• Previous Article
    Optimal dividend and capital injection strategy with fixed costs and restricted dividend rate for a dual model
  • JIMO Home
  • This Issue
  • Next Article
    A hybrid method combining genetic algorithm and Hooke-Jeeves method for constrained global optimization
October  2014, 10(4): 1261-1277. doi: 10.3934/jimo.2014.10.1261

Optimal pricing policy for deteriorating items with preservation technology investment

1. 

Institute of Systems Engineering, Tianjin University, Tianjin 300072, China, China, China

Received  February 2013 Revised  September 2013 Published  February 2014

This paper considers the problem of simultaneously determining the price and inventory control strategies for deteriorating items. It is assumed that the rate of deterioration can be reduced by means of effective preservation technology investment and the demand rate is a function of selling price. The goal of this study is to maximize the total profit per unit time by simultaneously determining the optimal selling price, length of replenishment cycle and preservation technology investment. First, for a given preservation technology investment, we prove that the optimal selling price and the optimal length of replenishment cycle exist and are unique. Next, it is shown that the total profit per unit time is a concave function of the preservation technology investment. Then, an effective algorithm is designed to find the optimal joint policy. Finally, numerical examples to illustrate the solution procedure and some managerial implications are provided.
Citation: Jianxiong Zhang, Zhenyu Bai, Wansheng Tang. Optimal pricing policy for deteriorating items with preservation technology investment. Journal of Industrial & Management Optimization, 2014, 10 (4) : 1261-1277. doi: 10.3934/jimo.2014.10.1261
References:
[1]

P. L. Abad, Optimal price and order size for a reseller under partial backordering,, Computers $&$ Operations Research, 28 (2001), 53. doi: 10.1016/S0305-0548(99)00086-6.

[2]

A. A. Alamri and Z. T. Balkhi, The effects of learning and forgetting on the optimal production lot size for deteriorating items with time varying demand and deterioration rates,, International Journal of Production Economics, 107 (2007), 125. doi: 10.1016/j.ijpe.2006.08.004.

[3]

M. Bakker, J. Riezebos and R. H. Teunter, Review of inventory systems with deterioration since 2001,, European Journal of Operational Research, 221 (2012), 275. doi: 10.1016/j.ejor.2012.03.004.

[4]

Z. T. Balkhi, On the global optimal solution to an integrated inventory system with general time varying demand, production and deterioration rates,, European Journal of Operational Research, 114 (1999), 29. doi: 10.1016/S0377-2217(98)00155-6.

[5]

H. J. Chang and C. Y. Dye, An EOQ model for deteriorating items with time varying demand and partial backlogging,, Journal of the Operational Research Society, 50 (1999), 1176. doi: 10.2307/3010088.

[6]

K. J. Chung and T. S. Huang, The optimal retailer's ordering policies for deteriorating items with limited storage capacity under trade credit financing,, International Journal of Production Economics, 106 (2007), 127. doi: 10.1016/j.ijpe.2006.05.008.

[7]

P. S. Deng, R. H. J. Lin and P. Chu, A note on the inventory models for deteriorating items with ramp type demand rate,, European Journal of Operational Research, 178 (2007), 112. doi: 10.1016/j.ejor.2006.01.028.

[8]

C. Y. Dye and T. P. Hsieh, An optimal replenishment policy for deteriorating items with effective investment in preservation technology,, European Journal of Operational Research, 218 (2012), 106. doi: 10.1016/j.ejor.2011.10.016.

[9]

B. C. Giri, A. Goswami and K. S. Chaudhuri, An EOQ model for deteriorating items with time varying demand and costs,, Journal of the Operational Research Society, 47 (1996), 1398. doi: 10.2307/3010205.

[10]

A. Goswami and K. S. Chaudhuri, An EOQ model for deteriorating items with shortages and a linear trend in demand,, Journal of the Operational Research Society, 42 (1991), 1105. doi: 10.2307/2582957.

