Pricing and replenishment strategy for a multi-market deteriorating product with time-varying and price-sensitive demand

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October 2013, 9(4): 769-787. doi: 10.3934/jimo.2013.9.769

Pricing and replenishment strategy for a multi-market deteriorating product with time-varying and price-sensitive demand

Po-Chung Yang ^1, , Hui-Ming Wee ^2, , Shen-Lian Chung ^3, and Yong-Yan Huang ^4,

1.	Marketing and Logistics Management Department, St. John’s University, Tamsui, Taipei 25135, Taiwan
2.	Industrial and Systems Engineering Department, Chung Yuan Christian University, Chungli, 32023, Taiwan
3.	Information Management Department, St. John’s University, Tamsui, Taipei 25135, Taiwan
4.	Industrial Engineering and Management Department, St. John’s University, Tamsui, Taipei 25135, Taiwan

Received August 2011 Revised March 2013 Published August 2013

Abstract
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Due to globalization and technological advances, increasing competition and falling prices have forced enterprises to reduce cost; this poses new challenges in pricing and replenishment strategy. The study develops a piecewise production-inventory model for a multi-market deteriorating product with time-varying and price-sensitive demand. Optimal product pricing and material replenishment strategy is derived to optimize the manufacturer's total profit. Sensitivity analyses of how the major parameters affect the decision variables were carried out. Finally, the single production cycle is extended to multiple production cycles. We find that the total profit for multiple production cycle increases 5.77/100 when compared with the single production cycle.

Keywords: Time-varying demand, multi-market, single and multiple production cycles., deterioration, price-sensitive demand.

Mathematics Subject Classification: Primary: 58F15, 58F17; Secondary: 53C3.

Citation: Po-Chung Yang, Hui-Ming Wee, Shen-Lian Chung, Yong-Yan Huang. Pricing and replenishment strategy for a multi-market deteriorating product with time-varying and price-sensitive demand. Journal of Industrial & Management Optimization, 2013, 9 (4) : 769-787. doi: 10.3934/jimo.2013.9.769

References:

