Optimal Policy for a Deteriorating Inventory Model with Finite Replenishment Rate and with Price Dependant Demand Rate and Cycle Length Dependant Price

In this paper, an inventory model with finite and constant replenishment rate, price dependant demand rate, time value of money and inflation, finite time horizon, lead time and exponential deterioration rate and with the objective of maximizing the present worth of the total system profit is developed. Using a dynamic programming based solution algorithm, the optimal sequence of the cycles can be found and also different optimal selling prices, optimal order quantities and optimal maximum inventories can be obtained for the cycles with unequal lengths, which have never been done before for this model. Also, a numerical example is used to show accuracy of the solution procedure.

Authors:

• Hamed Sabahno

Keywords:

• Deteriorating items
• Dynamic programming
• Finitereplenishment rate
• Inventory control
• Operation Research.

References:

[1] J.M.Chen. An inventory model for deteriorating items with
time-proportional demand and shortages under inflation and time
discounting. Int. J. Production Economics 55 (1998) 21-30.
[2] J.M. Chen and C.S. Lin. An optimal replenishment model for
inventory items with normally distributed deterioration. Production
planning and control, 2002, VOL. 13, NO. 5, 470┬▒480.
[3] P.N. Ghare and G.F. Schrader. A model for exponentially decaying
inventories. Journal of Industrial Engineering 15 (1963),pp. 238-243.
[4] S.K. Goyal, B.C.Giri. Recent trends in modeling of deteriorating
inventory. European Journal of Operational Research 134 (2001),1-16.
[5] S. Nahmias. Perishable inventory theory: A review. Operations
Research 30 3 (1982), pp. 680-708.
[6] F. Raafat. Survey of literature on continuously deteriorating inventory
model. Journal of the Operational Research Society 42 (1991), pp.
27-37.
[7] H.M. Wee and S.T. Law. Economic production lot size for
deteriorating items taking account of the time value of money.
Computers & Operations Research 26 (1999), pp. 545-558.
[8] H.M. Wee, S.T. Law.Replenishment and pricing policy for
deteriorating items taking into account the time-value of money.Int. J.
Production Economics 71 (2001) 213-220.
[9] H.M. Wee, W.T.Wang. A variable production scheduling policy for
deteriorating items with time-varying demand.Computers and
Operations Research 1999;26:237-54.
[10] T.M. Whitin. Theory of Inventory Management, Princeton University
Press, Princeton, NJ (1957).
[11] Yong-Wu Zhou, Hon-Shiang Lau, Shan-Lin Yang. A new variable
production scheduling strategy for deteriorating items with
time-varying demand and partial lost sale. Computers & Operations
Research 30 (2003) 1753-1776.