Disasters in a Markovian inventory system for perishable items

Advances in Applied Probability

Volumn 33, Issue 1, 2001, Pages 61-75

  Perry, David ^a   Stadje, Wolfgang ^b  

^a UNIVERSITY OF HAIFA   (Israel)

^b UNIVERSITY OF OSNABRÜCK   (Germany)

Author keywords

Cost functionals; Inventory system; Perishable items; Reflected Brownian motion; Stationary distribution; Virtual death process

Indexed keywords

APPROXIMATION THEORY; BROWNIAN MOVEMENT; COMPUTATIONAL METHODS; INVENTORY CONTROL; LAPLACE TRANSFORMS; MATHEMATICAL MODELS; POISSON DISTRIBUTION;

COST FUNCTIONALS; MARKOVIAN INVENTORY SYSTEM; MARKOVIAN MODEL; PERISHABLE INVENTORY SYSTEM; POISSON DISTRIBUTION TIMES; STATIONARY DISTRIBUTION;

MARKOV PROCESSES;

EID: 0035271986     PISSN: 00018678     EISSN: None     Source Type: Journal    
DOI: 10.1239/aap/999187897     Document Type: Article

References (20)

1. COHEN, J. W. (1977). On up- and downcrossings. J. Appl. Prob. 14, 405-410.
2. DOSHI, B. (1992). Level-crossing analysis of queues. In Queueing and Related Models (Oxford Statist. Sci. Ser. 9), eds U. N. Bhat and I. V. Basawa. Oxford University Press, pp. 3-33.
3. JAIN, G. AND SIGMAN, K. (1996). A Pollaczek-Khintchine formula for M/G/1 queues with disasters. J. Appl. Prob. 33, 1191-1200.
4. KALPAKAM, S. AND SAPNA, K. P. (1994). Continuous review (s, S) inventory system with random lifetimes and positive lead-times. Operat. Res. Lett. 16, 115-119.
5. KALPAKAM, S. AND SAPNA, K. P. (1996a). A lost sales (S - 1.S) perishable inventory system with renewal demand. Naval Res. Logist. 43, 129-142.
6. KALPAKAM, S. AND SAPNA, K. P. (1996b). An (s, S) perishable system with arbitrarily distributed leadtimes. Opsearch 33, 1-19.
7. KELLA, O. AND WHITT, W. (1992). Useful martingales for stochastic storage processes with Lévy input. J. Appl. Prob. 29, 396-403.
8. KIM, K. AND SEILA, A. F. (1993). A generalized cost model for stochastic clearing systems. Comput. Operat. Res. 20, 67-82.
9. LIU, L. (1990). Continuous review models for inventory with random lifetimes. Operat. Res. Lett. 9, 161-167.
10. NEWELL, G. F. (1982). Applications of Queueing Theory, 2nd edn. Chapman and Hall, London.
11. PERRY, D. (1999). Analysis of sampling control scheme for a perishable inventory system. Operat. Res. 47, 966-973.
12. PERRY, D. AND ASMUSSEN, S. (1995). Rejection rules in the M/G/1 type queue. Queueing Systems 19, 105-130.
13. PERRY, D. AND STADJE, W. (1999a). Perishable inventory systems with impatient demands. Math. Meth. Operat. Res. 50, 77-90.
14. PERRY, D. AND STADJE, W. ( 1999b) Heavy traffic analysis for a queueing system with bounded capacity for two types of customers. J. Appl. Prob. 36, 1155-1166.
15. RAVICHANDRAN, N. (1995). Stochastic analysis of a continuous review perishable inventory system with positive lead time and Poisson demand. Eur. J. Operat. Res. 84, 444-457.
16. SERFOZO, R. AND STIDHAM, S. (1978). Semi-stationary clearing processes. Stock. Proc. Appl. 6, 165-178.
17. STIDHAM, S. (1974). Stochastic clearing systems. Stoch. Proc. Appl. 2, 85-113.
18. STIDHAM, S. (1977). Cost models for stochastic clearing systems. Operat. Res. 25, 100-127.
19. STIDHAM, S. (1986). Clearing systems and (s, S) inventory systems with nonlinear costs and positive lead times. Operat. Res. 34, 276-280.
20. WHITT, W. (1974). Heavy traffic limit theorems for queues: a survey. In Mathematical Methods in Queueing Theory (Lecture Notes Econ. Math. Systems 98), ed. A. B. Clarke. Springer, Berlin, pp. 307-350.