An EOQ inventory model with time-varying demand and Weibull deterioration with shortages

An inventory model is considered in which inventory is depleted not only by demand, but also by deterioration. Hence, in this paper, we derive the EOQ model for inventory of items that deteriorate at a Weibull-distributed rate, assuming the demand rate with a continuous function of time. Moreover, the proposed model cannot be solved directly in a closed form, thus we used the computer software IMSL MATH/LIBRARY (1989) to find the optimal reorder time. Further, we also find that the optimal procedure is independent from the form of the demand rate. Finally, we also assume that the holding cost is a continuous, non-negative and non-decreasing function of time in order to generalize the EOQ model. Moreover, four numerical examples and sensitivity analyses are provided to assess the solution procedure.

[1]  A. Cohen,et al.  The Reflected Weibull Distribution , 1973 .

[2]  M. Goh.  EOQ models with general demand and holding cost functions , 1994 .

[3]  Pandu R. Tadikamalla.  An EOQ inventory model for items with gamma distributed deterioration , 1978 .

[4]  H. Weiss.  Economic order quantity models with nonlinear holding costs , 1982 .

[5]  P. M. Ghare.  A model for an exponentially decaying inventory , 1963 .

[6]  A. Goswami,et al.  An EOQ Model for Deteriorating Items with Time Varying Demand and Costs , 1996 .

[7]  Kun-Jen Chung,et al.  A Heuristic for Replenishment of Deteriorating Items with a Linear Trend in Demand , 1993 .

[8]  B. van der Veen,et al.  Introduction to the Theory of Operational Research , 1967 .

[9]  W. A. Donaldson.  Inventory Replenishment Policy for a Linear Trend in Demand An Analytical Solution , 1977 .

[10]  R. Misra,et al.  Optimum production lot size model for a system with deteriorating inventory , 1975 .

[11]  Tapan Kumar Datta,et al.  A Note on a Replenishment Policy for an Inventory Model with Linear Trend in Demand and Shortages , 1992 .

[12]  Edward A. Silver,et al.  A Simple Inventory Replenishment Decision Rule for a Linear Trend in Demand , 1979 .

[13]  Heung-Suk Hwang,et al.  A study on an inventory model for items with weibull ameliorating , 1997 .

[14]  A. K. Pal,et al.  An EOQ model for deteriorating inventory with alternating demand rates , 1997 .

[15]  A. K. Pal,et al.  Order level inventory system with ramp type demand rate for deteriorating items , 1998 .

[16]  Dirk Beyer,et al.  A Proof of the EOQ Formula Using Quasi-Variational Inequalities , 1998, Int. J. Syst. Sci..

[17]  A. Muhlemann,et al.  A variable holding cost rate EOQ model , 1980 .