Abstract
We study the long-run average performance of a fluid production/ inventory model which alternates between ON periods and OFF periods. During ON periods of random lengths items are added continuously, at some state-dependent rate, to the inventory. During OFF periods the content decreases (again at some state-dependent rate) back to some basic level. We derive the pertinent reward functionals in closed form. For this analysis the steady-state distributions of the stock level process and its jump counterpart are required. In several examples we use the obtained explicit formulas to maximize the long-run average net revenue numerically.
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References
S. Asmussen, and D. Perry, “An operational calculus for matrix-exponential distributions with applications to brownian motion (q, Q) inventory model,” Mathematics of Operations Research vol. 23 pp. 166–176, 1998.
R. C. Baker, and T. L. Urban, “A deterministic inventory system with an inventory-level-dependent demand rate,” Journal of the Operational Research Society vol. 39 pp. 823–825, 1988.
O. Berman, and D. Perry, “Two control policies for stochastic EOQ-type models,” Probability in the Engineering and Informational Sciences vol. 15 pp. 445–463, 2001.
O. Berman, and D. Perry, “An EOQ model with state-dependent demand rate,” European Journal of the Operational Research Society vol. 171 pp. 255–272, 2006.
O. J. Boxma, O. Kella, and D. Perry, “A fluid model with intermittent ON-OFF periods,” Probability in the Engineering and Information Sciences vol. 15 pp. 189–198, 2001.
A. Federgruen, and P. Zipkin, “An inventory model with limited production capacity and uncertain demands. I: the average-cost criterion,” Mathematics of Operations Research vol. 11 pp. 193–207, 1986.
A. Federgruen, and P. Zipkin, “An inventory model with limited production capacity and uncertain demands. II: the discounted-cost criterion,” Mathematics of Operations Research vol. 11 pp. 208–215, 1986.
Y. Gerchak, and Y. Wang, “Periodic-review inventory models with inventory-level-demand rate,” Naval Research Logistics vol. 41 pp. 99–116, 1994.
O. Kella, and W. Whitt, “A storage model with a two state random environment,” Operations Research vol. 40 pp. S257–S262, 1992.
S. Nahmias, Production and Operations Analysis, Third Edition, McGraw-Hill: New York, 1997.
D. Perry, and W. Stadje, “Duality of dams via mountain processes,” Operational Research Letters vol. 31 pp. 451–458, 2003.
E. L. Porteus, Foundations of Stochastic Inventory Theory, Stanford University Press: Stanford, USA, 2002. (Stanford business books)
J.-S. Song, and P. Zipkin, “Inventory control in a fluctuating demand environment,” Operational Research vol. 41 pp. 351–370, 1993.
Y. Wang, and Y. Gerchak, “Supply chain coordination when demand is shelf-space dependent,” Manufacturing and Service Operations Management vol. 3 pp. 82–87, 2001.
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Berman, O., Perry, D. & Stadje, W. Performance Analysis of a Fluid Production/Inventory Model with State-dependence. Methodol Comput Appl Probab 9, 465–481 (2007). https://doi.org/10.1007/s11009-006-9000-8
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DOI: https://doi.org/10.1007/s11009-006-9000-8
Keywords
- production/inventory model
- fluid model
- EOQ
- state-dependent production rate
- reward functionals
- stock-level process
- long-run average revenue
- maximization