AI Chat Paper
Note: Please note that the following content is generated by AMiner AI. SciOpen does not take any responsibility related to this content.
{{lang === 'zh_CN' ? '文章概述' : 'Summary'}}
{{lang === 'en_US' ? '中' : 'Eng'}}
Chat more with AI
PDF (5.9 MB)
Collect
Submit Manuscript AI Chat Paper
Show Outline
Outline
Show full outline
Hide outline
Outline
Show full outline
Hide outline
Open Access

An Optimal Pricing and Ordering Policy with Trapezoidal-Type Demand Under Partial Backlogged Shortages

Institute of Operations Research and Systems Engineering, College of Science, Tianjin University of Technology, Tianjin 300384, China
School of Electrical and Electronic Engineering, TianjinUniversity of Technology, Tianjin 300384, China
Show Author Information

Abstract

Based on the retail inventory operation of Heilan Home, this study incorporates the price factor into inventory environment involving trapezoidal time-varying products. A joint pricing and ordering issue with deteriorating items under partial backlogged shortages is firstly explored in a fixed selling cycle. The corresponding optimization model aiming at maximizing profit performance of inventory system is developed, the theoretical analysis of solving the model is further provided, and the modelling frame generalizes some inventory models in the existing studies. Then, a solving algorithm for the model is designed to determine the optimal price, initial ordering quantity, shortage time point, and the maximum inventory level. Finally, numerical examples are presented to illustrate the model, and the results show the robustness of the proposed model.

References

[1]

M. A. A. Khan, A. A. Shaikh, G. C. Panda, I. Konstantaras, and A. A. Taleizadeh, Inventory system with expiration date: Pricing and replenishment decisions, Comput . Ind . Eng ., vol. 132, pp. 232–247, 2019.

[2]
L. A. San-José, J. Sicilia, M. González-De-la-Rosa, and J. Febles-Acosta, Best pricing and optimal policy for an inventory system under time-and-price-dependent demand and backordering, Ann. Oper. Res., vol. 286, nos. 1&2, pp. 351–369, 2020.
[3]

M. Cheng and G. Wang, A note on the inventory model for deteriorating items with trapezoidal type demand rate, Comput . Ind . Eng ., vol. 56, no. 4, pp. 1296–1300, 2009.

[4]

M. Cheng, B. Zhang, and G. Wang, Optimal policy for deteriorating items with trapezoidal type demand and partial backlogging, Appl . Math . Model ., vol. 35, no. 7, pp. 3552–3560, 2011.

[5]

N. Singh, B. Vaish, and S. Singh, An EOQ model with Pareto distribution for deterioration, trapezoidal type demand and backlogging under trade credit policy, J. Comput. Math., vol. 3, no. 4, pp. 30–53, 2011.

[6]

1R. Uthayakumar and M. Rameswari, An economic production quantity model for defective items with trapezoidal type demand rate, J. Optim. Theory Appl., vol. 154, no. 3, pp. 1055–1079, 2012.

[7]

K. P. Lin, An extended inventory models with trapezoidal type demands, Appl . Math . Comput ., vol. 219, no. 24, pp. 11414–11419, 2013.

[8]

J. Wu, J. T. Teng, and K. Skouri, Optimal inventory policies for deteriorating items with trapezoidal-type demand patterns and maximum lifetimes under upstream and downstream trade credits, Ann . Oper . Res ., vol. 264, nos. 1&2, pp. 459–476, 2018.

[9]

C. Xu, D. Zhao, J. Min, and J. Hao, An inventory model for nonperishable items with warehouse mode selection and partial backlogging under trapezoidal-type demand, J . Oper . Res . Soc ., vol. 72, no. 4, pp. 744–763, 2021.

