IDEAS home Printed from https://ideas.repec.org/a/eee/ecmode/v46y2015icp334-345.html
   My bibliography  Save this article

A production inventory model for deteriorating item with ramp type demand allowing inflation and shortages under fuzziness

Author

Listed:
  • Pal, Shilpi
  • Mahapatra, G.S.
  • Samanta, G.P.

Abstract

Economic production quantity (EPQ) is the quantity of a product that should be manufactured in a single batch so as to minimize the total cost. In classical model EPQ only applies where the demand for a product and production rate is constant over the year. But in reality these parameters vary with time in different scenarios. In this paper we have considered a production inventory model for deteriorating items with ramp type demand rate under the effect of inflation and shortages under fuzziness. The deterioration rate is represented by a two-parameter Weibull distribution. As inflation erodes the value of money so we have also considered the effect of inflation when there is shortage in the stock under finite time horizon. Some parameters are vaguely or unclearly defined or whose values are imprecise or determined based on subjective beliefs of individuals. Therefore the inventory model is solved under fuzzy environment to evaluate the optimum solution of the model in different cases. We have optimized our solution by considering production time and production rate as decision variables in two separate cases. While incorporating symmetric triangular fuzzy number we use total λ-integral value to defuzzify the solution. Finally, utility of the model is presented by using some numerical examples and sensitivity analysis and the results are analyzed.

