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A multiproduct single machine economic production quantity (EPQ) inventory model with discrete delivery order, joint production policy and budget constraints

Author

Listed:
  • Amir Hossein Nobil

    (Islamic Azad University)

  • Amir Hosein Afshar Sedigh

    (University of Otago)

  • Leopoldo Eduardo Cárdenas-Barrón

    (Tecnológico de Monterrey)

Abstract

This paper develops a multiproduct economic production quantity inventory model for a vendor–buyer system in which several products are manufactured on a single machine. The vendor delivers the products to customer in small batches. The number of orders must be a discrete value. Moreover, benefitting from a just-in-time policy, the buyer decides the size of the delivered batches. Due to the fact that several products are manufactured on one machine, this makes that the production capacity be considered as a constraint. The aim of this study is to determine the optimal cycle length and the number of delivered batches for each product so that the total inventory cost is minimized. The problem under study is modeled as a mixed integer nonlinear programing problem considering maximum number of orders, capacity and budget constraints. Three different methods are developed and employed to solve this problem: an exact method, a heuristic algorithm and a hybrid genetic algorithm. Based on the results, the three algorithms have near efficiency with different running times. The results shows that the heuristic algorithm obtains a good solution in a short time and the hybrid genetic algorithm finds solutions with higher quality in an acceptable time. Finally, a sensitivity analysis is done to evaluate the effect of changes in the parameters of problem.

Suggested Citation

  • Amir Hossein Nobil & Amir Hosein Afshar Sedigh & Leopoldo Eduardo Cárdenas-Barrón, 2020. "A multiproduct single machine economic production quantity (EPQ) inventory model with discrete delivery order, joint production policy and budget constraints," Annals of Operations Research, Springer, vol. 286(1), pages 265-301, March.
    • Handle: RePEc:spr:annopr:v:286:y:2020:i:1:d:10.1007_s10479-017-2650-9
    DOI: 10.1007/s10479-017-2650-9
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    References listed on IDEAS