[10]

D. Rosenberg, Optimal price-inventory decisions: Profit vs. ROII, IIE Trans ., vol. 23, no. 1, pp. 17–22, 1991.

[11]
D. M. Hanssens and L. J. Parsons, Econometric and time-series market response models, in Operations Research and Management Science, M. Kalchschmidt and D. A. Samson, eds. Amsterdam, the Netherlands: Elsevier, 1993. pp. 409–464.
[12]

G. C. Panda, M. A. A. Khan, and A. A. Shaikh, A credit policy approach in a two-warehouse inventory model for deteriorating items with price- and stock-dependent demand under partial backlogging, J . Ind . Eng . Int ., vol. 15, no. 1, pp. 147–170, 2019.

[13]

N. H. Shah, D. B. Shah, and D. G, Patel, Optimal transfer, ordering and payment policies for joint supplier-buyer inventory model with price-sensitive trapezoidal demand and net credit, Int. J. Syst. Sci., vol. 46, no. 10, pp. 1752–1761, 2015.

[14]

J. Kaushik and S. Ashish, Inventory model for the deteriorating items with price and time-dependent trapezoidal type demand rate, Int. J. Adv. Sci. Tech., vol. 29, no. 1, pp. 1617–1629, 2020.

[15]
HLA, HLA achieves a total retail sales of over 30 billion, http://www.hla.com.cn/Index/article/detail/cid/1/id/93.html 2018/05/20, 2023.
[16]

J. Wu, K. Skouri, J. T. Teng, and Y. Hu, Two inventory systems with trapezoidal-type demand rate and time-dependent deterioration and backlogging, Expert Syst . Appl ., vol. 46, pp. 367–379, 2016.

[17]

S. R. Singh and M. Vishnoi, Two storage inventory model for perishable items with trapezoidal type demand under conditionally permissible delay in payment, Adv. Intell. Syst. Comput. , vol. 236, pp. 1369–1385, 2014.

[18]

B. Anil Kumar and S. K. Paikray, Cost optimization inventory model for deteriorating items with trapezoidal demand rate under completely backlogged shortages in crisp and fuzzy environment, RAIRO-Oper . Res ., vol. 56, no. 3, pp. 1969–1994, 2022.

[19]

V. Suhandi and P. Chen, One-time order inventory model for deteriorating and short market life items with trapezoidal type demand rate, Int. J. Ind. Eng. Theory. , vol. 29, no. 6, pp. 805–825, 2022.

[20]

E. S. Mills, Uncertainty and price theory, Q. J. Econ. , vol. 73, no. 1, pp. 116–130, 1959.

[21]

A. Federgruen and A. Heching, Combined pricing and inventory control under uncertainty, Oper . Res ., vol. 47, no. 3, pp. 454–475, 1999.

[22]
H. K. Alfares and A. M. Ghaithan, Inventory and pricing model with price-dependent demand, time-varying holding cost, and quantity discounts, Comput. Ind. Eng., vol. 94, pp. 170–177, 2016.
[23]

T. Otake and K. J. Min, Inventory and investment in quality improvement under return on investment maximization, Comput . Oper . Res ., vol. 28, no. 10, pp. 997–1012, 2001.

[24]

S. Goldberg, K. J. Arrow, S. Karlin, and H. Scarf, Studies in applied probability and management science, Am . Math . Mon ., vol. 70, no. 1, p. 105, 1963.

[25]

Y. F. Chen, S. Ray, and Y. Song, Optimal pricing and inventory control policy in periodic-review systems with fixed ordering cost and lost sales, Nav . Res . Logist ., vol. 53, no. 2, pp. 117–136, 2006.

[26]

J. Huang, M. Leng, and M. Parlar, Demand functions in decision modeling: A comprehensive survey and research directions, Decis . Sci ., vol. 44, no. 3, pp. 557–609, 2013.

[27]

T. Avinadav, A. Herbon, and U. Spiegel, Optimal ordering and pricing policy for demand functions that are separable into price and inventory age, Int . J . Prod . Econ ., vol. 155, pp. 406–417, 2014.

[28]

B. Mondal, A. K. Bhunia, and M. Maiti, An inventory system of ameliorating items for price dependent demand rate, Comput . Ind . Eng ., vol. 45, no. 3, pp. 443–456, 2003.