[11]

O. K. Gupta, N. H. Shah and A. R. Patel, An integrated deteriorating inventory model with permissible delay in payments and price-sensitive stock-dependent demand,, International Journal of Operational Research, 11 (2011), 425. doi: 10.1504/IJOR.2011.041801.

[12]

T. P. Hsieh and C. Y. Dye, A production inventory model incorporating the effect of preservation technology investment when demand is fluctuating with time,, Journal of Computational and Applied Mathematics, 239 (2013), 25. doi: 10.1016/j.cam.2012.09.016.

[13]

P. H. Hsu, H. M. Wee and H. M. Teng, Preservation technology investment for deteriorating inventory,, International Journal of Production Economics, 124 (2010). doi: 10.1016/j.ijpe.2009.11.034.

[14]

K. C. Hung, An inventory model with generalized type demand, deterioration and backorder rates,, European Journal of Operational Research, 208 (2011), 239. doi: 10.1016/j.ejor.2010.08.026.

[15]

H. H. Lee, The investment model in preventive maintenance in multi-level production systems,, International Journal of Production Economics, 112 (2008), 816. doi: 10.1016/j.ijpe.2007.07.004.

[16]

R. Maihami and I. N. Kamalabadi, Joint pricing and inventory control for non-instantaneous deteriorating items with partial backlogging and time and price dependent demand,, International Journal of Production Economics, 136 (2012), 116. doi: 10.1016/j.ijpe.2011.09.020.

[17]

B. Mandal and A. K. Pal, Order level inventory system with ramp type demand rate for deteriorating items,, Journal of Interdisciplinary Mathematics, 1 (1998), 49. doi: 10.1080/09720502.1998.10700243.

[18]

S. Mukhopadhyay, R. N. Mukherjee and K. S. Chaudhuri, Joint pricing and ordering policy for a deteriorating inventory,, Computers $&$ Industrial Engineering, 47 (2004), 339. doi: 10.1016/j.cie.2004.06.007.

[19]

A. Musa and B. Sani, Inventory ordering policies of delayed deteriorating items under permissible delay in payments,, International Journal of Production Economics, 136 (2012), 75. doi: 10.1016/j.ijpe.2011.09.013.

[20]

L. Y. Ouyang, C. T. Chang and J. T. Teng, An EOQ model for deteriorating items under trade credits,, Journal of the Operational Research Society, 56 (2005), 719. doi: 10.1057/palgrave.jors.2601881.

[21]

M. S. Sajadieh, M. R. Akbari Jokar, Optimizing shipment, ordering and pricing policies in a two-stage supply chain with price-sensitive demand,, Transportation Research Part E: Logistics and Transportation Review, 45 (2009), 302. doi: 10.1016/j.tre.2008.12.002.

[22]

S. S. Sana, Optimal selling price and lotsize with time varying deterioration and partial backlogging,, Applied Mathematics and Computation, 217 (2010), 185. doi: 10.1016/j.amc.2010.05.040.

[23]

N. H. Shah, H. N. Soni and K. A. Patel, Optimizing inventory and marketing policy for non-instantaneous deteriorating items with generalized type deterioration and holding cost rates,, Omega, 41 (2013), 421. doi: 10.1016/j.omega.2012.03.002.

[24]

Y. K. Shah and M. C. Jaiswal, An order-level inventory model for a system with constant rate of deterioration,, Opsearch, 14 (1977), 174.

[25]

K. Skouri, I. Konstantaras, S. Papachristos and I. Ganas, Inventory models with ramp type demand rate, partial backlogging and weibull deterioration rate,, European Journal of Operational Research, 192 (2009), 79. doi: 10.1016/j.ejor.2007.09.003.

[26]

J. T. Teng, H. L. Yang and L. Y. Ouyang, On an EOQ model for deteriorating items with time-varying demand and partial backlogging,, Journal of the Operational Research Society, 54 (2003), 432. doi: 10.1057/palgrave.jors.2601490.

