Inventory Management System with On/Off Control of Output Product Flow
The paper contains research of the inventory management model with On/Off control. We study mathematical model of inventory management system under following conditions: the rate of input product flow is a constant, the random part of demand is modeled as Poisson process with a piecewise-constant intensity. Firstly, some property of stationary probability density function of inventory level accumulated in system is developed. Then explicit expression for a stationary distribution of the inventory level is obtained for Phase-type distributions of purchase values of demands. For case arbitrary distribution of demands purchases values Fourier transform of the stationary probability density function is determined. Finally, the obtained results are discussed with illustrative numerical examples.
KeywordsMathematical model Inventory management On/Off control PH-distribution Arbitrary distribution
The publication was financially supported by the Ministry of Education and Science of the Russian Federation (the Agreement number 02.a03.21.0008).
- 5.Kitaeva, A., Subbotina, V., Zmeev, O.: The newsvendor problem with fast moving items and a compound Poisson price dependent demand. In: 15th IFAC Symposium on Information Control Problems in Manufacturing INCOM 2015, (IFAC-PapersOnLine), vol. 48, pp. 1375–1379. Elsevier (2015)Google Scholar
- 6.Kitaeva, A., Subbotina, V., Stepanova, N.: Estimating the compound Poisson demand’s parameters for single period problem for large lot size. In: 15th IFAC Symposium on Information Control Problems in Manufacturing INCOM 2015, (IFAC-PapersOnLine), vol. 48, pp. 1357–1361. Elsevier (2015)Google Scholar
- 7.Hillier, F.S., McGraw-Hill, G.J.: Introduction to Operations Research. Front Cover, Operations and research. Lieberman (2001)Google Scholar
- 12.Silver, E.A., Pyke, D.F., Peterson, R.: Inventory Management and Production Planning and Scheduling. Wiley, New York (1998)Google Scholar