Skip to main content
SpringerLink
Log in

An economic machining process model with interval parameters

  • ORIGINAL ARTICLE
  • Published:
The International Journal of Advanced Manufacturing Technology Aims and scope Submit manuscript

Abstract

The primary objective of a machining economics model is to determine the optimal cutting parameters that minimize production costs while satisfying some design constraints. When the parameters in a machining economics model have interval values, the associated problem becomes an interval machining economics problem, and the objective value will also have interval value; that is, lying in a range. This paper develops a solution method that is able to derive the interval unit production cost of a machining economic model with interval parameters. A pair of two-level machining economics problems is formulated to calculate the upper bound and lower bound of the unit production cost. Based on the duality theorem, the two-level machining economics problem is transformed into the one-level conventional geometric program. Solving the corresponding pair of geometric programs produces the interval of the unit production cost. The results indicate that the cost interval contains more information for making decisions.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Shin YC, Joo YS (1992) Optimization of machining conditions with practical constraints. Int J Prod Res 30:2907–2919

    Google Scholar 

  2. Armarego EJA, Smith AJR, Wang J (1993) Constrained optimization strategies and CAM software for single-pass peripheral milling. Int J Prod Res 31:2139–2160

    Google Scholar 

  3. Da AJ, Sadler JP, Fang XD, Jawahir IS (1995) Optimum machining performance in finish turning with complex grooved tool. ASME 2-1-3-1:703–714

    Google Scholar 

  4. Malakooti B, Zhou YQ, Tandler EC (1995) In-process regressions and adaptive multi-criteria neural networks for monitoring and supervising machining operations. J Intell Manuf 6:53–66

    Article  Google Scholar 

  5. Prasad AVSRK, Rao PN, Rao URK (1997) Optimal selection of process parameters for turning operations in a CAPP system. Int J Prod Res 35:1495–1522

    Article  MATH  Google Scholar 

  6. Wang J, Kuriyagawa T, Wei XP, Guo DM (2002) Optimization of cutting conditions for single-pass turning operations using a deterministic approach. Int J Mach Tools Manuf 42:1023–1033

    Article  Google Scholar 

  7. Kaspi M, Shabtay D (2003) Optimization of the machining economics problem for a multistage transfer machine under failure, opportunistic and integrated replacement strategies. Int J Prod Res 41:2229–2247

    Article  MATH  Google Scholar 

  8. Gopalakrishnan B, Al-Khayyal F (1991) Machine parameter selection for turning with constraints: an analytical approach based on geometric programming. Int J Prod Res 29:1897–1908

    MATH  Google Scholar 

  9. Narang RV, Fischer GW (1993) Development of a framework to automate process functions and to determine machining parameters. Int J Prod Res 31:1921–1942

    Google Scholar 

  10. Gupta R, Barta JL, Lai GK (1994) Profit rate maximization in multipass turning with constraints: a geometric programming approach. Int J Prod Res 32:1557–1569

    MATH  Google Scholar 

  11. Wang ZG, Wong YS, Rahman M (2004) Optimization of multi-pass milling using genetic algorithm and genetic simulated annealing. Int J Adv Manuf Technol 24:727–762

    Article  Google Scholar 

  12. Baskar N, Asokan P, Saravanan R, Prabhaharan G (2005) Optimization of machining parameters for milling operations using non-conventional methods. Int J Adv Manuf Technol 25:1078–1088

    Article  Google Scholar 

  13. Beightler CS, Philips DT (1976) Applied geometric programming. Wiley, New York

    MATH  Google Scholar 

  14. Childs T, Maekawa K, Obikawa T, Yamane Y (2000) Metal machining: theory and applications. Arnold, London

    Google Scholar 

  15. Lee YH, Yang BH, Moon KS (1999) An economic machining process model using fuzzy non-linear programming and neural network. Int J Prod Res 37:835–847

    Article  MATH  Google Scholar 

  16. Bhattacharya A, Faria-Gonzalaz R, Ham I (1970) Regression analysis for predicting surface finish and its application in determination of optimum cutting conditions. Trans ASME 92:711–714

    Google Scholar 

  17. Peterson EL (2001) The fundamental relations between geometric programming duality, parametric programming duality, and ordinary Lagrangian duality. Ann Oper Res 105:109–153

    Article  MATH  MathSciNet  Google Scholar 

  18. Rajgopal J, Bricker DL (2002) Solving posynomial geometric programming problems via generalized linear programming. Comput Optim Appl 21:95–109

    Article  MATH  MathSciNet  Google Scholar 

  19. Duffin RJ, Peterson EL, Zenter C (1967) Geometric programming- theory and applications. Wiley, New York

    Google Scholar 

Download references

Acknowledgements

This research was supported by the National Science Council of Republic of China under Contract NSC94-2416-H-238-001. The authors are indebted to the referees for their constructive comments that significantly improved the quality of this paper.

Author information

Authors and Affiliations

  1. Graduate School of Business and Management, Vanung University, Chung-Li, Tao-Yuan 320, Taiwan, People’s Republic of China

    Rong-Tsu Wang & Shiang-Tai Liu

Authors
  1. Rong-Tsu Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Shiang-Tai Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Shiang-Tai Liu.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Wang, RT., Liu, ST. An economic machining process model with interval parameters. Int J Adv Manuf Technol 33, 900–910 (2007). https://doi.org/10.1007/s00170-006-0525-3

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00170-006-0525-3

Keywords

Search

Navigation