[27]

C. Uckun, F. Karaesmen and S. Savas, Investment in improved inventory accuracy in a decentralized supply chain,, International Journal of Production Economics, 113 (2008), 546. doi: 10.1016/j.ijpe.2007.10.012.

[28]

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.

[29]

K. S. Wu and L. Y. Ouyang, Replenishment policy for deteriorating items with ramp type demand rate,, Proceedings of the National Science Council, 24 (2000), 279.

[30]

X. L. Xu and X. Q. Cai, Price and delivery-time competition of perishable products: Existence and uniqueness of Nash equilibrium,, Journal of Industrial and Management Optimization, 4 (2008), 843. doi: 10.3934/jimo.2008.4.843.

[31]

C. T. Yang, L. Y. Ouyang, H. F. Yen and K. L. Lee, Joint pricing and ordering policies for deteriorating item with retail price-dependent demand in response to announced supply price increase,, Journal of Industrial and Management Optimization, 9 (2013), 437. doi: 10.3934/jimo.2013.9.437.

[32]

M. J. Yao and Y. C. Wang, Theoretical analysis and a search procedure for the joint replenishment problem with deteriorating products,, Journal of Industrial and Management Optimization, 1 (2005), 359. doi: 10.3934/jimo.2005.1.359.

[33]

P. S. You, Inventory policy for products with price and time-dependent demands,, Journal of the Operational Research Society, 56 (2005), 870. doi: 10.1057/palgrave.jors.2601905.

[34]

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, 4 (2008), 827. doi: 10.3934/jimo.2008.4.827.

show all references

References:
[1]

P. L. Abad, Optimal price and order size for a reseller under partial backordering,, Computers $&$ Operations Research, 28 (2001), 53. doi: 10.1016/S0305-0548(99)00086-6.

[2]

A. A. Alamri and Z. T. Balkhi, The effects of learning and forgetting on the optimal production lot size for deteriorating items with time varying demand and deterioration rates,, International Journal of Production Economics, 107 (2007), 125. doi: 10.1016/j.ijpe.2006.08.004.

[3]

M. Bakker, J. Riezebos and R. H. Teunter, Review of inventory systems with deterioration since 2001,, European Journal of Operational Research, 221 (2012), 275. doi: 10.1016/j.ejor.2012.03.004.

[4]

Z. T. Balkhi, On the global optimal solution to an integrated inventory system with general time varying demand, production and deterioration rates,, European Journal of Operational Research, 114 (1999), 29. doi: 10.1016/S0377-2217(98)00155-6.

[5]

H. J. Chang and C. Y. Dye, An EOQ model for deteriorating items with time varying demand and partial backlogging,, Journal of the Operational Research Society, 50 (1999), 1176. doi: 10.2307/3010088.

[6]

K. J. Chung and T. S. Huang, The optimal retailer's ordering policies for deteriorating items with limited storage capacity under trade credit financing,, International Journal of Production Economics, 106 (2007), 127. doi: 10.1016/j.ijpe.2006.05.008.

[7]

P. S. Deng, R. H. J. Lin and P. Chu, A note on the inventory models for deteriorating items with ramp type demand rate,, European Journal of Operational Research, 178 (2007), 112. doi: 10.1016/j.ejor.2006.01.028.

[8]

C. Y. Dye and T. P. Hsieh, An optimal replenishment policy for deteriorating items with effective investment in preservation technology,, European Journal of Operational Research, 218 (2012), 106. doi: 10.1016/j.ejor.2011.10.016.

[9]

B. C. Giri, A. Goswami and K. S. Chaudhuri, An EOQ model for deteriorating items with time varying demand and costs,, Journal of the Operational Research Society, 47 (1996), 1398. doi: 10.2307/3010205.

