DOI QR코드

DOI QR Code

(s,S)-정책하의 연속형 내부재고를 갖는 M/M/1 대기행렬모형 분석

Analysis of an M/M/1 Queue with an Attached Continuous-type (s,S)-inventory

  • 박진수 (용인대학교 경영정보학과) ;
  • 이현근 (조선대학교 산업공학과) ;
  • 김종현 (조선대학교 산업공학과) ;
  • 윤은혁 (조선대학교 산업공학과) ;
  • 백정우 (조선대학교 산업공학과)
  • 투고 : 2018.08.13
  • 심사 : 2018.10.18
  • 발행 : 2018.10.31

초록

본 논문은 연속형 내부재고를 갖는 M/M/1 대기행렬모형을 다룬다. 고객은 포아송과정으로 도착하고 선입선출 서비스를 받는다. 각 고객의 서비스시간은 독립적이며 동일한 지수분포를 따른다. 고객은 서비스를 받기 위해 일반분포를 따르는 확률변수 H의 내부재고를 소비하며, 서비스 완료시점에 감소한다고 가정한다. 재고시스템은 전통적인 (s,S)-정책에 따라 운용되며, 재고의 조달 시간은 일반분포를 따른다고 가정한다. 재고가 없는 기간에 도착한 고객은 유실된다. 본 논문은 이처럼 운영되는 재고-대기행렬모형의 고객수 및 재고량에 대한 안정상태 결합확률분포를 유도하고 수치예를 보인다. 또한 장기적인 비용을 최소화하는 재고운용정책을 고찰한다.

This study focuses on an M/M/1 queue with an attached continuous-type inventory. The customers arrive into the system according to the Poisson process, and are served in their arrival order; i.e., first-come-first-served. The service times are assumed to be independent and identically distributed exponential random variable. At a service completion epoch, the customer consumes a random amount of inventory. The inventory is controlled by the traditional (s, S)-inventory policy with a generally distributed lead time. A customer that arrives during a stock-out period assumed to be lost. For the number of customers and the inventory size, we derive a product-form stationary joint probability distribution and provide some numerical examples. Besides, an operational strategy for the inventory that minimizes the long-term cost will also be discussed.

키워드

참고문헌

  1. Baek, J. W., Moon, S. K., "The M/M/1 Queue with a Production-Inventory System and Lost Sales," Applied Mathematics and Computation, Vol. 233, pp. 534-544, 2014. https://doi.org/10.1016/j.amc.2014.02.033
  2. Baek, J.W., Bae, Y.H., Lee, H.W. and Ahn, S., "Continuous-type (s,Q)-inventory Model with an Attached M/M/1 Queue and Lost Sales," Performance Evaluation, Vol. 125, pp. 68-79, 2018.
  3. Barron Y., Hermel D., "Shortage Decision Policies for a Fluid Production Model with Map Arrivals," International Journal of production Research, Vol. 55, pp. 3946-3969, 2017. https://doi.org/10.1080/00207543.2016.1218083
  4. Berman, O, Kim, E., "Stochastic Models for Inventory Management at Service Facilities," Stochastic Models, Vol. 15, No. 4, pp. 695-718, 1999. https://doi.org/10.1080/15326349908807558
  5. Berman, O, Sapna, K., "Inventory Management at Service Facilities for Systems with Arbitrarily Distributed Service Times," Stochastic Models, Vol. 16, No. 3&4, pp. 343-360, 2000. https://doi.org/10.1080/15326340008807592
  6. Berman, O., Kaplan, E. H., Shevishak, D. G., "Deterministic Approximations for Inventory Management at Service Facilities," IIE Transactions, Vol. 25, No. 5, pp. 98-104, 1993. https://doi.org/10.1080/07408179308964320
  7. Bozer, Y. A., McGinnis, L. F., "Kitting Versus Line Stocking: A Conceptual Framework and a Descriptive Model," International Journal of Production Economics, Vol. 28, No. 1, pp. 1-19, 1992. https://doi.org/10.1016/0925-5273(92)90109-K
  8. Brynzer, H., Johansson, M. I., "Design and Performance of Kitting and Order Picking Systems," International Journal of production economics, Vol. 41, No. 1, pp. 115-125, 1995. https://doi.org/10.1016/0925-5273(95)00083-6
  9. Harrison, J. M., "Assembly-like Queues," Journal of Applied Probability, pp. 354-367, 1973.
  10. He, Q.-M., Jewkes, E., "Performance Measures of a Make-to-Order Inventory-Production System," IIE Transactions, Vol. 32, No. 5, pp. 409-419, 2000. https://doi.org/10.1080/07408170008963917
  11. Krishnamoorthy, A., Lakshmy, B., Manikandan, R., "A Survey on Inventory Models with Positive Service Time," OPSEARCH, Vol. 48, No. 2, pp. 153-169. 2011. https://doi.org/10.1007/s12597-010-0032-z
  12. Krishnamoorthy, A., Narayanan, V. C., "Production Inventory with Service Time and Vacation to the Server," IMA Journal of Management Mathematics, Vol. 22, No. 1, pp. 33-45, 2011. https://doi.org/10.1093/imaman/dpp025
  13. Krishnamoorthy, A., Viswanath, N. C., "Stochastic Decomposition in Production Inventory with Service Time," European Journal of Operational Research, Vol. 228, No. 2, pp. 358-366, 2013. https://doi.org/10.1016/j.ejor.2013.01.041
  14. Lipper, E., Sengupta, B., "Assembly-like Queues with Nite Capacity: Bounds, Asymptotics and Approximations," Queueing Systems, Vol. 1, No. 1, pp. 67-83, 1986. https://doi.org/10.1007/BF01149328
  15. Marand A.J., Li H., Thorstenson A., "Joint Inventory Control and Pricing in a Service-Inventory System," International Journal of Production Economics, 10.1016/j.ijpe.2017.07.008, 2017.
  16. Saffari, M., Asmussen, S., Haji, R., "The M/M/1 Queue with Inventory, Lost Sale, and General Lead Times," Queueing Systems, Vol. 75, No. 1, pp. 65-77, 2013. https://doi.org/10.1007/s11134-012-9337-3
  17. Schwarz, M., Daduna, H., "Queueing Systems with Inventory Management with Random Lead Times and with Backordering," Mathematical Methods of Operations Research, Vol. 64, No. 3, pp. 383-414, 2006. https://doi.org/10.1007/s00186-006-0085-1
  18. Schwarz, M., Sauer, C., Daduna, H., Kulik, R., Szekli, R., "M/M/1 Queueing Systems with Inventory," Queueing Systems, Vol. 54, No. 1, pp. 55-78, 2006. https://doi.org/10.1007/s11134-006-8710-5
  19. Schwarz, M., Wichelhaus, C., Daduna, H., "Product Form Models for Queueing Networks with an Inventory," Stochastic Models, Vol. 23, No. 4, pp. 627-663, 2007. https://doi.org/10.1080/15326340701645975