Suggested Citation

  • Pal, Shilpi & Mahapatra, G.S. & Samanta, G.P., 2015. "A production inventory model for deteriorating item with ramp type demand allowing inflation and shortages under fuzziness," Economic Modelling, Elsevier, vol. 46(C), pages 334-345.
    • Handle: RePEc:eee:ecmode:v:46:y:2015:i:c:p:334-345
    DOI: 10.1016/j.econmod.2014.12.031
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0264999314005033
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.econmod.2014.12.031?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. De, Sujit Kumar & Sana, Shib Sankar, 2013. "Fuzzy order quantity inventory model with fuzzy shortage quantity and fuzzy promotional index," Economic Modelling, Elsevier, vol. 31(C), pages 351-358.
    2. Yang, Hui-Ling & Teng, Jinn-Tsair & Chern, Maw-Sheng, 2010. "An inventory model under inflation for deteriorating items with stock-dependent consumption rate and partial backlogging shortages," International Journal of Production Economics, Elsevier, vol. 123(1), pages 8-19, January.
    3. R. Begum & R.R. Sahoo & S.K. Sahu, 2012. "A replenishment policy for items with price-dependent demand, time-proportional deterioration and no shortages," International Journal of Systems Science, Taylor & Francis Journals, vol. 43(5), pages 903-910.
    4. Chandra Jaggi & Aditi Khanna & Priyanka Verma, 2011. "Two-warehouse partial backlogging inventory model for deteriorating items with linear trend in demand under inflationary conditions," International Journal of Systems Science, Taylor & Francis Journals, vol. 42(7), pages 1185-1196.
    5. Skouri, K. & Konstantaras, I. & Papachristos, S. & Ganas, I., 2009. "Inventory models with ramp type demand rate, partial backlogging and Weibull deterioration rate," European Journal of Operational Research, Elsevier, vol. 192(1), pages 79-92, January.
    6. Pal, Shilpi & Mahapatra, G.S. & Samanta, G.P., 2014. "An EPQ model of ramp type demand with Weibull deterioration under inflation and finite horizon in crisp and fuzzy environment," International Journal of Production Economics, Elsevier, vol. 156(C), pages 159-166.
    7. Wu, Kun-Shan & Ouyang, Liang-Yuh & Yang, Chih-Te, 2006. "An optimal replenishment policy for non-instantaneous deteriorating items with stock-dependent demand and partial backlogging," International Journal of Production Economics, Elsevier, vol. 101(2), pages 369-384, June.
    8. Hou, Kuo-Lung, 2006. "An inventory model for deteriorating items with stock-dependent consumption rate and shortages under inflation and time discounting," European Journal of Operational Research, Elsevier, vol. 168(2), pages 463-474, January.
    9. Chung-Ho Chen & Chih-Lun Lu, 2011. "Optimum profit model considering production, quality and sale problem," International Journal of Systems Science, Taylor & Francis Journals, vol. 42(12), pages 1917-1933.
    10. Swati Agrawal & Snigdha Banerjee, 2011. "Two-warehouse inventory model with ramp-type demand and partially backlogged shortages," International Journal of Systems Science, Taylor & Francis Journals, vol. 42(7), pages 1115-1126.
    11. Chung, Chun-Jen & Wee, Hui-Ming, 2011. "Short life-cycle deteriorating product remanufacturing in a green supply chain inventory control system," International Journal of Production Economics, Elsevier, vol. 129(1), pages 195-203, January.
    12. K. Skouri & I. Konstantaras & S. Manna & K. Chaudhuri, 2011. "Inventory models with ramp type demand rate, time dependent deterioration rate, unit production cost and shortages," Annals of Operations Research, Springer, vol. 191(1), pages 73-95, November.
    13. Yang, Hui-Ling, 2012. "Two-warehouse partial backlogging inventory models with three-parameter Weibull distribution deterioration under inflation," International Journal of Production Economics, Elsevier, vol. 138(1), pages 107-116.
    14. Sarkar, Biswajit & Sarkar, Sumon, 2013. "An improved inventory model with partial backlogging, time varying deterioration and stock-dependent demand," Economic Modelling, Elsevier, vol. 30(C), pages 924-932.
    15. Sarkar, Biswajit & Sarkar, Sumon, 2013. "Variable deterioration and demand—An inventory model," Economic Modelling, Elsevier, vol. 31(C), pages 548-556.
    16. Datta, T. K. & Pal, A. K., 1991. "Effects of inflation and time-value of money on an inventory model with linear time-dependent demand rate and shortages," European Journal of Operational Research, Elsevier, vol. 52(3), pages 326-333, June.
    17. Giannoccaro, Ilaria & Pontrandolfo, Pierpaolo & Scozzi, Barbara, 2003. "A fuzzy echelon approach for inventory management in supply chains," European Journal of Operational Research, Elsevier, vol. 149(1), pages 185-196, August.
    18. Hui-Ling Yang, 2011. "A partial backlogging production-inventory lot-size model for deteriorating items with time-varying production and demand rate over a finite time horizon," International Journal of Systems Science, Taylor & Francis Journals, vol. 42(8), pages 1397-1407.
    19. Yang, Hui-Ling & Teng, Jinn-Tsair & Chern, Maw-Sheng, 2002. "A forward recursive algorithm for inventory lot-size models with power-form demand and shortages," European Journal of Operational Research, Elsevier, vol. 137(2), pages 394-400, March.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Janssen, Larissa & Claus, Thorsten & Sauer, Jürgen, 2016. "Literature review of deteriorating inventory models by key topics from 2012 to 2015," International Journal of Production Economics, Elsevier, vol. 182(C), pages 86-112.
    2. G. Durga Bhavani & Ieva Meidute-Kavaliauskiene & Ghanshaym S. Mahapatra & Renata Činčikaitė, 2022. "A Sustainable Green Inventory System with Novel Eco-Friendly Demand Incorporating Partial Backlogging under Fuzziness," Sustainability, MDPI, vol. 14(15), pages 1-20, July.
    3. M. Palanivel & R. Uthayakumar, 2016. "Two-warehouse inventory model for non-instantaneous deteriorating items with partial backlogging and inflation over a finite time horizon," OPSEARCH, Springer;Operational Research Society of India, vol. 53(2), pages 278-302, June.
    4. Castellano, Davide & Glock, Christoph H., 2024. "Economic production quantity for a decaying item with stochastic demand and positive lead time," International Journal of Production Economics, Elsevier, vol. 267(C).
    5. Santosh Shekhawat & Nazek Alessa & Himanshu Rathore & Kalpna Sharma, 2022. "A Green Approach—Cost Optimization for a Manufacturing Supply Chain with MFIFO Warehouse Dispatching Policy and Inspection Policy," Sustainability, MDPI, vol. 14(21), pages 1-17, November.
