Journal of Korea Society of Industrial Information Systems (한국산업정보학회논문지)

Korea Society of Industrial Information Systems (한국산업정보학회)
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Analysis of an M/M/1 Queue with an Attached Continuous-type (s,S)-inventory

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

  • 박진수 (용인대학교 경영정보학과) ;
  • 이현근 (조선대학교 산업공학과) ;
  • 김종현 (조선대학교 산업공학과) ;
  • 윤은혁 (조선대학교 산업공학과) ;
  • 백정우 (조선대학교 산업공학과)
  • Received : 2018.08.13
  • Accepted : 2018.10.18
  • Published : 2018.10.31
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Abstract

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.

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.

Keywords

References

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