[1]	Z. T. Balkhi and L. Benkherouf, A production lot size inventory model for deteriorating items and arbitrary production and demand rates,, European Journal of Operational Research, 92 (1996), 302. doi: 10.1016/0377-2217(95)00148-4. Google Scholar
[2]	H. J. Chang, J. T. Teng, L. Y. Ouyang and C. Y. Dye, Retailer's optimal pricing and lot sizing policies for deteriorating items with partial backlogging,, European Journal of Operational Research, 168 (2006), 51. doi: 10.1016/j.ejor.2004.05.003. Google Scholar
[3]	P. M. Ghare and S. F. Schrader, A model for exponentially decaying inventory,, Journal of Industrial Engineering, 14 (1963), 238. Google Scholar
[4]	Y. He, S. Y. Wang and K. K. Lai, An optimal production-inventory model for deteriorating items with multiple-market demand,, European Journal of Operational Research, 203 (2010), 593. doi: 10.1016/j.ejor.2009.09.003. Google Scholar
[5]	S. Kang and I. Kim, A study on the price and production level of the deteriorating inventory system,, International Journal of Production Research, 21 (1983), 449. doi: 10.1080/00207548308942422. Google Scholar
[6]	M. Khouja, The effect of large order quantities on expected profit in the single-period model,, International Journal of Production Economics, 72 (2001), 227. doi: 10.1016/S0925-5273(00)00150-X. Google Scholar
[7]	P. Kouvelis and G. J. Gutierrez, The newsvendor problem in a global market: Optimal centralized and decentralized control policies for a two-market stochastic inventory system,, Management Science, 43 (1997), 571. doi: 10.1287/mnsc.43.5.571. Google Scholar
[8]	S. X. Li, Z. Hung and A. Ashley, Inventory channel coordination and bargaining in a manufacturer-retailer system,, Annals of Operations Research, 68 (1996), 47. doi: 10.1007/BF02205448. Google Scholar
[9]	W. Luo and L. Chen, Approximation schemes for scheduling a maintenance and linear deteriorating jobs,, Journal of Industrial and Management Optimization, 8 (2012), 271. doi: 10.3934/jimo.2012.8.271. Google Scholar
[10]	K. L. Mak, A production lot size inventory model for deteriorating items,, Computers & Industrial Engineering, 6 (1982), 309. doi: 10.1016/0360-8352(82)90009-2. Google Scholar
[11]	S. K. Manna and K. S. Chaudhuri, An EOQ model with ramp type demand rate, time dependent deterioration rate, unit production cost and shortages,, European Journal of Operational Research, 171 (2006), 557. doi: 10.1016/j.ejor.2004.08.041. Google Scholar
[12]	S. Papachristos and K. Skouri, An optimal replenishment policy for deteriorating items with time-varying demand and partial-exponential,, Operations Research Letters, 27 (2000), 175. doi: 10.1016/S0167-6377(00)00044-4. Google Scholar
[13]	F. Raafat, P. M. Wolfe and H. K. Eldin, An inventory model for deteriorating items,, Computers & Industrial Engineering, 20 (1991), 89. doi: 10.1016/0360-8352(91)90043-6. Google Scholar
[14]	H. M. Wee, Economic production lot size model for deteriorating items with partial back-ordering,, Computers & Industrial Engineering, 24 (1993), 449. doi: 10.1016/0360-8352(93)90040-5. Google Scholar
[15]	H. M. Wee, Joint pricing and replenishment policy for deteriorating inventory with declining market,, International Journal of Production Economics, 40 (1995), 163. doi: 10.1016/0925-5273(95)00053-3. Google Scholar
[16]	H. M. Wee and J. F. Jong, An integrated multi-lot-size production inventory model for deteriorated items,, Management & System, 5 (1998), 97. doi: 10.1016/j.cor.2005.01.006. Google Scholar
[17]	Z. K. Weng, Modeling quantity discount under general price-sensitive demand functions: Optimal policies and relations,, European Journal of Operational Research, 86 (1995), 300. Google Scholar
[18]	Z. K. Weng and R. T. Wong, General models for the supplier's all-unit quantity discount policy,, Navel Research Logistics, 40 (1993), 971. doi: 10.1002/1520-6750(199312)40:7<971::AID-NAV3220400708>3.0.CO;2-T. Google Scholar
[19]	K. S. Wu, L. Y. Ouyang and C. T. Yang, An optimal replenishment policy for non-instantaneous deteriorating items with stock-dependent demand and partial backlogging,, International Journal of Production Economics, 101 (2006), 369. doi: 10.1016/j.ijpe.2005.01.010. Google Scholar
[20]	P. C. Yang and H. M. Wee, An integrated multi-lot size inventory model for deteriorating items,, Computers & Operations Research, 30 (2003), 671. doi: 10.1016/S0305-0548(02)00032-1. Google Scholar
[21]	P. C. Yang and H. M. Wee, A win-win strategy for an integrated vendor-buyer deteriorating inventory system,, Mathematical Modelling and Analysis, 11 (2006), 105. Google Scholar
[22]	P. C. Yang, H. M. Wee, S. L. Chung and P. C. Ho, Sequential and global optimization for a closed-loop deteriorating inventory supply chain,, Mathematical and Computer Modelling, 52 (2010), 161. doi: 10.1016/j.mcm.2010.02.005. Google Scholar
[23]	P. C. Yang, H. M. Wee, B. S. Liu and O. K. Fong, Mitigating hi-tech products risks due to rapid technological innovation,, Omega, 39 (2011), 456. doi: 10.1016/j.omega.2010.09.007. Google Scholar
[24]	J. C. P. Yu, H. M. Wee and K. J. Wang, Supply chain partnership for three-echelon deteriorating inventory model,, Journal of Industrial and Management Optimization, 5 (2008), 827. doi: 10.3934/jimo.2008.4.827. Google Scholar

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References:

