The optimization of process target means in different markets

Fallah Nezhad, Mohammad Saber; Tarafdar, Hossein; Hosseini, Leila

doi:10.48313/jqem.2025.215014

The optimization of process target means in different markets

Document Type : Original Article

Authors

Mohammad Saber Fallah Nezhad

Hossein Tarafdar

Leila Hosseini

Department of Industrial Engineering, Yazd University, Yazd, Iran.

https://doi.org/10.48313/jqem.2025.215014

Abstract

Purpose: Calculating the optimal target mean for a process is recognized as an essential research area, with many proposed models in the literature. Previous studies have typically focused on a single market. The main difference in this research lies in the number of markets considered; unlike previous works, this study examines n different markets simultaneously.
Methodology: This study aims to determine the optimal process quality mean for a limited number of markets based on the target values of quality characteristics in each market. We propose a model to calculate this optimal mean across n markets with different price/cost structures. A key innovation of this research is the incorporation of probability distributions that reflect the likelihood of the quality characteristic falling within specific quality ranges in each market.
Findings: The model considers the probability that the quality characteristic falls within each market's defined quality range. To analyze and solve the model, absorbing Markov chains are used. A numerical example is presented in which the model is applied to two markets, and the optimal target mean and corresponding optimal revenue are obtained.
Originality/Value: Based on the results from the numerical example, the optimal target mean and revenue were determined for the two markets. A sensitivity analysis was conducted to assess the influence of various model parameters on these parameters, demonstrating how changes in parameters impact the model's outcomes.

Keywords

Optimization

Quality

Market

Absorbing Markov chain

Taguchi loss function

[1] Hunter, W. G., & Kartha, C. P. (1977). Determining the most profitable target value for a production process. Journal of quality technology, 9(4), 176–181. https://doi.org/10.1080/00224065.1977.11980794

[2] Bisgaard, S., Hunter, W. G., & Pallesen, L. (1984). Economic selection of quality manufactured product. Technometrics, 26(1), 9–18. https://doi.org/10.1080/00401706.1984.10487917

[3] Golhar, D. Y. (1987). Determination of the best mean contents for a canning problem. Journal of quality technology, 19(2), 82–84. https://doi.org/10.1080/00224065.1987.11979042

[4] Boucher, T. O., & Jafari, M. A. (1991). The optimum target value for single filling operations with quality sampling plans. Journal of quality technology, 23(1), 44–47. https://doi.org/10.1080/00224065.1991.11979282

[5] Al-Sultan, K. S. (1994). An algorithm for the determination of the optimum target values for two machines in series with quality sampling plans. The international journal of production research, 32(1), 37–45. https://doi.org/10.1080/00207549408956914

[6] Tang, K., & LO, J. J. (1993). Determination of the optimal process mean when inspection is based on a correlated variable. IIE transactions, 25(3), 66–72. https://doi.org/10.1080/07408179308964292

[7] Hong, S. H. (1999). Optimum mean value and screening limits for production processes with multi-class screening. International journal of production research, 37(1), 155–163. https://doi.org/10.1080/002075499191986

[8] Lee, M. K., Hong, S. H., & Elsayed, E. A. (2001). The optimum target value under single and two-stage screenings. Journal of quality technology, 33(4), 506–514. https://doi.org/10.1080/00224065.2001.11980108

[9] Lee, M. K., & Elsayed, E. A. (2002). Process mean and screening limits for filling processes under two-stage screening procedure. European journal of operational research, 138(1), 118–126. https://doi.org/10.1016/S0377-2217(01)00128-X

[10] Rahim, M. A., & Al-Sultan, K. S. (2000). Joint determination of the optimum target mean and variance of a process. Journal of quality in maintenance engineering, 6(3), 192–199. https://doi.org/10.1108/13552510010341207

[11] Rahim, M. A., & Tuffaha, F. (2004). Integrated model for determining the optimal initial settings of the process mean and the optimal production run assuming quadratic loss functions. International journal of production research, 42(16), 3281–3300. https://doi.org/10.1080/00207540410001666233

[12] Kim, Y. J., Cho, B. R., & Phillips, M. D. (2000). Determination of the optimal process mean with the consideration of variance reduction and process capability. Quality engineering, 13(2), 251–260. https://doi.org/10.1080/08982110108918648

[13] Teeravaraprug, J., & Cho, B. R. (2002). Designing the optimal process target levels for multiple quality characteristics. International journal of production research, 40(1), 37–54. https://doi.org/10.1080/00207540110073046

[14] Phillips, M. D., & Cho, B. R. (2000). A nonlinear model for determining the most economic process mean under a beta distribution. International journal of reliability, quality and safety engineering, 7(01), 61–74. https://doi.org/10.1142/S0218539300000067

[15] Arcelus, F. J., & Rahim, M. A. (1991). Joint determination of optimum variable and attribute target means. Naval research logistics (NRL), 38(6), 851–864. https://doi.org/10.1002/nav.3800380605