[29]

V. K. Mishra, L. S. Singh, and R. Kumar, An inventory model for deteriorating items with time-dependent demand and time-varying holding cost under partial backlogging, J . Ind . Eng . Int ., vol. 9, no. 1, pp. 1–5, 2013.

[30]

J. T. Teng and C. T. Chang, Economic production quantity models for deteriorating items with price- and stock-dependent demand, Comput . Oper . Res ., vol. 32, no. 2, pp. 297–308, 2005.

[31]

G. Sridevi, K. N. Devi, and K. S. Rao, Inventory model for deteriorating items with Weibull rate of replenishment and selling price dependent demand, Int . J . Oper . Res ., vol. 9, no. 3, p. 329, 2010.

[32]

K. S. Rao and S. E. Rao, Inventory model under permissible delay in payments and inflation with generalised Pareto lifetime, Int . J . Procure . Manag ., vol. 8, no. 1, p. 202, 2015.

[33]
C. K. Jaggi, S. Tiwari, and S. K. Goel, Credit financing in economic ordering policies for non-instantaneous deteriorating items with price dependent demand and two storage facilities, Ann. Oper. Res., vol. 248, nos. 1&2, pp. 253–280, 2017.
[34]

J. T. Teng, M. S. Chern, H. L. Yang, and Y. J. Wang, Deterministic lot-size inventory models with shortages and deterioration for fluctuating demand, Oper . Res . Lett ., vol. 24, nos. 1&2, pp. 65–72, 1999.

[35]

H. L. Yang, J. T. Teng, and M. S. Chen, Deterministic inventory lot-size models under inflation with shortages and deterioration for fluctuating demand, 3.0.CO;2-8"> Nav . Res . Logist ., vol. 48, no. 2, pp. 144–158, 2001.

[36]

P. Chu, K. L. Yang, S. K. Liang, and T. Niu, Note on inventory model with a mixture of back orders and lost sales, Eur . J . Oper . Res ., vol. 159, no. 2, pp. 470–475, 2004.

[37]

C. Y. Dye, H. J. Chang, and J. T. Teng, A deteriorating inventory model with time-varying demand and shortage-dependent partial backlogging, Eur . J . Oper . Res ., vol. 172, no. 2, pp. 417–429, 2006.

[38]

C. Y. Dye, Joint pricing and ordering policy for a deteriorating inventory with partial backlogging, Omega , vol. 35, no. 2, pp. 184–189, 2007.

[39]

P. L. Abad, Optimal price and order size under partial backordering incorporating shortage, backorder and lost sale costs, Int. J. Prod. Econ., vol. 114, no. 1, pp. 179–186, 2008.

[40]

L. E. Cárdenas-Barrón and S. S. Sana, A production-inventory model for a two-echelon supply chain when demand is dependent on sales teams׳ initiatives, Int . J . Prod . Econ ., vol. 155, pp. 249–258, 2014.

[41]

A. A. Taleizadeh and D. W. Pentico, An economic order quantity model with partial backordering and all-units discount, Int . J . Prod . Econ ., vol. 155, pp. 172–184, 2014.

[42]

R. Li, Y. Liu, J. T. Teng, and Y. C. Tsao, Optimal pricing, lot-sizing and backordering decisions when a seller demands an advance-cash-credit payment scheme, Eur. J. Oper. Res., vol. 278, no. 1, pp. 283–295, 2019.

[43]

P. L. Abad, Optimal price and order size for a reseller under partial backordering, Comput . Oper . Res ., vol. 28, no. 1, pp. 53–65, 2001.

[44]

C. Y. Dye and L. Y. Ouyang, An EOQ model for perishable items under stock-dependent selling rate and time-dependent partial backlogging, Eur . J . Oper . Res ., vol. 163, no. 3, pp. 776–783, 2005.

[45]

B. C. Giri, A. K. Jalan, and K. S. Chaudhuri, An economic production lot size model with increasing demand, shortages and partial backlogging, Int. Trans. Oper. Res., vol. 12, no. 2, pp. 235–245, 2005.