[10]

A. Goswami and K. S. Chaudhuri, An EOQ model for deteriorating items with shortages and a linear trend in demand,, Journal of the Operational Research Society, 42 (1991), 1105. doi: 10.2307/2582957.

[11]

O. K. Gupta, N. H. Shah and A. R. Patel, An integrated deteriorating inventory model with permissible delay in payments and price-sensitive stock-dependent demand,, International Journal of Operational Research, 11 (2011), 425. doi: 10.1504/IJOR.2011.041801.

[12]

T. P. Hsieh and C. Y. Dye, A production inventory model incorporating the effect of preservation technology investment when demand is fluctuating with time,, Journal of Computational and Applied Mathematics, 239 (2013), 25. doi: 10.1016/j.cam.2012.09.016.

[13]

P. H. Hsu, H. M. Wee and H. M. Teng, Preservation technology investment for deteriorating inventory,, International Journal of Production Economics, 124 (2010). doi: 10.1016/j.ijpe.2009.11.034.

[14]

K. C. Hung, An inventory model with generalized type demand, deterioration and backorder rates,, European Journal of Operational Research, 208 (2011), 239. doi: 10.1016/j.ejor.2010.08.026.

[15]

H. H. Lee, The investment model in preventive maintenance in multi-level production systems,, International Journal of Production Economics, 112 (2008), 816. doi: 10.1016/j.ijpe.2007.07.004.

[16]

R. Maihami and I. N. Kamalabadi, Joint pricing and inventory control for non-instantaneous deteriorating items with partial backlogging and time and price dependent demand,, International Journal of Production Economics, 136 (2012), 116. doi: 10.1016/j.ijpe.2011.09.020.

[17]

B. Mandal and A. K. Pal, Order level inventory system with ramp type demand rate for deteriorating items,, Journal of Interdisciplinary Mathematics, 1 (1998), 49. doi: 10.1080/09720502.1998.10700243.

[18]

S. Mukhopadhyay, R. N. Mukherjee and K. S. Chaudhuri, Joint pricing and ordering policy for a deteriorating inventory,, Computers $&$ Industrial Engineering, 47 (2004), 339. doi: 10.1016/j.cie.2004.06.007.

[19]

A. Musa and B. Sani, Inventory ordering policies of delayed deteriorating items under permissible delay in payments,, International Journal of Production Economics, 136 (2012), 75. doi: 10.1016/j.ijpe.2011.09.013.

[20]

L. Y. Ouyang, C. T. Chang and J. T. Teng, An EOQ model for deteriorating items under trade credits,, Journal of the Operational Research Society, 56 (2005), 719. doi: 10.1057/palgrave.jors.2601881.

[21]

M. S. Sajadieh, M. R. Akbari Jokar, Optimizing shipment, ordering and pricing policies in a two-stage supply chain with price-sensitive demand,, Transportation Research Part E: Logistics and Transportation Review, 45 (2009), 302. doi: 10.1016/j.tre.2008.12.002.

[22]

S. S. Sana, Optimal selling price and lotsize with time varying deterioration and partial backlogging,, Applied Mathematics and Computation, 217 (2010), 185. doi: 10.1016/j.amc.2010.05.040.

[23]

N. H. Shah, H. N. Soni and K. A. Patel, Optimizing inventory and marketing policy for non-instantaneous deteriorating items with generalized type deterioration and holding cost rates,, Omega, 41 (2013), 421. doi: 10.1016/j.omega.2012.03.002.

[24]

Y. K. Shah and M. C. Jaiswal, An order-level inventory model for a system with constant rate of deterioration,, Opsearch, 14 (1977), 174.

[25]

K. Skouri, I. Konstantaras, S. Papachristos and I. Ganas, Inventory models with ramp type demand rate, partial backlogging and weibull deterioration rate,, European Journal of Operational Research, 192 (2009), 79. doi: 10.1016/j.ejor.2007.09.003.