[1]	Z. T. Balkhi and L. Benkherouf, A production lot size inventory model for deteriorating items and arbitrary production and demand rates,, European Journal of Operational Research, 92 (1996), 302. doi: 10.1016/0377-2217(95)00148-4. Google Scholar
[2]	H. J. Chang, J. T. Teng, L. Y. Ouyang and C. Y. Dye, Retailer's optimal pricing and lot sizing policies for deteriorating items with partial backlogging,, European Journal of Operational Research, 168 (2006), 51. doi: 10.1016/j.ejor.2004.05.003. Google Scholar
[3]	P. M. Ghare and S. F. Schrader, A model for exponentially decaying inventory,, Journal of Industrial Engineering, 14 (1963), 238. Google Scholar
[4]	Y. He, S. Y. Wang and K. K. Lai, An optimal production-inventory model for deteriorating items with multiple-market demand,, European Journal of Operational Research, 203 (2010), 593. doi: 10.1016/j.ejor.2009.09.003. Google Scholar
[5]	S. Kang and I. Kim, A study on the price and production level of the deteriorating inventory system,, International Journal of Production Research, 21 (1983), 449. doi: 10.1080/00207548308942422. Google Scholar
[6]	M. Khouja, The effect of large order quantities on expected profit in the single-period model,, International Journal of Production Economics, 72 (2001), 227. doi: 10.1016/S0925-5273(00)00150-X. Google Scholar
[7]	P. Kouvelis and G. J. Gutierrez, The newsvendor problem in a global market: Optimal centralized and decentralized control policies for a two-market stochastic inventory system,, Management Science, 43 (1997), 571. doi: 10.1287/mnsc.43.5.571. Google Scholar
[8]	S. X. Li, Z. Hung and A. Ashley, Inventory channel coordination and bargaining in a manufacturer-retailer system,, Annals of Operations Research, 68 (1996), 47. doi: 10.1007/BF02205448. Google Scholar
[9]	W. Luo and L. Chen, Approximation schemes for scheduling a maintenance and linear deteriorating jobs,, Journal of Industrial and Management Optimization, 8 (2012), 271. doi: 10.3934/jimo.2012.8.271. Google Scholar
[10]	K. L. Mak, A production lot size inventory model for deteriorating items,, Computers & Industrial Engineering, 6 (1982), 309. doi: 10.1016/0360-8352(82)90009-2. Google Scholar
[11]	S. K. Manna and K. S. Chaudhuri, An EOQ model with ramp type demand rate, time dependent deterioration rate, unit production cost and shortages,, European Journal of Operational Research, 171 (2006), 557. doi: 10.1016/j.ejor.2004.08.041. Google Scholar
[12]	S. Papachristos and K. Skouri, An optimal replenishment policy for deteriorating items with time-varying demand and partial-exponential,, Operations Research Letters, 27 (2000), 175. doi: 10.1016/S0167-6377(00)00044-4. Google Scholar
[13]	F. Raafat, P. M. Wolfe and H. K. Eldin, An inventory model for deteriorating items,, Computers & Industrial Engineering, 20 (1991), 89. doi: 10.1016/0360-8352(91)90043-6. Google Scholar
[14]	H. M. Wee, Economic production lot size model for deteriorating items with partial back-ordering,, Computers & Industrial Engineering, 24 (1993), 449. doi: 10.1016/0360-8352(93)90040-5. Google Scholar
[15]	H. M. Wee, Joint pricing and replenishment policy for deteriorating inventory with declining market,, International Journal of Production Economics, 40 (1995), 163. doi: 10.1016/0925-5273(95)00053-3. Google Scholar
[16]	H. M. Wee and J. F. Jong, An integrated multi-lot-size production inventory model for deteriorated items,, Management & System, 5 (1998), 97. doi: 10.1016/j.cor.2005.01.006. Google Scholar
[17]	Z. K. Weng, Modeling quantity discount under general price-sensitive demand functions: Optimal policies and relations,, European Journal of Operational Research, 86 (1995), 300. Google Scholar
[18]	Z. K. Weng and R. T. Wong, General models for the supplier's all-unit quantity discount policy,, Navel Research Logistics, 40 (1993), 971. doi: 10.1002/1520-6750(199312)40:7<971::AID-NAV3220400708>3.0.CO;2-T. Google Scholar
[19]	K. S. Wu, L. Y. Ouyang and C. T. Yang, An optimal replenishment policy for non-instantaneous deteriorating items with stock-dependent demand and partial backlogging,, International Journal of Production Economics, 101 (2006), 369. doi: 10.1016/j.ijpe.2005.01.010. Google Scholar
[20]	P. C. Yang and H. M. Wee, An integrated multi-lot size inventory model for deteriorating items,, Computers & Operations Research, 30 (2003), 671. doi: 10.1016/S0305-0548(02)00032-1. Google Scholar
[21]	P. C. Yang and H. M. Wee, A win-win strategy for an integrated vendor-buyer deteriorating inventory system,, Mathematical Modelling and Analysis, 11 (2006), 105. Google Scholar
[22]	P. C. Yang, H. M. Wee, S. L. Chung and P. C. Ho, Sequential and global optimization for a closed-loop deteriorating inventory supply chain,, Mathematical and Computer Modelling, 52 (2010), 161. doi: 10.1016/j.mcm.2010.02.005. Google Scholar
[23]	P. C. Yang, H. M. Wee, B. S. Liu and O. K. Fong, Mitigating hi-tech products risks due to rapid technological innovation,, Omega, 39 (2011), 456. doi: 10.1016/j.omega.2010.09.007. Google Scholar
[24]	J. C. P. Yu, H. M. Wee and K. J. Wang, Supply chain partnership for three-echelon deteriorating inventory model,, Journal of Industrial and Management Optimization, 5 (2008), 827. doi: 10.3934/jimo.2008.4.827. Google Scholar

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