An Inventory Model with Poisson Demand and Linear Lost Sales
In this article, we shall construct a lost sales inventory model with Poisson demand. Lost sales are linear increasing function of waiting time in the stockout period. Then, the optimal planning and shortage periods are determined such that the expected profit per unit time is maximized.There are two special cases are also discussed.One is the whole period is stockout, and the other is the whole period is non-stockout. And we also find the optimal supply cycle and optimal order quantity of goods such that expected profit per unit time is maximized.
Inventory, Partially Backordered, Poisson Demand
Axsäter, S.,``A heuristic for triggering emergency orders in an inventory system”,European Journal of Operational Research, 176, No. 2, 2007, pp.880-891.
Bijvank, M. & Vis, I.F.A, ``Lost-sales inventory theory: A review”. European Journal of Operational Research, 215, 2011, pp.1-13.
Bijvank, M. & Johansen, S.G. ``Periodic review lost sales inventory models with compound Poisson demand and constant lead times of any length”, European Journal of Operational Research, 220, 2012, pp.101-114.
Caine, G. J. &Plaut, R. H., ``Optimal inventory policy when stockouts alter demand”, Naval Research Logistics Quarterly, Vol. 23, 1976, pp. 1-13.
Chen,M.S.& Chen, Y.C.,``A note on the optimal supply cycle when the whole period is stockout” Asia-Pacific Journal of Operational Research, Vol. 27, No.5, 2010, pp.611-616
Chen, Y. C. ,``A probabilistic approach for traditional EOQ model,” Journal of Information & Optimization Sciences, Vol. 24, No. 2, 2003, pp.1-5.
Chiang, C., ``Optimal ordering policies for periodic-review systems with replenishment cycles”, European Journal of Operational Research, 170, 2006, pp. 44-56.
Antonio Arreola-Risa& G. A. DeCroix, ``Inventory management under random supply disruptions and partial backorders”, Naval Research Logistics, Vol. 45, (1998), pp.687-703.
Montgomery, D. C., Bazaraa, M. S. &Keswani, A. K.,``Inventory models with a mixture of backorders and lost sales”, Naval Research Logistics Quarterly, Vol. 20, 1973, pp. 255-263.
Ouyang, L. Y., Chuang, B. R. & Lin, Y. J.,``Effective investment to reduce lost-sales rate in a periodic review inventory model”, OR Spectrum 29, 2007, pp.681-697.
Schwartz, B. L., ``Optimal Inventory Policies in Perturbed Demand Models”, Management Science, Vol., 12, No. 8, 1970, pp. 509-518.