[26]

J. T. Teng, H. L. Yang and L. Y. Ouyang, On an EOQ model for deteriorating items with time-varying demand and partial backlogging,, Journal of the Operational Research Society, 54 (2003), 432. doi: 10.1057/palgrave.jors.2601490.

[27]

C. Uckun, F. Karaesmen and S. Savas, Investment in improved inventory accuracy in a decentralized supply chain,, International Journal of Production Economics, 113 (2008), 546. doi: 10.1016/j.ijpe.2007.10.012.

[28]

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.

[29]

K. S. Wu and L. Y. Ouyang, Replenishment policy for deteriorating items with ramp type demand rate,, Proceedings of the National Science Council, 24 (2000), 279.

[30]

X. L. Xu and X. Q. Cai, Price and delivery-time competition of perishable products: Existence and uniqueness of Nash equilibrium,, Journal of Industrial and Management Optimization, 4 (2008), 843. doi: 10.3934/jimo.2008.4.843.

[31]

C. T. Yang, L. Y. Ouyang, H. F. Yen and K. L. Lee, Joint pricing and ordering policies for deteriorating item with retail price-dependent demand in response to announced supply price increase,, Journal of Industrial and Management Optimization, 9 (2013), 437. doi: 10.3934/jimo.2013.9.437.

[32]

M. J. Yao and Y. C. Wang, Theoretical analysis and a search procedure for the joint replenishment problem with deteriorating products,, Journal of Industrial and Management Optimization, 1 (2005), 359. doi: 10.3934/jimo.2005.1.359.

[33]

P. S. You, Inventory policy for products with price and time-dependent demands,, Journal of the Operational Research Society, 56 (2005), 870. doi: 10.1057/palgrave.jors.2601905.

[34]

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, 4 (2008), 827. doi: 10.3934/jimo.2008.4.827.

[1]

Maryam Ghoreishi, Abolfazl Mirzazadeh, Gerhard-Wilhelm Weber, Isa Nakhai-Kamalabadi. Joint pricing and replenishment decisions for non-instantaneous deteriorating items with partial backlogging, inflation- and selling price-dependent demand and customer returns. Journal of Industrial & Management Optimization, 2015, 11 (3) : 933-949. doi: 10.3934/jimo.2015.11.933

[2]

Chih-Te Yang, Liang-Yuh Ouyang, Hsiu-Feng Yen, Kuo-Liang Lee. Joint pricing and ordering policies for deteriorating item with retail price-dependent demand in response to announced supply price increase. Journal of Industrial & Management Optimization, 2013, 9 (2) : 437-454. doi: 10.3934/jimo.2013.9.437

[3]

Magfura Pervin, Sankar Kumar Roy, Gerhard Wilhelm Weber. Deteriorating inventory with preservation technology under price- and stock-sensitive demand. Journal of Industrial & Management Optimization, 2017, 13 (5) : 1-28. doi: 10.3934/jimo.2019019

[4]

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

[5]

Muhammad Waqas Iqbal, Biswajit Sarkar. Application of preservation technology for lifetime dependent products in an integrated production system. Journal of Industrial & Management Optimization, 2017, 13 (5) : 1-28. doi: 10.3934/jimo.2018144

[6]

Nan Li, Song Wang. Pricing options on investment project expansions under commodity price uncertainty. Journal of Industrial & Management Optimization, 2019, 15 (1) : 261-273. doi: 10.3934/jimo.2018042

[7]

Biswajit Sarkar, Buddhadev Mandal, Sumon Sarkar. Preservation of deteriorating seasonal products with stock-dependent consumption rate and shortages. Journal of Industrial & Management Optimization, 2017, 13 (1) : 187-206. doi: 10.3934/jimo.2016011

[8]