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    1. Mark Daskin & Collette Coullard & Zuo-Jun Shen, 2002. "An Inventory-Location Model: Formulation, Solution Algorithm and Computational Results," Annals of Operations Research, Springer, vol. 110(1), pages 83-106, February.
    2. H. Wang & H. Pham, 1999. "Some maintenance models and availability withimperfect maintenance in production systems," Annals of Operations Research, Springer, vol. 91(0), pages 305-318, January.
    3. Taleizadeh, Ata Allah & Cárdenas-Barrón, Leopoldo Eduardo & Mohammadi, Babak, 2014. "A deterministic multi product single machine EPQ model with backordering, scraped products, rework and interruption in manufacturing process," International Journal of Production Economics, Elsevier, vol. 150(C), pages 9-27.
    4. Jiafu Tang & Kai-Leung Yung & Iko Kaku & Jianbo Yang, 2008. "The scheduling of deliveries in a production-distribution system with multiple buyers," Annals of Operations Research, Springer, vol. 161(1), pages 5-23, July.
    5. Viswanathan, S., 1998. "Optimal strategy for the integrated vendor-buyer inventory model," European Journal of Operational Research, Elsevier, vol. 105(1), pages 38-42, February.
    6. Shima Shafiee-Gol & Mohammad Mahdi Nasiri & Ata Allah Taleizadeh, 2016. "Pricing and production decisions in multi-product single machine manufacturing system with discrete delivery and rework," OPSEARCH, Springer;Operational Research Society of India, vol. 53(4), pages 873-888, December.
    7. Ata Allah Taleizadeh & Seyed Jafar Sadjadi & Seyed Taghi Akhavan Niaki, 2011. "Multiproduct EPQ model with single machine, backordering and immediate rework process," European Journal of Industrial Engineering, Inderscience Enterprises Ltd, vol. 5(4), pages 388-411.
    8. Brojeswar Pal & Shib Sana & Kripasindhu Chaudhuri, 2013. "Maximising profits for an EPQ model with unreliable machine and rework of random defective items," International Journal of Systems Science, Taylor & Francis Journals, vol. 44(3), pages 582-594.
    9. Pasandideh, Seyed Hamid Reza & Niaki, Seyed Taghi Akhavan & Nobil, Amir Hossein & Cárdenas-Barrón, Leopoldo Eduardo, 2015. "A multiproduct single machine economic production quantity model for an imperfect production system under warehouse construction cost," International Journal of Production Economics, Elsevier, vol. 169(C), pages 203-214.
    10. Cardenas-Barron, Leopoldo Eduardo, 2001. "The economic production quantity (EPQ) with shortage derived algebraically," International Journal of Production Economics, Elsevier, vol. 70(3), pages 289-292, April.
    11. Da Wen & Pan Ershun & Wang Ying & Liao Wenzhu, 2016. "An economic production quantity model for a deteriorating system integrated with predictive maintenance strategy," Journal of Intelligent Manufacturing, Springer, vol. 27(6), pages 1323-1333, December.
    12. 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.
    13. Pal, Brojeswar & Sana, Shib Sankar & Chaudhuri, Kripasindhu, 2012. "A three layer multi-item production–inventory model for multiple suppliers and retailers," Economic Modelling, Elsevier, vol. 29(6), pages 2704-2710.
    14. Yuan-Shyi Peter Chiu & Chih-An Katherine Lin & Huei-Hsin Chang & Victoria Chiu, 2010. "Mathematical modelling for determining economic batch size and optimal number of deliveries for EPQ model with quality assurance," Mathematical and Computer Modelling of Dynamical Systems, Taylor & Francis Journals, vol. 16(4), pages 373-388, July.
    15. Kenneth R. Baker, 1970. "Note--On Madigan's Approach to the Deterministic Multi-Product Production and Inventory Problem," Management Science, INFORMS, vol. 16(9), pages 636-638, May.
    16. Donald Erlenkotter, 1989. "Note---An Early Classic Misplaced: Ford W. Harris's Economic Order Quantity Model of 1915," Management Science, INFORMS, vol. 35(7), pages 898-900, July.
    17. Seyed Mohsen Mousavi & Ardeshir Bahreininejad & S. Nurmaya Musa & Farazila Yusof, 2017. "A modified particle swarm optimization for solving the integrated location and inventory control problems in a two-echelon supply chain network," Journal of Intelligent Manufacturing, Springer, vol. 28(1), pages 191-206, January.
    18. Jack Rogers, 1958. "A Computational Approach to the Economic Lot Scheduling Problem," Management Science, INFORMS, vol. 4(3), pages 264-291, April.
    19. Erlenkotter, Donald, 2014. "Ford Whitman Harris's economical lot size model," International Journal of Production Economics, Elsevier, vol. 155(C), pages 12-15.
    20. Pal, S. & Goswami, A. & Chaudhuri, K. S., 1993. "A deterministic inventory model for deteriorating items with stock-dependent demand rate," International Journal of Production Economics, Elsevier, vol. 32(3), pages 291-299, November.
    21. Sujit De & Shib Sana, 2015. "Backlogging EOQ model for promotional effort and selling price sensitive demand- an intuitionistic fuzzy approach," Annals of Operations Research, Springer, vol. 233(1), pages 57-76, October.
    22. Wee, Hui Ming & Widyadana, Gede Agus, 2013. "Single-vendor single-buyer inventory model with discrete delivery order, random machine unavailability time and lost sales," International Journal of Production Economics, Elsevier, vol. 143(2), pages 574-579.
    23. C. Loren Doll & D. Clay Whybark, 1973. "An Iterative Procedure for the Single-Machine Multi-Product Lot Scheduling Problem," Management Science, INFORMS, vol. 20(1), pages 50-55, September.
    24. Yu-Chung Tsao, 2015. "A piecewise nonlinear optimization for a production-inventory model under maintenance, variable setup costs, and trade credits," Annals of Operations Research, Springer, vol. 233(1), pages 465-481, October.
    25. Ben-Daya, Mohamed, 2002. "The economic production lot-sizing problem with imperfect production processes and imperfect maintenance," International Journal of Production Economics, Elsevier, vol. 76(3), pages 257-264, April.
    26. Jinn-Tsair Teng & Leopoldo Cárdenas-Barrón & Kuo-Ren Lou & Hui Wee, 2013. "Optimal economic order quantity for buyer–distributor–vendor supply chain with backlogging derived without derivatives," International Journal of Systems Science, Taylor & Francis Journals, vol. 44(5), pages 986-994.
    27. 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.
    28. Donald Erlenkotter, 1990. "Ford Whitman Harris and the Economic Order Quantity Model," Operations Research, INFORMS, vol. 38(6), pages 937-946, December.
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