    6. Sudip Adak & G. S. Mahapatra, 2022. "Effect of reliability on multi-item inventory system with shortages and partial backlog incorporating time dependent demand and deterioration," Annals of Operations Research, Springer, vol. 315(2), pages 1551-1571, August.
    7. Pourmohammad Zia, Nadia & Taleizadeh, Ata Allah, 2015. "A lot-sizing model with backordering under hybrid linked-to-order multiple advance payments and delayed payment," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 82(C), pages 19-37.
    8. Dai, Zhuo & Aqlan, Faisal & Gao, Kuo, 2017. "Optimizing multi-echelon inventory with three types of demand in supply chain," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 107(C), pages 141-177.
    9. Anushri Maji & Asoke Kumar Bhunia & Shyamal Kumar Mondal, 2022. "A production-reliability-inventory model for a series-parallel system with mixed strategy considering shortage, warranty period, credit period in crisp and stochastic sense," OPSEARCH, Springer;Operational Research Society of India, vol. 59(3), pages 862-907, September.
    10. Saha, Subrata & Sarkar, Biswajit & Sarkar, Mitali, 2023. "Application of improved meta-heuristic algorithms for green preservation technology management to optimize dynamical investments and replenishment strategies," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 209(C), pages 426-450.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Bakker, Monique & Riezebos, Jan & Teunter, Ruud H., 2012. "Review of inventory systems with deterioration since 2001," European Journal of Operational Research, Elsevier, vol. 221(2), pages 275-284.
    2. Pal, Shilpi & Mahapatra, G.S. & Samanta, G.P., 2014. "An EPQ model of ramp type demand with Weibull deterioration under inflation and finite horizon in crisp and fuzzy environment," International Journal of Production Economics, Elsevier, vol. 156(C), pages 159-166.
    3. Sarkar, Biswajit & Sarkar, Sumon, 2013. "Variable deterioration and demand—An inventory model," Economic Modelling, Elsevier, vol. 31(C), pages 548-556.
    4. M. Palanivel & R. Uthayakumar, 2015. "Finite horizon EOQ model for non-instantaneous deteriorating items with price and advertisement dependent demand and partial backlogging under inflation," International Journal of Systems Science, Taylor & Francis Journals, vol. 46(10), pages 1762-1773, July.
    5. Janssen, Larissa & Claus, Thorsten & Sauer, Jürgen, 2016. "Literature review of deteriorating inventory models by key topics from 2012 to 2015," International Journal of Production Economics, Elsevier, vol. 182(C), pages 86-112.
    6. M. Palanivel & R. Uthayakumar, 2016. "Two-warehouse inventory model for non-instantaneous deteriorating items with partial backlogging and inflation over a finite time horizon," OPSEARCH, Springer;Operational Research Society of India, vol. 53(2), pages 278-302, June.
    7. Biswajit Sarkar & Sharmila Saren & Leopoldo Cárdenas-Barrón, 2015. "An inventory model with trade-credit policy and variable deterioration for fixed lifetime products," Annals of Operations Research, Springer, vol. 229(1), pages 677-702, June.
    8. R. Udayakumar & K. V. Geetha, 2017. "Economic ordering policy for single item inventory model over finite time horizon," International Journal of System Assurance Engineering and Management, Springer;The Society for Reliability, Engineering Quality and Operations Management (SREQOM),India, and Division of Operation and Maintenance, Lulea University of Technology, Sweden, vol. 8(2), pages 734-757, November.
    9. Pahl, Julia & Voß, Stefan, 2014. "Integrating deterioration and lifetime constraints in production and supply chain planning: A survey," European Journal of Operational Research, Elsevier, vol. 238(3), pages 654-674.
    10. Pentico, David W. & Drake, Matthew J., 2011. "A survey of deterministic models for the EOQ and EPQ with partial backordering," European Journal of Operational Research, Elsevier, vol. 214(2), pages 179-198, October.
    11. Maryam Ghoreishi & Gerhard-Wilhelm Weber & Abolfazl Mirzazadeh, 2015. "An inventory model for non-instantaneous deteriorating items with partial backlogging, permissible delay in payments, inflation- and selling price-dependent demand and customer returns," Annals of Operations Research, Springer, vol. 226(1), pages 221-238, March.
    12. Ghiami, Yousef & Beullens, Patrick, 2016. "Planning for shortages? Net Present Value analysis for a deteriorating item with partial backlogging," International Journal of Production Economics, Elsevier, vol. 178(C), pages 1-11.
    13. Krishna Prasad & Bani Mukherjee, 2016. "Optimal inventory model under stock and time dependent demand for time varying deterioration rate with shortages," Annals of Operations Research, Springer, vol. 243(1), pages 323-334, August.
    14. Bhunia, A.K. & Shaikh, Ali Akbar, 2015. "An application of PSO in a two-warehouse inventory model for deteriorating item under permissible delay in payment with different inventory policies," Applied Mathematics and Computation, Elsevier, vol. 256(C), pages 831-850.
    15. Wee, Hui-Ming & Huang, Yen-Deng & Wang, Wan-Tsu & Cheng, Yung-Lung, 2014. "An EPQ model with partial backorders considering two backordering costs," Applied Mathematics and Computation, Elsevier, vol. 232(C), pages 898-907.
    16. Wang, Wan-Chih & Teng, Jinn-Tsair & Lou, Kuo-Ren, 2014. "Seller’s optimal credit period and cycle time in a supply chain for deteriorating items with maximum lifetime," European Journal of Operational Research, Elsevier, vol. 232(2), pages 315-321.
    17. Nita H. Shah & Chetansinh R. Vaghela, 2017. "Economic order quantity for deteriorating items under inflation with time and advertisement dependent demand," OPSEARCH, Springer;Operational Research Society of India, vol. 54(1), pages 168-180, March.
    18. Kun-Jen Chung & Jui-Jung Liao & Shy-Der Lin & Sheng-Tu Chuang & Hari Mohan Srivastava, 2019. "The Inventory Model for Deteriorating Items under Conditions Involving Cash Discount and Trade Credit," Mathematics, MDPI, vol. 7(7), pages 1-20, July.
    19. Tai, Allen H. & Xie, Yue & Ching, Wai-Ki, 2016. "Inspection policy for inventory system with deteriorating products," International Journal of Production Economics, Elsevier, vol. 173(C), pages 22-29.
    20. Sarkar, Biswajit & Sarkar, Sumon, 2013. "An improved inventory model with partial backlogging, time varying deterioration and stock-dependent demand," Economic Modelling, Elsevier, vol. 30(C), pages 924-932.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:ecmode:v:46:y:2015:i:c:p:334-345. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/inca/30411 .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.