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Production-Inventory Systems with Unreliable Machines

Author

Listed:
  • M. Berg

    (University of Haifa, Hafa, Israel)

  • M. J. M. Posner

    (University of Toronto, Toronto, Ontario, Canada)

  • H. Zhao

    (University of Toronto, Toronto, Ontario, Canada)

Abstract

A broad class of production-inventory systems is studied in which a number of producing machines are susceptible to failure following which they must be repaired to make them operative again. The machines' production can also be stopped deliberately due to stocking capacity limitations or any other relevant considerations. The interplay between the processes involved, namely, production, demand, and failure/repair or reliability, in conjunction with the shutdown policy used, determine the inventory accumulation process and possible shortages. We first obtain the stationary distribution of the inventory process for different assumptions on the random behavior of the production, demand, and reliability processes. By employing level-crossing techniques, a mathematical analysis is carried out for a “core” model, which then serves the role of the nucleus for the study of a wide range of models. We compute performance measures that characterize the operation of the production-inventory system with respect to its service-level to customers, expected inventory stocked, machines' utilization, repairmen utilization, and so on. A numerical illustration is provided which shows the effect of machine breakdowns on service and inventory levels.

Suggested Citation

  • M. Berg & M. J. M. Posner & H. Zhao, 1994. "Production-Inventory Systems with Unreliable Machines," Operations Research, INFORMS, vol. 42(1), pages 111-118, February.
    • Handle: RePEc:inm:oropre:v:42:y:1994:i:1:p:111-118
    DOI: 10.1287/opre.42.1.111
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    Citations

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    Cited by:

    1. Chiu, Singa Wang & Chou, Chung-Li & Wu, Wen-Kuei, 2013. "Optimizing replenishment policy in an EPQ-based inventory model with nonconforming items and breakdown," Economic Modelling, Elsevier, vol. 35(C), pages 330-337.
    2. Moshe Dror & Kenneth R. Smith & Candace Arai Yano, 2009. "Deux Chemicals Inc. Goes Just-in-Time," Interfaces, INFORMS, vol. 39(6), pages 503-515, December.
    3. Mohebbi, Esmail, 2006. "A production-inventory model with randomly changing environmental conditions," European Journal of Operational Research, Elsevier, vol. 174(1), pages 539-552, October.
    4. Israel David & Eitan Greenshtein & Avraham Mehrez, 1997. "A dynamic‐programming approach to continuous‐review obsolescent inventory problems," Naval Research Logistics (NRL), John Wiley & Sons, vol. 44(8), pages 757-774, December.
    5. Süleyman Demirel & Roman Kapuscinski & Man Yu, 2018. "Strategic Behavior of Suppliers in the Face of Production Disruptions," Management Science, INFORMS, vol. 64(2), pages 533-551, February.
    6. Fahimeh Shamsaei & Mathieu Vyve, 2017. "Solving integrated production and condition-based maintenance planning problems by MIP modeling," Flexible Services and Manufacturing Journal, Springer, vol. 29(2), pages 184-202, June.
    7. Harun Öztürk, 2021. "Optimal production run time for an imperfect production inventory system with rework, random breakdowns and inspection costs," Operational Research, Springer, vol. 21(1), pages 167-204, March.
    8. Om Prakash & A.R. Roy & A. Goswami, 2014. "Stochastic manufacturing system with process deterioration and machine breakdown," International Journal of Systems Science, Taylor & Francis Journals, vol. 45(12), pages 2539-2551, December.
    9. Ben A. Chaouch, 2007. "Inventory control and periodic price discounting campaigns," Naval Research Logistics (NRL), John Wiley & Sons, vol. 54(1), pages 94-108, February.
    10. Chiu, Singa Wang & Wang, Shan-Ling & Chiu, Yuan-Shyi Peter, 2007. "Determining the optimal run time for EPQ model with scrap, rework, and stochastic breakdowns," European Journal of Operational Research, Elsevier, vol. 180(2), pages 664-676, July.
    11. Ata Allah Taleizadeh, 2018. "A constrained integrated imperfect manufacturing-inventory system with preventive maintenance and partial backordering," Annals of Operations Research, Springer, vol. 261(1), pages 303-337, February.
    12. Giri, B. C. & Dohi, T., 2004. "Optimal lot sizing for an unreliable production system based on net present value approach," International Journal of Production Economics, Elsevier, vol. 92(2), pages 157-167, November.
    13. Peymankar, Mahboobe & Dehghanian, Farzad & Ghiami, Yousef & Abolbashari, Mohammad Hassan, 2018. "The effects of contractual agreements on the economic production quantity model with machine breakdown," International Journal of Production Economics, Elsevier, vol. 201(C), pages 203-215.
    14. B C Giri & T Dohi, 2005. "Exact formulation of stochastic EMQ model for an unreliable production system," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 56(5), pages 563-575, May.
    15. Chiu, Singa Wang, 2008. "Production lot size problem with failure in repair and backlogging derived without derivatives," European Journal of Operational Research, Elsevier, vol. 188(2), pages 610-615, July.
    16. Seyed M.R. Iravani & Izak Duenyas & Tava Lennon Olsen, 2000. "A Production/Inventory System Subject to Failure with Limited Repair Capacity," Operations Research, INFORMS, vol. 48(6), pages 951-964, December.
    17. Azoury, Katy S. & Miyaoka, Julia, 2020. "Optimal and simple approximate solutions to a production-inventory system with stochastic and deterministic demand," European Journal of Operational Research, Elsevier, vol. 286(1), pages 178-189.
    18. Mohammad Firouz & Linda Li & Burcu B. Keskin, 2022. "Managing equipment rentals: Unreliable fleet, impatient customers, and finite commitment capacity," Production and Operations Management, Production and Operations Management Society, vol. 31(11), pages 3963-3981, November.
    19. 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.
    20. 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.
    21. Chakraborty, Tulika & Giri, B.C. & Chaudhuri, K.S., 2008. "Production lot sizing with process deterioration and machine breakdown," European Journal of Operational Research, Elsevier, vol. 185(2), pages 606-618, March.

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