Shouyu Ma, Zied Jemai, Evren Sahin, Yves Dallery. Analysis of the Newsboy Problem subject to price dependent demand and multiple discounts. Journal of Industrial & Management Optimization, 2018, 14 (3) : 931-951. doi: 10.3934/jimo.2017083

[9]

M. M. Ali, L. Masinga. A nonlinear optimization model for optimal order quantities with stochastic demand rate and price change. Journal of Industrial & Management Optimization, 2007, 3 (1) : 139-154. doi: 10.3934/jimo.2007.3.139

[10]

Magfura Pervin, Sankar Kumar Roy, Gerhard Wilhelm Weber. Multi-item deteriorating two-echelon inventory model with price- and stock-dependent demand: A trade-credit policy. Journal of Industrial & Management Optimization, 2019, 15 (3) : 1345-1373. doi: 10.3934/jimo.2018098

[11]

Xing Huang, Chang Liu, Feng-Yu Wang. Order preservation for path-distribution dependent SDEs. Communications on Pure & Applied Analysis, 2018, 17 (5) : 2125-2133. doi: 10.3934/cpaa.2018100

[12]

Guodong Yi, Xiaohong Chen, Chunqiao Tan. Optimal pricing of perishable products with replenishment policy in the presence of strategic consumers. Journal of Industrial & Management Optimization, 2017, 13 (5) : 1-19. doi: 10.3934/jimo.2018112

[13]

Ata Allah Taleizadeh, Solaleh Sadat Kalantari, Leopoldo Eduardo Cárdenas-Barrón. Determining optimal price, replenishment lot size and number of shipments for an EPQ model with rework and multiple shipments. Journal of Industrial & Management Optimization, 2015, 11 (4) : 1059-1071. doi: 10.3934/jimo.2015.11.1059

[14]

Yunqiang Yin, T. C. E. Cheng, Jianyou Xu, Shuenn-Ren Cheng, Chin-Chia Wu. Single-machine scheduling with past-sequence-dependent delivery times and a linear deterioration. Journal of Industrial & Management Optimization, 2013, 9 (2) : 323-339. doi: 10.3934/jimo.2013.9.323

[15]

Ji-Bo Wang, Mengqi Liu, Na Yin, Ping Ji. Scheduling jobs with controllable processing time, truncated job-dependent learning and deterioration effects. Journal of Industrial & Management Optimization, 2017, 13 (2) : 1025-1039. doi: 10.3934/jimo.2016060

[16]

Mitali Sarkar, Young Hae Lee. Optimum pricing strategy for complementary products with reservation price in a supply chain model. Journal of Industrial & Management Optimization, 2017, 13 (3) : 1553-1586. doi: 10.3934/jimo.2017007

[17]

Shichen Zhang, Jianxiong Zhang, Jiang Shen, Wansheng Tang. A joint dynamic pricing and production model with asymmetric reference price effect. Journal of Industrial & Management Optimization, 2019, 15 (2) : 667-688. doi: 10.3934/jimo.2018064

[18]

Zhiping Zhou, Xinbao Liu, Jun Pei, Panos M. Pardalos, Hao Cheng. Competition of pricing and service investment between iot-based and traditional manufacturers. Journal of Industrial & Management Optimization, 2018, 14 (3) : 1203-1218. doi: 10.3934/jimo.2018006

[19]

Amin Sakzad, Mohammad-Reza Sadeghi. On cycle-free lattices with high rate label codes. Advances in Mathematics of Communications, 2010, 4 (4) : 441-452. doi: 10.3934/amc.2010.4.441

[20]

Bibhas C. Giri, Bhaba R. Sarker. Coordinating a multi-echelon supply chain under production disruption and price-sensitive stochastic demand. Journal of Industrial & Management Optimization, 2017, 13 (5) : 1-21. doi: 10.3934/jimo.2018115

2017 Impact Factor: 0.994

Metrics

  • PDF downloads (20)
  • HTML views (0)
  • Cited by (20)

Other articles
by authors

[Back to Top]