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Optimal reliability, production lot size and safety stock in an imperfect production system

Author

Listed:
  • Biswajit Sarkar
  • Shib Sankar Sana
  • Kripasindhu Chaudhuri

Abstract

This paper is concerned with the joint determination of optimal production lot size, safety stock and reliability parameter under the realistic assumptions that the production facility is subject to random breakdown of machinery system and also to change in the variable reliability parameter. Reliability of a machinery system is a decision variable that can be increased by more investment in production technology. In this model, preventive and corrective maintenance, safety stock for repair times and shortages are adopted to generalise the model. Except machinery breakdown, the manufacturing system may shift from in-control state to out-of-control state. During out-of-control state, a certain percentage of total production consists of defective items which can be reworked immediately at a cost to make as good as perfect quality items. The cost function is maximised by Khun-Tucker method. Numerical results are provided to illustrate both the study of the optimal solutions and sensitivity of different changes in key parameters.

Suggested Citation

  • Biswajit Sarkar & Shib Sankar Sana & Kripasindhu Chaudhuri, 2010. "Optimal reliability, production lot size and safety stock in an imperfect production system," International Journal of Mathematics in Operational Research, Inderscience Enterprises Ltd, vol. 2(4), pages 467-490.
    • Handle: RePEc:ids:ijmore:v:2:y:2010:i:4:p:467-490
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    Citations

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    Cited by:

    1. 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.
    2. Manoranjan De & Barun Das & Manoranjan Maiti, 2016. "EPL models for complementary and substitute items under imperfect production process with promotional cost and selling price dependent demands," OPSEARCH, Springer;Operational Research Society of India, vol. 53(2), pages 259-277, June.
    3. 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.
    4. Mitali Sarkar & Sungjun Kim & Jihed Jemai & Baishakhi Ganguly & Biswajit Sarkar, 2019. "An Application of Time-Dependent Holding Costs and System Reliability in a Multi-Item Sustainable Economic Energy Efficient Reliable Manufacturing System," Energies, MDPI, vol. 12(15), pages 1-19, July.
    5. Pal, Brojeswar & Sana, Shib Sankar & Chaudhuri, Kripasindhu, 2012. "A multi-echelon supply chain model for reworkable items in multiple-markets with supply disruption," Economic Modelling, Elsevier, vol. 29(5), pages 1891-1898.
    6. Ashoke Kumar Bera & Dipak Kumar Jana, 2017. "Multi-item imperfect production inventory model in Bi-fuzzy environments," OPSEARCH, Springer;Operational Research Society of India, vol. 54(2), pages 260-282, June.
    7. Iqra Asghar & Biswajit Sarkar & Sung-jun Kim, 2019. "Economic Analysis of an Integrated Production–Inventory System under Stochastic Production Capacity and Energy Consumption," Energies, MDPI, vol. 12(16), pages 1-27, August.
    8. Chang Wook Kang & Misbah Ullah & Mitali Sarkar & Muhammad Omair & Biswajit Sarkar, 2019. "A Single-Stage Manufacturing Model with Imperfect Items, Inspections, Rework, and Planned Backorders," Mathematics, MDPI, vol. 7(5), pages 1-18, May.
    9. Sinisterra, Wilfrido Quiñones & Lima, Victor Hugo Resende & Cavalcante, Cristiano Alexandre Virginio & Aribisala, Adetoye Ayokunle, 2023. "A delay-time model to integrate the sequence of resumable jobs, inspection policy, and quality for a single-component system," Reliability Engineering and System Safety, Elsevier, vol. 230(C).
    10. Sarkar, Mitali & Sarkar, Biswajit, 2013. "An economic manufacturing quantity model with probabilistic deterioration in a production system," Economic Modelling, Elsevier, vol. 31(C), pages 245-252.
    11. Amir Hossein Nobil & Amir Hosein Afshar Sedigh & Behrouz Afshar-Nadjafi, 2020. "Lot-sizing problem for a defective processing system with categorized items, backordering and pricing policy," Journal of Revenue and Pricing Management, Palgrave Macmillan, vol. 19(4), pages 255-265, August.
    12. Ouyang, Liang-Yuh & Chang, Chun-Tao, 2013. "Optimal production lot with imperfect production process under permissible delay in payments and complete backlogging," International Journal of Production Economics, Elsevier, vol. 144(2), pages 610-617.
    13. Hamideh Jeddi & Mahdi Doostparast, 2022. "Allocation of redundancies in systems: a general dependency-base framework," Annals of Operations Research, Springer, vol. 312(1), pages 259-273, May.
    14. Sarkar, Biswajit & Saren, Sharmila, 2016. "Product inspection policy for an imperfect production system with inspection errors and warranty cost," European Journal of Operational Research, Elsevier, vol. 248(1), pages 263-271.
    15. R. Uthayakumar & M. Rameswari, 2012. "An Economic Production Quantity Model for Defective Items with Trapezoidal type Demand Rate," Journal of Optimization Theory and Applications, Springer, vol. 154(3), pages 1055-1079, September.
    16. Guchhait, Partha & Kumar Maiti, Manas & Maiti, Manoranjan, 2013. "Production-inventory models for a damageable item with variable demands and inventory costs in an imperfect production process," International Journal of Production Economics, Elsevier, vol. 144(1), pages 180-188.
    17. Juhyun Lee & Byunghoon Kim & Suneung Ahn, 2019. "Maintenance Optimization for Repairable Deteriorating Systems under Imperfect Preventive Maintenance," Mathematics, MDPI, vol. 7(8), pages 1-17, August.
    18. Pal, Brojeswar & Sana, Shib Sankar & Chaudhuri, Kripasindhu, 2014. "Joint pricing and ordering policy for two echelon imperfect production inventory model with two cycles," International Journal of Production Economics, Elsevier, vol. 155(C), pages 229-238.
    19. Mubashir Hayat & Bashir Salah & Misbah Ullah & Iftikhar Hussain & Razaullah Khan, 2020. "Shipment Policy for an Economic Production Quantity Model Considering Imperfection and Transportation Cost," Sustainability, MDPI, vol. 12(21), pages 1-16, October.
    20. Sarkar, Biswajit & Sarkar, Sumon, 2013. "Variable deterioration and demand—An inventory model," Economic Modelling, Elsevier, vol. 31(C), pages 548-556.
    21. Udayan Chanda & Alok Kumar, 2019. "Optimization of EOQ Model for New Products Under Multi-Stage Adoption Process," International Journal of Innovation and Technology Management (IJITM), World Scientific Publishing Co. Pte. Ltd., vol. 16(02), pages 1-25, April.
    22. Sana, Shib Sankar, 2012. "A collaborating inventory model in a supply chain," Economic Modelling, Elsevier, vol. 29(5), pages 2016-2023.
    23. Waseem Sajjad & Misbah Ullah & Razaullah Khan & Mubashir Hayat, 2022. "Developing a Comprehensive Shipment Policy through Modified EPQ Model Considering Process Imperfections, Transportation Cost, and Backorders," Logistics, MDPI, vol. 6(3), pages 1-20, June.

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