Optimizing price, order quantity, and backordering level using a nonlinear holding cost and a power demand pattern

  1. Cárdenas-Barrón, Leopoldo Eduardo 1
  2. Sicilia, Joaquín 2
  3. Mandal, Buddhadev 1
  4. San-José, Luis A. 3
  5. Abdul-Jalbar, Beatriz 2
  1. 1 Instituto Tecnológico y de Estudios Superiores de Monterrey
    info

    Instituto Tecnológico y de Estudios Superiores de Monterrey

    Monterrey, México

    ROR https://ror.org/03ayjn504

  2. 2 Universidad de La Laguna
    info

    Universidad de La Laguna

    San Cristobal de La Laguna, España

    ROR https://ror.org/01r9z8p25

  3. 3 Universidad de Valladolid
    info

    Universidad de Valladolid

    Valladolid, España

    ROR https://ror.org/01fvbaw18

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Revue:
Computers & Operations Research

ISSN: 0305-0548

Année de publication: 2021

Volumen: 133

Pages: 105339

Type: Article

DOI: 10.1016/J.COR.2021.105339 GOOGLE SCHOLAR lock_openAccès ouvert editor

D'autres publications dans: Computers & Operations Research

Résumé

It is well-known that the demand rate for some products depends on several factors, such as price, time, and stock, among others. Moreover, the holding cost can vary over time. More specifically, it increases with time since a long period of storage requires more expensive warehouse facilities. This research introduces an inventory model with shortages for a single product where the demand rate depends simultaneously on both the selling price and time according to a power pattern. Shortages are completely backordered. Demand for the product jointly combines the impact of the selling price and a time power function, which is performed as an addition. Furthermore, the holding cost is a power of the time that the product is held in storage. The main objective is to derive the optimal inventory policy such that the total profit per unit of time is maximized. For optimizing the inventory problem, some theo-retical results are derived first to prove that the total profit function is strictly pseudo concave with respect to the decision variables. Next, an efficient algorithm that obtains the optimal solution is provided. The proposed in-ventory model is a general model because it contains several published inventory models as special cases. Some numerical examples are presented and solved to illustrate and validate the proposed inventory model. Also, a sensitivity analysis is conducted in order to highlight and generate significant insights.