[16] Arcelus, F. J., & Rahim, M. A. (1994). Simultaneous economic selection of a variables and an attribute target mean. Journal of quality technology, 26(2), 125–133. https://doi.org/10.1080/00224065.1994.11979512

[17] Rahim, M. A., Bhadury, J., & Al-Sultan, K. S. (2002). Joint economic selection of target mean and variance. Engineering optimization, 34(1), 1–14. https://doi.org/10.1080/03052150210913

[18] Bowling, S. R., Khasawneh, M. T., Kaewkuekool, S., & Cho, B. R. (2004). A Markovian approach to determining optimum process target levels for a multi-stage serial production system. European journal of operational research, 159(3), 636–650. https://doi.org/10.1016/S0377-2217(03)00429-6

[19] Case, K. E., & Bennett, G. K. (1977). The economic effect of measurement error on variables acceptance sampling. THE international journal of production research, 15(2), 117–128. https://doi.org/10.1080/00207547708943110

[20] Owen, D. B., & Chou, Y. M. (1983). Effect of measurement error and instrument bias on operating characteristics for variables sampling plans. Journal of quality technology, 15(3), 107–117. https://doi.org/10.1080/00224065.1983.11978857

[21] Kanazuka, T. (1986). The effect of measurement error on the power of X-R charts. Journal of quality technology, 18(2), 91–95. https://doi.org/10.1080/00224065.1986.11978992

[22] Tang, K., & Schneider, H. (1990). Cost effectiveness of using a correlated variable in a complete inspection plan when inspection error is present. Naval research logistics (nrl), 37(6), 893–904. https://doi.org/10.1002/1520-6750(199012)37:6%3C893::AID-NAV3220370608%3E3.0.CO;2-B

[23] Tsai, H. T., Moskowitz, H., & Tang, J. E. N. (1995). A one-sided single screening procedure based on individual unit misclassification error. IIE transactions, 27(6), 695–706. https://doi.org/10.1080/07408179508936786

[24] Chen, S. L., & Chung, K. J. (1996). Selection of the optimal precision level and target value for a production process: the lower-specification-limit case. IIE transactions, 28(12), 979–985. https://doi.org/10.1080/15458830.1996.11770752

[25] Hong, S. H., & Elsayed, E. A. (1999). The optimum mean for processes with normally distributed measurement error. Journal of quality technology, 31(3), 338–344. https://doi.org/10.1080/00224065.1999.11979932

[26] Duffuaa, S. O., & Siddiqui, A. W. (2003). Process targeting with multi-class screening and measurement error. International journal of production research, 41(7), 1373–1391. http://dx.doi.org/10.1080/00207540701644243

[27] Hong, S. H., & Cho, B. R. (2007). Joint optimization of process target mean and tolerance limits with measurement errors under multi-decision alternatives. European journal of operational research, 183(1), 327–335. https://doi.org/10.1016/j.ejor.2006.09.063

[28] Chen, C. H., & Lai, M. T. (2007). Determining the optimum process mean based on quadratic quality loss function and rectifying inspection plan. European journal of operational research, 182(2), 755–763. https://doi.org/10.1016/j.ejor.2006.09.035

[29] Lee, M. K., Kwon, H. M., Hong, S. H., & Kim, Y. J. (2007). Determination of the optimum target value for a production process with multiple products. International journal of production economics, 107(1), 173–178. https://doi.org/10.1016/j.ijpe.2006.08.007

[30] Chen, C. H., & Khoo, M. B. C. (2009). Optimum process mean and manufacturing quantity settings for serial production system under the quality loss and rectifying inspection plan. Computers & industrial engineering, 57(3), 1080–1088. https://doi.org/10.1016/j.cie.2009.04.016

[31] Goethals, P. L., & Cho, B. R. (2011). Reverse programming the optimal process mean problem to identify a factor space profile. European journal of operational research, 215(1), 204–217. https://doi.org/10.1016/j.ejor.2011.06.004

[32] Darwish, M. A., Abdulmalek, F., & Alkhedher, M. (2013). Optimal selection of process mean for a stochastic inventory model. European journal of operational research, 226(3), 481–490. https://doi.org/10.1016/j.ejor.2012.11.022

[33] Nezhad, M. S. F., & Nasab, H. H. (2012). Absorbing Markov chain models to determine optimum process target levels in production systems with dual correlated quality characteristics. Pakistan journal of statistics and operation research, 8(2), 205–212. https://doi.org/10.18187/pjsor.v8i2.268

[34] Fallah, N. M. S., & Akhavan, N. S. T. (2010). Absorbing Markov chain models to determine optimum process target levels in production systems with rework and scrapping. Journal of industrial engineering, 6(2010), 1–6. https://www.sid.ir/EN/VEWSSID/J_pdf/1029920100601.pdf