Document Type : Research Paper
Author
Abstract
Due to fierce competition and customer demand, manufacturers have started selling products with different warranty policies and pro-rata warranty is one of the most widely used warranty policy. In this paper we propose a warranty model for pro-rata, fixed period warranty policy with risk averse manufacturer that determines optimal warranty price under inflationary condition.
This model has been proposed for products with time dependent failure intensity with Non homogeneous Poisson’s process for failure intensity function, and concave utility function. Using the exponential utility function, the decision model is developed to maximize the manufacturer’s certainty profit equivalent. Risk preference model is developed to find the optimal warranty price through the use of the manufacturer’s utility function for profit. Finally, the sensitivity of the warranty price models is analyzed using numerical examples with respect to such factors as (1) the manufacturer's risk preferences, (2) product failure rate parameters, (3) warranty period length, and (4) inflation and discount rate
Keywords
سرمد، ز.، بازرگان، ع.، حجازی، ا. ) 0165 (. روش های تحقیق در علوم رفتاری. نشر آگه )چاپ
08 (، تهران.
نصراللهی، م.، اصغری زاده، ع.، جعفر نژاد، ا.، و صنیعی منفرد، م.ع. ) 0161 (. توسعه سیاست
جدید وارانتی PRW - .052 005 .)0( برای برآورد هزینه ها. مدیریت صنعتی 9
نصراللهی، م.، اصغری زاده، ع. ) 0164 (. مدل تعیین قیمت وارانتی PRW با خریداران ریسک
- .045 010 .)0( گریز. پژوهش های مدیریت در ایران 02
Blischke, W.R. & Murthy, D.N.P. (1992). Product warranty management I: Taxonomy for warranty policies. European Journal of Operational Research 62, 127-148.
Blischke, W.R. & Murthy, D.N.P. (1995), Product Warranty Handbook, Marcel Dekker, Inc. New York.
Boom, A. (1998). Product risk sharing by warranties in a monopoly market with risk-averse consumers. Journal of Economic Behavior & Organization 33, 241-257.
Chirstozov, D., Chukova, S. & Mateev, P. (2009). On two types of warranties: warranty of malfunctioning and warranty of misinforming. Asia-Pacific Journal of Operational Research 26(3), 399-420.
Chun, Y.H. & Tang, K. (1995). Determining the optimal warranty price based on the producer'sand customers' risk preferences. European Journal of Operational Research 85, 97-110.
Eshraghnia Jahromi, A. & Vahdani, H. (2009). Replacement-Repair Policy Based on a Simulation Model for Multi-State Deteriorating Products Under Warranty. Transaction E: Industrial Engineering 16(1), 26-35.
Giri, B.C. & Bardhan, S. (2011). Coordinating a two-echelon supply chain under inflation and time value of money. International Journal of Industrial Engineering Computations 2. 811-818.
Huang, H.Z., Liu, Z.J., Li, Y., Liu, Y. & He, L. (2008). A warranty cost model with intermittent and heterogeneous usage. Maintenance and reliability 4, 9-15.
Jung, K.M., Park, M, & Park, D.H. (2015). Cost optimization model following extended renewing two-phase Warranty, Computers & Industrial Engineering 79, 188–194.
Li, Y.K. (2000), Jensen’s Inequality, Mathematical Excalibur 5(4), 1-4.
Moskowitz, H. & Plante, R. (1984). Effect of Risk Aversion on Single Sample Attribute Inspection Plans. Management Science, 30(10), 1226-1237.
Murthy, D.N.P. & Blischke, W.R. (1992), Product warranty and management II: An integrated framework for study. European Journal of Operational Research 62, 261-281.
Murthy, D. N. P., & Djamaludin, I. (2002). New product warranty: A literature review. International Journal of Production Economics, 79, 231–260.
Padmanabhan, V. & Rao, R.C. (1993). Warranty policy and extended service contracts: Theory and an application to automobiles. Marketing Science 12(3), 230-247.
