GENERAL PRODUCTION AND SALES SYSTEM WITH SCBZ MACHINE TIME AND MARKOVIAN MANPOWER
Keywords:
Storage System, Production and Sale, Repair and Recruitment, Joint Laplace Transform.Abstract
A study on production and sales system is performed. A machine produces random number of products during the operation time. After the operation time, sale time starts which has one among two distinct distributions depending on the magnitude of production time within or exceeding a random threshold magnitude. Two models are treated considering manpower system exposed to a departure process; the machine has SCBZ failure pattern with repair; manpower recruitments and sales time have general distributions. The system fails when both manpower and machine are in failed state. In model 1, the sales are done one by one and in model 2, when the operation time is more than a threshold, the sales are done altogether and when it is less than the threshold, the sales are done one by one. The Joint Laplace transform of the variables, their means and the Co-variances with numerical results are presented.
Downloads
References
Arrow, K. Karlin, S. and Scarf, H. (1958). Studies in Mathematical Theory of
Inventory and Production, Stanford University Press, Stanford, California.
Danial, J.K. and Ramanarayanan, R, (1988). An (S, s) inventory system with
rest periods to the server, Naval Research Logistics (Quarterly), 35, p. 119-
Kun- Shan Wu, Ouyang and Liang -Yuh, (2001). (Q, r, L) inventory model
with defective items, Computer and Industrial Engineering, 39, p. 173-185.
Harikumar, K, (2014). General manpower and machine system with
Markovian production and general sales, IOSR Journal of Mathematics
[IOSR-JM], 10(6), Ver. VI, p. 54-62.
Madhusoodhanan, P., Sekar, P. and Ramanarayanan, R. (2015). General
production and sales system with SCBZ machine time and manpower, IOSR
Journal of Mathematics [IOSR JM], 11(2), Ver. I, p. 39-46.
Madhusoodhana, P., Sekar, P and Ramanarayanan, R, (2015). Probabilistic
analysis of general production and sales system with exponential machine time
and manpower, Global Journal of Pure and Applied Mathematics (GJPAM),
(2), p. 601-609.
Madhusoodhanan, P. (2015). General production and sales by Markovian
manpower and machine system, International Journal of Mathematical
Archive, 6(7), p. 80-87.
Murthy, S. and Ramanarayanan, R. (2008). Two ordering levels inventory
system with different lead times and rest time to the server, Inter. J. of Applied
Math., 21(2), p. 265-280.
Murthy, S. and Ramanarayanan, R. (2008). Two (s, S) inventories with
perishable units, The Journal of Modern Mathematics and Statistics, 2, No.3,
p. 102-108.
Murthy, S. and Ramanarayanan, R. (2008). Inventory system exposed to
calamity with SCBZ arrival property, the Journal of Modern Mathematics and
Statistics, 2, No. 3, p. 109-119.
Murthy, S. and Ramanarayanan, R. (2008). General analysis of (s, S)
inventory system with defective supplies, Inter. J. Applied math., 21, No.3, p.
-507.
Ramanarayanan, R. and Jacob, M. J. (1998). General analysis of (S, s)
inventory systems with random lead time and bulk demands,
Cashieru.C.E.R.O, No.3, 4, p. 119-123.
Snehalatha, M., Sekar, P. and Ramanarayanan, R. (2015). Probabilistic
analysis of general manpower SCBZ machine system with exponential
production, general sales and general recruitment, IOSR Journal of
Mathematics [IOSR JM], 11(2), Ver. VI, PP 12-21.
Usha, K, Nithyapriya, N. and Ramanarayanan, R. (2012). Probabilistic
analysis of storage systems with random sales time depending on production,
Int. J. Contemp. Math. Sciences, Vol.7, no.19, p. 943-951.
