced.
J.W. Sutherland et al. / CIRP Annals - Manufacturing Technology 59 (2010) 49–52
51
Table 2 Variable ranges investigated for each factor. Variable name
Value
Variable name
Value
Yield (units/km2), r Product mass (kg) Products per tonne, c Reman. efficiency, hR Inventory factor, hS Holding cost factor, hP Construction factor, a Operating factor, b
0.0335 1,250 0.800 0.750 0.300 0.150 0.700 0.800
Ordering cost ($), COR Product cost ($/unit), CP Sales cost ($/unit), SC Trans. cost rt. ($/t/km), CD PS,base (Prod thousands) CC,base ($ million) CO,base ($ million) Facility life (years), L
20,000 1000 1000 20.55 10.011 13.125 2.625 10
Fig. 1. Unit cost versus plant size for various transportation cost rates.
Fig. 3. Unit cost ($/product) as a function of product yield and transportation cost rate.
Fig. 2. Optimal plant size (annual output) as a function of product yield and transportation cost rate.
As noted above, a minimum remanufacturing unit cost exists as a function of facility size. To obtain this minimum, the derivative of the unit cost with respect to facility size is taken as pffiffiffiffiffiffiffiffiffi dC u C OR 0:5ð2=3Þð 1=pÞð1 þ 1=hR ÞC D ¼ þ dPS PS2 hR rcðPS =hR rÞ0:5 þ
ða 1ÞC C;base PS a2 ðb 1ÞC O;base P S b2 : þ ðhR PS;base Þa L ðhR PS;base Þb
plant size. These factors were investigated for their influence on facility size and unit cost, with value ranges as shown in Table 2. Unless otherwise stated, all other variables were set at the levels indicated in Table 1. The behavior of optimal facility size as a function of product yield, essentially the density of end-of-use products within a service area, and transportation cost rate are shown with a contour plot in Fig. 2. The figure shows that the optimal facility size is increasingly sensitive to transportation costs as the yield increases. The optimal facility size is highly sensitive to changes in product yield when the transportation cost rate is low. Fig. 3 displays unit cost contours for the same conditions as Fig. 2. The unit cost
(14)
The minimum unit cost can then be determined by equating Eq. (14) to zero and solving for PS. In this case, a closed form expression for optimal remanufacturing facility size cannot be determined, but the facility size can be solved for numerically. It is evident from Eqs. (13) and (14) that the unit purchase price, CP, the holding cost factor, hP, and the cost associated with reselling the product, SC, are independent of annual output and do not influence optimal facility size when minimizing unit cost. However, product yield, r, product mass, 1/c, remanufacturing efficiency, hR, and transportation cost rate, CD, do affect the optimal
Table 1 Model coefficient values for engine remanufacturing base case. Variable
Range
Variable
Range
r
0.005–0.100 0.100–0.500
hR c
0.500–0.900 0.500–1.330
CD
Fig. 4. Optimal plant size (annual output) as a function of product yield and remanufacturing efficiency.
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(1) For high product yields, a high density of end-of-use products, the optimal facility size is very sensitive to the transportation cost rate. Higher yields lead to larger optimal facility size, and higher transportation cost rates reduce the facility size. (2) Larger facility sizes produce lower remanufacturing unit costs, and small facility sizes result in large unit costs. (3) The holding cost and costs of product recovery affect the remanufacturing unit cost; however, they do not influence the optimal size of the remanufacturing facility. (4) Remanufacturing efficiency and product mass both influence facility size. In general, as remanufacturing efficiency increases or the mass of the product decreases, the optimal facility size increases.
Fig. 5. Optimal plant size (annual output) as a function of product yield and number of products per tonne.
contours appear to have a similar shape to the facility size contours, with larger facility sizes corresponding to smaller unit costs. The unit cost is most sensitive to changes in product yield for higher transportation cost rates, and the unit cost is most sensitive to changes in transportation cost rate when the product yield is large. Fig. 4 shows the behavior of optimal plant size as a function of product yield and remanufacturing efficiency. Product yield appears to have a stronger effect on plant size than remanufacturing efficiency; and optimal plant size increases with both factors. For higher yields, the role of efficiency appears to be stronger. The number of products per tonne, c, was varied in Fig. 5, along with varying the product yield. The effect of c is nearly comparable to that of product yield, with the effect of c being larger at higher yields. At higher values for c, the plant size is highly sensitive to product yield. 4. Summary and conclusions Product value recovery through remanufacturing represents an excellent opportunity to improve sustainability. A financially successful remanufacturing operation, however, requires careful consideration of all costs. With this in mind, a model was developed that considers facility, transportation, and other costs to identify the optimal size for a diesel engine remanufacturing facility. From the work described herein, the following conclusions may be drawn:
The results of this work suggest that care is needed during facility planning for remanufacturing operations. Special attention must be given to such issues as product yield, transportation costs, remanufacturing efficiency, and product mass. As is evident, selecting an appropriate size for a remanufacturing facility promotes both environmental and economic sustainability of a business. Acknowledgements Support from the National Science Foundation is gratefully acknowledged (under CBET-0524872). Discussions with A.R. Clarke-Sather during the early phases of this work were very helpful. Special thanks to Joseph Allen of Caterpillar for providing background information.
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