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Multi-Product Production System with the Reduced Failure Rate and the Optimum Energy Consumption under Variable Demand

Author

Listed:
  • Shaktipada Bhuniya

    (Department of Mathematics and Statistics, Banasthali Vidyapith, Banasthali, Rajasthan 304 022, India)

  • Biswajit Sarkar

    (Department of Industrial & Management Engineering, Hanyang University, Ansan Gyeonggi-do 15588, Korea)

  • Sarla Pareek

    (Department of Mathematics and Statistics, Banasthali Vidyapith, Banasthali, Rajasthan 304 022, India)

Abstract

The advertising of any smart product is crucial in generating customer demand, along with reducing sale prices. Naturally, a decrease in price always increases the demand for any smart product. This study introduces a multi-product production process, taking into consideration the advertising- and price-dependent demands of products, where the failure rate of the production system is reduced under the optimum energy consumption. For long-run production systems, unusual energy consumption and machine failures occur frequently, which are reduced in this study. All costs related with the production system are included in the optimum energy costs. The unit production cost is dependent on the production rate of the machine and its failure rate. The aim of this study is to obtain the optimum profit with a reduced failure rate, under the optimum advertising costs and the optimum sale price. The total profit of the model becomes a complex, non-linear function, with respect to the decision variables. For this reason, the model is solved numerically by an iterative method. However, the global optimality is proved numerically, by using the Hessian matrix. The numerical results obtained show that for smart production, the maximum profit always occurs at the optimum values of the decision variables.

Suggested Citation

  • Shaktipada Bhuniya & Biswajit Sarkar & Sarla Pareek, 2019. "Multi-Product Production System with the Reduced Failure Rate and the Optimum Energy Consumption under Variable Demand," Mathematics, MDPI, vol. 7(5), pages 1-20, May.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:5:p:465-:d:234000
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    References listed on IDEAS