[46]

S. Pareek and G. Sharma, An inventory model with weibull distribution deteriorating item with exponential declining demand and partial backlogging, Int. J. Multidipli. Res. , vol. 4, no. 7, pp. 145–154, 2014.

[47]

M. G. Arif, An inventory model for deteriorating items with non-linear selling price dependent demand and exponentially partial backlogging shortage, Ann . Pure Appl . Math ., vol. 16, no. 1, pp. 105–116, 2018.

[48]

M. Gupta, S. Tiwari, and C. K. Jaggi, Retailer’s ordering policies for time-varying deteriorating items with partial backlogging and permissible delay in payments in a two-warehouse environment, Ann . Oper . Res ., vol. 295, no. 1, pp. 139–161, 2020.

[49]

A. K. Bhunia and M. Maiti, A two warehouse inventory model for deteriorating items with a linear trend in demand and shortages, J . Oper . Res . Soc ., vol. 49, no. 3, pp. 287–292, 1998.

[50]

H. L. Yang, Two-warehouse inventory models for deteriorating items with shortages under inflation, Eur . J . Oper . Res ., vol. 157, no. 2, pp. 344–356, 2004.

[51]

K. Skouri, I. Konstantaras, S. Papachristos, and I. Ganas, Inventory models with ramp type demand rate, partial backlogging and Weibull deterioration rate, Eur. J. Oper. Res., vol. 192, no. 1, pp. 79–92, 209.

[52]

S. Agrawal and S. Banerjee, Two-warehouse inventory model with ramp-type demand and partially backlogged shortages, Int . J . Syst . Sci ., vol. 42, no. 7, pp. 1115–1126, 2011.

[53]
S. Agrawal, S. Banerjee, and S. Papachristos, Inventory model with deteriorating items, ramp-type demand and partially backlogged shortages for a two warehouse system, Appl. Math. Model., vol. 37, nos. 20&21, pp. 8912–8929, 2013.
[54]

T. Sarkar, S. K. Ghosh, and K. S. Chaudhuri, An optimal inventory replenishment policy for a deteriorating item with time-quadratic demand and time-dependent partial backlogging with shortages in all cycles, Appl . Math . Comput ., vol. 218, no. 18, pp. 9147–9155, 2012.

[55]

S. Panda, S. Senapati, and M. Basu, Optimal replenishment policy for perishable seasonal products in a season with ramp-type time dependent demand, Comput . Ind . Eng ., vol. 54, no. 2, pp. 301–314, 2008.

[56]
C. K. Jaggi, S. Tiwari, and S. K. Goel, Credit financing in economic ordering policies for non-instantaneous deteriorating items with price dependent demand and two storage facilities, Ann. Oper. Res., vol. 248, nos. 1&2, pp. 253–280, 2017.
[57]

B. Mandal and A. K. Pal, Order level inventory system with ramp type demand rate for deteriorating items, J . Interdiscip . Math ., vol. 1, no. 1, pp. 49–66, 1998.

[58]

J. W. Wu, B. Tan, C. Lin, and W. C. Lee, An EOQ inventory model with ramp type demand rate for items with weibull deterioration, Int . J . Inf . Manag . Sci ., vol. 10, no. 3, pp. 41–51, 1999.

[59]

K. S. Wu, An EOQ inventory model for items with Weibull distribution deterioration, ramp type demand rate and partial backlogging, Prod. Plan. Contr., vol. 12, no. 8, pp. 787–793, 2001.

Tsinghua Science and Technology
Pages 1709-1727
Cite this article:
Xu C, Bai M, Wu C, et al. An Optimal Pricing and Ordering Policy with Trapezoidal-Type Demand Under Partial Backlogged Shortages. Tsinghua Science and Technology, 2024, 29(6): 1709-1727. https://doi.org/10.26599/TST.2023.9010040

66

Views

10

Downloads

0

Crossref

0

Web of Science

0

Scopus

0

CSCD

Altmetrics

Received: 12 December 2022
Revised: 09 March 2023
Accepted: 04 May 2023
Published: 20 June 2024
© The Author(s) 2024.

The articles published in this open access journal are distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/).

Return