Références bibliographiques

  • Abdul-Jalbar, (2009), International Journal of Production Economics, 122, pp. 519, 10.1016/j.ijpe.2009.04.017
  • Aggarwal, (1982), Economic Computation and Economic Cybernetics Studies and Research, 17, pp. 57
  • Akan, (2021), Computers & Industrial Engineering, 154, pp. 1, 10.1016/j.cie.2021.107149
  • Alfares, (2007), International Journal of Production Economics, 108, pp. 259, 10.1016/j.ijpe.2006.12.013
  • Alfares, (2019), Arabian Journal for Science and Engineering, 44, pp. 1737, 10.1007/s13369-018-3593-4
  • Cambini, (2009), vol. 616
  • Cárdenas-Barrón, (2020), Computers and Industrial Engineering, 139, pp. 105557, 10.1016/j.cie.2018.12.004
  • Chang, (2004), Asia-Pacific Journal of Operational Research, 21, pp. 435, 10.1142/S0217595904000321
  • Datta, (1988), Indian Journal of Pure and Applied Mathematics, 19, pp. 1043
  • Dye, (2004), International Journal of Information and Management Sciences, 15, pp. 81
  • Edalatpour, (2019), Production Engineering, 1–11
  • Fang, (2021), European Journal of Operational Research, 293, pp. 594, 10.1016/j.ejor.2020.08.002
  • Feng, (2021), Journal of Management Science and Engineering, 6, pp. 1, 10.1016/j.jmse.2021.01.002
  • Ferguson, (2007), European Journal of Operational Research, 180, pp. 485, 10.1016/j.ejor.2006.04.031
  • Giri, (1998), European Journal of Operational Research, 105, pp. 467, 10.1016/S0377-2217(97)00086-6
  • Girlich, (1990), Engineering Costs and Production Economics, 19, pp. 327, 10.1016/0167-188X(90)90060-U
  • Goh, (1994), European Journal of Operational Research, 73, pp. 50, 10.1016/0377-2217(94)90141-4
  • Hadley, (1963)
  • Harris, (1913), Factory, The Magazine of Management, 10, pp. 135
  • Hemmati, (2021), Computers & Industrial Engineering, 10.1016/j.cie.2021.107297
  • Herbon, (2017), European Journal of Operational Research, 260, pp. 546, 10.1016/j.ejor.2016.12.033
  • Jadidi, (2017), Computers and Industrial Engineering, 114, pp. 45, 10.1016/j.cie.2017.09.038
  • Jung, (2008), International Journal of Information and Management Sciences, 19, pp. 667
  • Kabirian, (2012), Journal of Global Optimization, 54, pp. 1, 10.1007/s10898-011-9737-7
  • Khalilpourazari, (2017), Journal of Industrial and Production Engineering, 34, pp. 42, 10.1080/21681015.2016.1192068
  • Krishnaraj, (2012), The Bulletin of Society for Mathematical Services and Standards, 2, pp. 33, 10.18052/www.scipress.com/BSMaSS.2.33
  • Kumar, (2011), International Journal of Mathematical Science, 10, pp. 435
  • Kunreuther, (1971), Econometrica, 39, pp. 173, 10.2307/1909147
  • Lee, (2002), International Journal of Information and Management Sciences, 13, pp. 19
  • Mahata, (2009), International Journal of Applied Mathematics and Computer Sciences, 5, pp. 94
  • Mao, X.L., Xiao, X.P., 2009. Optimal inventory policy for non-instantaneous items with stock-dependent holding cost function and shortage. In: 2009 IEEE International Conference on Grey Systems and Intelligent Services (GSIS 2009), IEEE, pp. 1772–1778.
  • Marand, (2019), International Journal of Production Economics, 209, pp. 78, 10.1016/j.ijpe.2017.07.008
  • Mishra, (2012), General Mathematics Notes, 10, pp. 41
  • Naddor, (1966)
  • Paknejad, (2018), International Journal of Management Science and Engineering Management, 13, pp. 237
  • Panda, (2017), Tékhne, 15, pp. 117, 10.1016/j.tekhne.2017.09.002
  • Pando, (2012), International Journal of Systems Science, 43, pp. 2160, 10.1080/00207721.2011.565134
  • Pando, (2013), International Journal of Production Economics, 145, pp. 294, 10.1016/j.ijpe.2013.04.050
  • Pando, (2018), Computers and Industrial Engineering, 117, pp. 81, 10.1016/j.cie.2018.01.008
  • Pando, (2019), Applied Mathematical Modelling, 66, pp. 643, 10.1016/j.apm.2018.10.007
  • Prasher, (2013), Prestige International Journal of Management and IT-Sanchayan, 2, pp. 114, 10.37922/PIJMIT.2013.V02i01.009
  • Rajeswari, (2011), International Journal of Mathematical Archive, 2, pp. 1501
  • Rajeswari, (2012), American Journal of Operations Research, 2, pp. 247, 10.4236/ajor.2012.22029
  • Rajeswari, (2017), International Journal of Computer Applications, 169, pp. 6, 10.5120/ijca2017914259
  • Rubio-Herrero, (2018), European Journal of Operational Research, 265, pp. 962, 10.1016/j.ejor.2017.08.055
  • San-José, (2015), Omega, 54, pp. 147, 10.1016/j.omega.2015.01.007
  • San-José, (2017), Applied Mathematical Modelling, 46, pp. 618, 10.1016/j.apm.2017.01.082
  • San-José, (2018), European Journal of Operational Research, 270, pp. 889, 10.1016/j.ejor.2017.10.042
  • San-José, (2018), Engineering Optimization, 50, pp. 1164, 10.1080/0305215X.2017.1414205
  • San-José, (2019), Computers and Industrial Engineering, 129, pp. 426, 10.1016/j.cie.2019.01.054
  • San-José, (2020), Annals of Operations Research, 286, pp. 351, 10.1007/s10479-018-2953-5
  • Sarbjit, S., Shivraj, S. (2011). Deterministic and probabilistic EOQ models for products having power demand pattern. In Proceedings of the World Congress on Engineering (Vol. 1).
  • Sazvar, (2012), IFAC Proceedings Volumes, 45, pp. 493, 10.3182/20120523-3-RO-2023.00239
  • Sazvar, (2013), IFAC Proceedings Volumes, 46, pp. 1702, 10.3182/20130619-3-RU-3018.00507
  • Sazvar, (2013), The International Journal of Advanced Manufacturing Technology, 64, pp. 1087, 10.1007/s00170-012-4042-2
  • Sicilia, (2012), Asia-Pacific Journal of Operational Research, 29, pp. 1250025, 10.1142/S021759591250025X
  • Sicilia, (2013), European Journal of Industrial Engineering, 7, pp. 577, 10.1504/EJIE.2013.057381
  • Sicilia, (2014), International Journal of Production Economics, 155, pp. 163, 10.1016/j.ijpe.2013.11.020
  • Sicilia, (2014), International Journal of Production Economics, 155, pp. 155, 10.1016/j.ijpe.2014.01.024
  • Sicilia, (2015), International Journal of Production Research, 53, pp. 3603, 10.1080/00207543.2014.983618
  • Singh, (2011), JP Journal of Mathematical Sciences, 1, pp. 99
  • Singh, (2009), International Journal of Operations and Quantitative Management, 15, pp. 65
  • Smith, (2007), Production Planning and Control, 18, pp. 310, 10.1080/09537280701270374
  • Tripathi, R.P., 2019. Economic order quantity models for price dependent demand and different holding cost functions, Jordan Journal of Mathematics and Statistics 12 (1), 15–33.
  • Tripathi, (2017), American Journal of Applied Sciences, 14, pp. 607, 10.3844/ajassp.2017.607.613
  • Tripathy, (2010), International Journal of Contemporary Mathematical Sciences, 5, pp. 1895
  • Urban, (2008), International Journal of Production Economics, 114, pp. 399, 10.1016/j.ijpe.2008.02.014
  • Valliathal, (2011), Optimization Letters, 5, pp. 515, 10.1007/s11590-010-0216-8
  • Weiss, (1982), European Journal of Operational Research, 9, pp. 56, 10.1016/0377-2217(82)90010-8