The Optimal Base-Stock Level in Assembly lines

조립 생산 시스템에서 최적 Base-Stock 수준

  • Ko, Sung-Seok (Department of Industrial Engineering, Konkuk University) ;
  • Seo, Dong-Won (College of Management and International Relations, Kyung Hee University)
  • Published : 2007.09.30

Abstract

In this study, we consider an assembly line operated under a base-stock policy. A product consists of two parts, and a finished product transfers to a warehouse in which demands are satisfied. Assume that demands arrive according to a Poisson process and processing times at each production line are exponentially distributed. Whenever a demand arrives, it is satisfied immediately from an inventory in the warehouse if available; otherwise, it is backlogged and satisfied later by the next product exiting from production lines. In either case, an arriving demand automatically triggers the production of a part at both production lines. These two parts will be assembled into a product that eventually transfers to the warehouse. We obtain a closed form formula of approximation for delay time or lead time distribution of a demand when a base- stock level is s. Moreover, it can be applied to the optimal base-stock level which minimizes the total inventory cost. Numerical examples are presented to show our optimal base-stock level's quality.

Keywords

References

  1. Clark, A. J. and Scarf, H.; 'Optimal policies for a multi-echelon inventory problem,' Management Science, 6 : 475-490, 1960 https://doi.org/10.1287/mnsc.6.4.475
  2. Federgruen, A. and Zipkin, P.; 'An inventory model with limited production capacity and uncertain demands, I : average cost criterion,' Math. Oper. Res., 11 : 193-207, 1986 https://doi.org/10.1287/moor.11.2.193
  3. Federgruen, A. and Zipkin, P.; 'An inventory model with limited production capacity and uncertain demands, III : the discounted cost criterion,' Math. Oper. Res., 11 : 208-215, 1986 https://doi.org/10.1287/moor.11.2.208
  4. Glasserman, P. and Wang, Y.; 'Leadtirne inventory trade-off in assembly to order systems,' Oper. Res., 46 : 858-871, 1998 https://doi.org/10.1287/opre.46.6.858
  5. Haji, R. and Newell, G.; 'A relation between stationary queue and waiting time distribution,' J. Appl. Prob., 8 : 617-620, 1971 https://doi.org/10.2307/3212186
  6. Ko, S. and Serfozo R.; 'Response times in M/M/s fork-join networks,' Adv. Appl. Prob., 36 : 854-871, 2004 https://doi.org/10.1239/aap/1093962238
  7. Rosling, K.; 'Optimal inventory policies for assembly systems under random demands,' Oper. Res., 37 : 565-579, 1989 https://doi.org/10.1287/opre.37.4.565
  8. Schmidt, C. P. and Nahmias, S., 'Optimal policy for a two-stage assem bly system under random demand,' Oper. Res., 33 : 1130-1145, 1985 https://doi.org/10.1287/opre.33.5.1130