Pandey, R.K. & Gupta, S. (2011). Supply Chain Inventory Model with Time Dependent Demand for Decaying Items under Inflation. International Transactions in Applied Sciences 3(1), 122-130.
Park, M. & Pham, H. (2016). Cost models for age replacement policies and block replacement policies under warranty, Applied Mathematical Modelling 40, 5689-5702.
Popovic, V., Stamenkovic, D. & Rakicevic, B. (2012). Choosing the Right Warranty Policy – from the Customer’s to the Manufacturer’s Point of View. International Journal of Applied Physics and Mathematics 2(5), 333-335.
Rahman, A & Chattopadhyay, G. (2010). Modeling risks to manufacturer and buyer for lifetime warranty policies. International Journal of Management Science and Engineering Management, 5(3), 203-209.
Ritchken, P.H. & Tapiero, C.S. (1986) Warranty design under buyer and seller risk aversion, Naval Research Logistics Quarterly 33, 657-671.
Sarker, B.R., Jamal, A.M.M. & Wang, S., (2000), Supply chain models for perishable products under inflation and permissible delay in payment, Computers & Operations Research 27, 59-75
Stamenković, D., Popović, V., Spasojević-Brkić, V. & Radivojević, J. (2011). Combination free replacement and pro-rata warranty policy optimization model. Journal of Applied Engineering Science 9(4), 457-464.
Thomas, M.U. (2010).Warranty Modeling. Wiley Encyclopedia of Operations Research and Management Science, edited by James J. Cochran. John Wiley & Sons, Inc.
Thomas, M.U. & Rao, S.S (1999). Warranty economic decision models: A summary and some suggested directions for future research. Operations research 47(6), 807-820.
Wang, Y., Liu, Z. & Liu, Y. (2015). Optimal preventive maintenance strategy for repairable items under two-dimensional warranty, ReliabilityEngineeringandSystemSafety142, 326–333.
Yang, D., He, Z. & He, S. (2016). Warranty claims forecasting based on a general imperfect repair model considering usage rate, Reliability Engineering and System Safety 145, 147-154.
Yeh, C.W. & Fang, C.C., (2014) Optimal pro-rata warranty decision with consideration of the marketing strategy under insufficient historical reliability data, International Journal of Advanced Manufacturing and Technology 71,1757–1772.
Zhou, Z., Li, Y. & Tang, K. (2009). Dynamic pricing and warranty policies for products with fixed lifetime. European Journal of Operational Research 196, 940–948.
Zolbec, S. (2004). Jensen’s Inequality for Nonconvex Functions, Mathematical Communications 9, 119-124.
08 (، تهران.
نصراللهی، م.، اصغری زاده، ع.، جعفر نژاد، ا.، و صنیعی منفرد، م.ع. ) 0161 (. توسعه سیاست
جدید وارانتی PRW - .052 005 .)0( برای برآورد هزینه ها. مدیریت صنعتی 9
نصراللهی، م.، اصغری زاده، ع. ) 0164 (. مدل تعیین قیمت وارانتی PRW با خریداران ریسک
- .045 010 .)0( گریز. پژوهش های مدیریت در ایران 02
Blischke, W.R. & Murthy, D.N.P. (1992). Product warranty management I: Taxonomy for warranty policies. European Journal of Operational Research 62, 127-148.
Blischke, W.R. & Murthy, D.N.P. (1995), Product Warranty Handbook, Marcel Dekker, Inc. New York.
Boom, A. (1998). Product risk sharing by warranties in a monopoly market with risk-averse consumers. Journal of Economic Behavior & Organization 33, 241-257.
Chirstozov, D., Chukova, S. & Mateev, P. (2009). On two types of warranties: warranty of malfunctioning and warranty of misinforming. Asia-Pacific Journal of Operational Research 26(3), 399-420.
Chun, Y.H. & Tang, K. (1995). Determining the optimal warranty price based on the producer'sand customers' risk preferences. European Journal of Operational Research 85, 97-110.
