Analysis of a Maintenance·Repair Service Center Model Operating under Alternating Complementary Dyadic Policies

상호보완적인 이변수 운영정책이 교대로 적용되는 정비서비스센터 모형분석

  • Rhee, Hahn-Kyou (Dept. of Industrial and Management Engineering, Hannam University)
  • 이한교 (한남대학교 산업경영공학과)
  • Received : 2017.02.09
  • Accepted : 2017.03.17
  • Published : 2017.03.25

Abstract

Different from general operating policies applied for various waiting line situations, two complementary dyadic operating policies are applied alternatingly to a single server maintenance service center model. That is, either of the two dyadic Min (N, T) or Max (N, T) policy is applied to operate such center first and the other operating policy should be applied later, and then the same sequence of both operating policies is followed repeatedly. This operating policy is denoted by the Minimax (N, T) policy. Purpose: Because of the newly introduced operating policy, important system characteristics of the considered service center model such as the expected busy and idle periods, the expected number of customers in the service center and so on should be derived to provide necessary information for determination of the optimal operating policy. Methods: Based on concepts of the newly introduced Minimax (N, T) policy, all necessary system characteristics should be redefined and then derived by constructing appropriate relations between complementary two dyadic operating policies. Results: Desired system characteristics are obtained successfully using simple procedures developed by utilizing peculiar structure of the Minimax (N, T) policy. Conclusion: Applying Minimax (N, T) operating policy is equivalent to applying the simple N and T operating policies alternatingly.

Keywords

References

  1. Teghem, J. (1986). "Control of the Service Process in a Queueing System". European Journal of Operational Research, Vol. 23, No. 2, pp. 141-158. https://doi.org/10.1016/0377-2217(86)90234-1
  2. Yadin, M. and Naor, P. (1963). "Queueing System with Removable Service Station". Operational Research Quarterly, Vol. 14, No. 4, pp. 393-405. https://doi.org/10.1057/jors.1963.63
  3. Heyman, D. (1977). "The T-policy for the M/G/1 Queue". Management Science, Vol. 23, No. 7, pp. 775-778. https://doi.org/10.1287/mnsc.23.7.775
  4. Balachandran, K.R. and Tijms, H. (1975). "On the D-policy for the M/G/1 Queue". Management Science, Vol. 21, No. 9, pp. 1073-1076.
  5. Rhee, H. K. (1997). "Development of a New Methodology to find the Expected Busy Periods for a Controllable M/G/1 Queueing Models operating Under the Multi-variable Operating Policies: Concepts and applications to the dyadic policies". Journal of the Korean Institute of Industrial Engineers, Vol. 23, No. 4, pp. 729-739.
  6. Gakis, K. G., Rhee, H. K., and Sivazlian, B. D. (1995). "Distributions and First Moments of the Busy and Idle Periods in Controllable M/G/1 Queueing Models with Simple and Dyadic Policies". Stochastic Analysis and Applications, Vol. 13, No. 1, pp. 47-81. https://doi.org/10.1080/07362999508809382
  7. Rhee, H. K. and Oh, H. S. (2009). "Development of the Most Generalized Form of the Triadic Operating Policy and Derivation of its Corresponding Expected Busy Period". Journal of the Society of Korea Industrial and Systems Engineering, Vol. 32, No. 4, pp. 161-168.
  8. Rhee, H. K. and Sivazlian, B. D. (1990). "Distribution of the Busy Period in a Controllable M/M/2 Queue Operating under the Triadic (0, K, N, M) Policy". Journal of Applied Probability, Vol. 27, No. 2, pp. 425-432. https://doi.org/10.2307/3214662
  9. Kleinrock, L. (1975). Queueing Systems, Vol. 1: Theory, John Wiley & Sons, New York, NY.