    as
    1. Yanting Du & Guangdi Hu & Shun Xiang & Ke Zhang & Hongxing Liu & Feng Guo, 2018. "Estimation of the Diesel Particulate Filter Soot Load Based on an Equivalent Circuit Model," Energies, MDPI, vol. 11(2), pages 1-13, February.
    2. Mitali Sarkar & Biswajit Sarkar & Muhammad Waqas Iqbal, 2018. "Effect of Energy and Failure Rate in a Multi-Item Smart Production System," Energies, MDPI, vol. 11(11), pages 1-21, October.
    3. Tiwari, Sunil & Cárdenas-Barrón, Leopoldo Eduardo & Goh, Mark & Shaikh, Ali Akbar, 2018. "Joint pricing and inventory model for deteriorating items with expiration dates and partial backlogging under two-level partial trade credits in supply chain," International Journal of Production Economics, Elsevier, vol. 200(C), pages 16-36.
    4. Tiwari, Sunil & Jaggi, Chandra K. & Gupta, Mamta & Cárdenas-Barrón, Leopoldo Eduardo, 2018. "Optimal pricing and lot-sizing policy for supply chain system with deteriorating items under limited storage capacity," International Journal of Production Economics, Elsevier, vol. 200(C), pages 278-290.
    5. Biswajit Sarkar & Kripasindhu Chaudhuri & Shib Sankar Sana, 2010. "A stock-dependent inventory model in an imperfect production process," International Journal of Procurement Management, Inderscience Enterprises Ltd, vol. 3(4), pages 361-378.
    6. Régis Chenavaz & Sajjad M. Jasimuddin, 2017. "An analytical model of the relationship between product quality and advertising," Post-Print hal-01685892, HAL.
    7. 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.
    8. Haraldsson, Joakim & Johansson, Maria T., 2018. "Review of measures for improved energy efficiency in production-related processes in the aluminium industry – From electrolysis to recycling," Renewable and Sustainable Energy Reviews, Elsevier, vol. 93(C), pages 525-548.
    9. Giri, B.C. & Sharma, S., 2014. "Manufacturer's pricing strategy in a two-level supply chain with competing retailers and advertising cost dependent demand," Economic Modelling, Elsevier, vol. 38(C), pages 102-111.
    10. Hyun Kim, Chang & Hong, Yushin, 1999. "An optimal production run length in deteriorating production processes," International Journal of Production Economics, Elsevier, vol. 58(2), pages 183-189, January.
    11. Srimathy Mohan & Gopalakrishnan Mohan & Ashok Chandrasekhar, 2008. "Multi-item, economic order quantity model with permissible delay in payments and a budget constraint," European Journal of Industrial Engineering, Inderscience Enterprises Ltd, vol. 2(4), pages 446-460.
    12. 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.
    13. Sarkar, Biswajit & Moon, Ilkyeong, 2014. "Improved quality, setup cost reduction, and variable backorder costs in an imperfect production process," International Journal of Production Economics, Elsevier, vol. 155(C), pages 204-213.
    14. Sana, Shib Sankar, 2010. "A production-inventory model in an imperfect production process," European Journal of Operational Research, Elsevier, vol. 200(2), pages 451-464, January.
    15. Pal, Brojeswar & Sana, Shib Sankar & Chaudhuri, Kripasindhu, 2012. "Multi-item EOQ model while demand is sales price and price break sensitive," Economic Modelling, Elsevier, vol. 29(6), pages 2283-2288.
    16. Sana, Shib Sankar & Goyal, Suresh Kumar & Chaudhuri, Kripasindhu, 2007. "An imperfect production process in a volume flexible inventory model," International Journal of Production Economics, Elsevier, vol. 105(2), pages 548-559, February.
    17. Jiseong Noh & Jong Soo Kim & Biswajit Sarkar, 2019. "Two-echelon supply chain coordination with advertising-driven demand under Stackelberg game policy," European Journal of Industrial Engineering, Inderscience Enterprises Ltd, vol. 13(2), pages 213-244.
    18. Yung-Fu Huang & Chih-Sung Lai & Maw-Liann Shyu, 2007. "Retailer's EOQ Model with Limited Storage Space Under Partially Permissible Delay in Payments," Mathematical Problems in Engineering, Hindawi, vol. 2007, pages 1-18, September.
    19. 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.
    20. Leopoldo Eduardo Cárdenas-Barrón & Kun-Jen Chung & Nima Kazemi & Ehsan Shekarian, 2018. "Optimal inventory system with two backlog costs in response to a discount offer: corrections and complements," Operational Research, Springer, vol. 18(1), pages 97-104, April.
    21. Biswajit Sarkar & Sharmila Saren & Debjani Sinha & Sun Hur, 2015. "Effect of Unequal Lot Sizes, Variable Setup Cost, and Carbon Emission Cost in a Supply Chain Model," Mathematical Problems in Engineering, Hindawi, vol. 2015, pages 1-13, November.
    22. Giuseppe Todde & Lelia Murgia & Maria Caria & Antonio Pazzona, 2018. "A Comprehensive Energy Analysis and Related Carbon Footprint of Dairy Farms, Part 2: Investigation and Modeling of Indirect Energy Requirements," Energies, MDPI, vol. 11(2), pages 1-13, February.
    23. Sarkar, Biswajit & Sarkar, Sumon, 2013. "Variable deterioration and demand—An inventory model," Economic Modelling, Elsevier, vol. 31(C), pages 548-556.
    24. Arunava Majumder & Rekha Guchhait & Biswajit Sarkar, 2017. "Manufacturing quality improvement and setup cost reduction in a vendor-buyer supply chain model," European Journal of Industrial Engineering, Inderscience Enterprises Ltd, vol. 11(5), pages 588-612.
    25. Sana, Shib Sankar, 2010. "An economic production lot size model in an imperfect production system," European Journal of Operational Research, Elsevier, vol. 201(1), pages 158-170, February.
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    2. 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.
    3. Yuan-Shyi Peter Chiu & Victoria Chiu & Tsu-Ming Yeh & Hua-Yao Wu, 2020. "Incorporating Outsourcing Strategy and Quality Assurance into a Multiproduct Manufacturer–Retailer Coordination Replenishing Decision," Mathematics, MDPI, vol. 8(12), pages 1-19, December.
    4. Fath U Min Ullah & Noman Khan & Tanveer Hussain & Mi Young Lee & Sung Wook Baik, 2021. "Diving Deep into Short-Term Electricity Load Forecasting: Comparative Analysis and a Novel Framework," Mathematics, MDPI, vol. 9(6), pages 1-22, March.

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