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A closed-form solution for the distribution free continuous review integrated inventory model

Author

Listed:
  • Anuraag Gutgutia

    (Indian Institute of Technology Kharagpur)

  • J. K. Jha

    (Indian Institute of Technology Kharagpur)

Abstract

In this paper, we develop an integrated inventory model in a single-vendor single-buyer supply chain under an unknown demand distribution at the buyer. It is assumed that each lot delivered to the buyer contains a random fraction of defective items, and lead time can be reduced at an extra crashing cost. We also consider that the unmet demand at the buyer during the stockout period is partially backordered. A model is formulated to minimize the total expected relevant costs of the system considering an exact expression of the service level constraint to ensure that a certain percentage of customer orders are filled by the buyer. Closed-form expressions are derived for the optimal order quantity and safety factor for given lead time and shipment frequency, and then an algorithm is proposed to find the global optimal solution. Finally, a numerical example is presented to illustrate the solution procedure and sensitivity analysis is carried out to analyze the proposed model.

Suggested Citation

  • Anuraag Gutgutia & J. K. Jha, 2018. "A closed-form solution for the distribution free continuous review integrated inventory model," Operational Research, Springer, vol. 18(1), pages 159-186, April.
    • Handle: RePEc:spr:operea:v:18:y:2018:i:1:d:10.1007_s12351-016-0258-5
    DOI: 10.1007/s12351-016-0258-5
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    References listed on IDEAS

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    1. Huang, Chao-Kuei, 2004. "An optimal policy for a single-vendor single-buyer integrated production-inventory problem with process unreliability consideration," International Journal of Production Economics, Elsevier, vol. 91(1), pages 91-98, September.
    2. Papachristos, S. & Konstantaras, I., 2006. "Economic ordering quantity models for items with imperfect quality," International Journal of Production Economics, Elsevier, vol. 100(1), pages 148-154, March.
    3. Ouyang, Liang-Yuh & Wu, Kun-Shan & Ho, Chia-Huei, 2007. "An integrated vendor-buyer inventory model with quality improvement and lead time reduction," International Journal of Production Economics, Elsevier, vol. 108(1-2), pages 349-358, July.
    4. Glock, C. H. & Kim, T., 2012. "A joint economic lot sizemodel with returnable transport items," Publications of Darmstadt Technical University, Institute for Business Studies (BWL) 59079, Darmstadt Technical University, Department of Business Administration, Economics and Law, Institute for Business Studies (BWL).
    5. Liang-Yuh Ouyang & Kun-Shan Wu & Chia-Huei Ho, 2006. "The Single-Vendor Single-Buyer Integrated Inventory Problem With Quality Improvement And Lead Time Reduction — Minimax Distribution-Free Approach," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 23(03), pages 407-424.
    6. Ouyang, Liang-Yuh & Wu, Kun-Shan & Ho, Chia-Huei, 2004. "Integrated vendor-buyer cooperative models with stochastic demand in controllable lead time," International Journal of Production Economics, Elsevier, vol. 92(3), pages 255-266, December.
    7. L-Y Ouyang & C-K Chen & H-C Chang, 1999. "Lead time and ordering cost reductions in continuous review inventory systems with partial backorders," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 50(12), pages 1272-1279, December.
    8. Salameh, M. K. & Jaber, M. Y., 2000. "Economic production quantity model for items with imperfect quality," International Journal of Production Economics, Elsevier, vol. 64(1-3), pages 59-64, March.
    9. Lin, Yu-Jen, 2008. "Minimax distribution free procedure with backorder price discount," International Journal of Production Economics, Elsevier, vol. 111(1), pages 118-128, January.
    10. Maddah, Bacel & Jaber, Mohamad Y., 2008. "Economic order quantity for items with imperfect quality: Revisited," International Journal of Production Economics, Elsevier, vol. 112(2), pages 808-815, April.
    11. Chung, Kun-Jen, 2008. "A necessary and sufficient condition for the existence of the optimal solution of a single-vendor single-buyer integrated production-inventory model with process unreliability consideration," International Journal of Production Economics, Elsevier, vol. 113(1), pages 269-274, May.
    12. Goyal, Suresh Kumar & Cardenas-Barron, Leopoldo Eduardo, 2002. "Note on: Economic production quantity model for items with imperfect quality - a practical approach," International Journal of Production Economics, Elsevier, vol. 77(1), pages 85-87, May.
    13. Glock, C. H., 2012. "The joint economic lot size problem: a review," Publications of Darmstadt Technical University, Institute for Business Studies (BWL) 57811, Darmstadt Technical University, Department of Business Administration, Economics and Law, Institute for Business Studies (BWL).
    14. Glock, Christoph H., 2012. "The joint economic lot size problem: A review," International Journal of Production Economics, Elsevier, vol. 135(2), pages 671-686.
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    3. Eugenia Babiloni & Ester Guijarro & Juan R. Trapero, 2023. "Stock control analytics: a data-driven approach to compute the fill rate considering undershoots," Operational Research, Springer, vol. 23(1), pages 1-25, March.
    4. Irfanullah Khan & Jihed Jemai & Han Lim & Biswajit Sarkar, 2019. "Effect of Electrical Energy on the Manufacturing Setup Cost Reduction, Transportation Discounts, and Process Quality Improvement in a Two-Echelon Supply Chain Management under a Service-Level Constrai," Energies, MDPI, vol. 12(19), pages 1-32, September.
    5. Qi, Mingyao & Yang, Ying & Cheng, Chun, 2023. "Location and inventory pre-positioning problem under uncertainty," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 177(C).
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    7. Haider Ali & Reshma Nasreen & Neetu Arneja & Chandra K. Jaggi, 2023. "Optimization of a periodically assessing model with manageable lead time under SLC with back order rebate for deteriorating items," 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. 14(1), pages 241-266, February.
    8. John P. Saldanha & Bradley S. Price & Douglas J. Thomas, 2023. "A nonparametric approach for setting safety stock levels," Production and Operations Management, Production and Operations Management Society, vol. 32(4), pages 1150-1168, April.
    9. Haider Ali & Reshma Nasreen & Neetu Arneja & Chandra K. Jaggi, 2024. "Periodic inventory model with controllable lead time and back order discount for decaying items," OPSEARCH, Springer;Operational Research Society of India, vol. 61(3), pages 1441-1471, September.
    10. Tiwari, Sunil & Kazemi, Nima & Modak, Nikunja Mohan & Cárdenas-Barrón, Leopoldo Eduardo & Sarkar, Sumon, 2020. "The effect of human errors on an integrated stochastic supply chain model with setup cost reduction and backorder price discount," International Journal of Production Economics, Elsevier, vol. 226(C).

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