Eshraghnia Jahromi, A. & Vahdani, H. (2009). Replacement-Repair Policy Based on a Simulation Model for Multi-State Deteriorating Products Under Warranty. Transaction E: Industrial Engineering 16(1), 26-35.
Giri, B.C. & Bardhan, S. (2011). Coordinating a two-echelon supply chain under inflation and time value of money. International Journal of Industrial Engineering Computations 2. 811-818.
Huang, H.Z., Liu, Z.J., Li, Y., Liu, Y. & He, L. (2008). A warranty cost model with intermittent and heterogeneous usage. Maintenance and reliability 4, 9-15.
Jung, K.M., Park, M, & Park, D.H. (2015). Cost optimization model following extended renewing two-phase Warranty, Computers & Industrial Engineering 79, 188–194.
Li, Y.K. (2000), Jensen’s Inequality, Mathematical Excalibur 5(4), 1-4.
Moskowitz, H. & Plante, R. (1984). Effect of Risk Aversion on Single Sample Attribute Inspection Plans. Management Science, 30(10), 1226-1237.
Murthy, D.N.P. & Blischke, W.R. (1992), Product warranty and management II: An integrated framework for study. European Journal of Operational Research 62, 261-281.
Murthy, D. N. P., & Djamaludin, I. (2002). New product warranty: A literature review. International Journal of Production Economics, 79, 231–260.
Padmanabhan, V. & Rao, R.C. (1993). Warranty policy and extended service contracts: Theory and an application to automobiles. Marketing Science 12(3), 230-247.
Pandey, R.K. & Gupta, S. (2011). Supply Chain Inventory Model with Time Dependent Demand for Decaying Items under Inflation. International Transactions in Applied Sciences 3(1), 122-130.
Park, M. & Pham, H. (2016). Cost models for age replacement policies and block replacement policies under warranty, Applied Mathematical Modelling 40, 5689-5702.
Popovic, V., Stamenkovic, D. & Rakicevic, B. (2012). Choosing the Right Warranty Policy – from the Customer’s to the Manufacturer’s Point of View. International Journal of Applied Physics and Mathematics 2(5), 333-335.
Rahman, A & Chattopadhyay, G. (2010). Modeling risks to manufacturer and buyer for lifetime warranty policies. International Journal of Management Science and Engineering Management, 5(3), 203-209.
Ritchken, P.H. & Tapiero, C.S. (1986) Warranty design under buyer and seller risk aversion, Naval Research Logistics Quarterly 33, 657-671.
Sarker, B.R., Jamal, A.M.M. & Wang, S., (2000), Supply chain models for perishable products under inflation and permissible delay in payment, Computers & Operations Research 27, 59-75
Stamenković, D., Popović, V., Spasojević-Brkić, V. & Radivojević, J. (2011). Combination free replacement and pro-rata warranty policy optimization model. Journal of Applied Engineering Science 9(4), 457-464.
Thomas, M.U. (2010).Warranty Modeling. Wiley Encyclopedia of Operations Research and Management Science, edited by James J. Cochran. John Wiley & Sons, Inc.
Thomas, M.U. & Rao, S.S (1999). Warranty economic decision models: A summary and some suggested directions for future research. Operations research 47(6), 807-820.
Wang, Y., Liu, Z. & Liu, Y. (2015). Optimal preventive maintenance strategy for repairable items under two-dimensional warranty, ReliabilityEngineeringandSystemSafety142, 326–333.
Yang, D., He, Z. & He, S. (2016). Warranty claims forecasting based on a general imperfect repair model considering usage rate, Reliability Engineering and System Safety 145, 147-154.
Yeh, C.W. & Fang, C.C., (2014) Optimal pro-rata warranty decision with consideration of the marketing strategy under insufficient historical reliability data, International Journal of Advanced Manufacturing and Technology 71,1757–1772.
Zhou, Z., Li, Y. & Tang, K. (2009). Dynamic pricing and warranty policies for products with fixed lifetime. European Journal of Operational Research 196, 940–948.
Zolbec, S. (2004). Jensen’s Inequality for Nonconvex Functions, Mathematical Communications 9, 119-124.
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