An EOQ Inventory Model for Time-varying Deteriorating Items with Cubic Demand under Salvage Value and Shortages

Biswaranjan Mandal

doi:10.11648/j.ijssam.20200504.11

Abstract

In this paper, an Economic Order Quantity (EOQ) inventory model is developed for time-varying deteriorating items. Researchers are constantly developing deteriorating inventory models to become more realistic. Many items like paddy, wheat, potato, onion, radioactive substance etc. are becoming damage over time. So time dependent deterioration is more realistic than a constant rate of deterioration of goods used in the present market. The assumption of constant demand rate may not be always appropriate for many inventory items like milk, vegetables etc, the age of these items has a negative impact on demand dure to loss of quality of such products, on the other hand, demand is becoming increased initially when new branded fashionable products like cosmetics, mobile, computer etc are launched in the market. So the demand rate is considered as a cubic function of time and time dependent holding cost. We also want to give importance on salvage value of an inventory system. The model is solved with salvages value associated to the units deteriorating during the cycle. Shortages are allowed and fully backlogged. Finally the model is illustrated with the help of a numerical example, some particular cases are derived and a comparative study of the optimal solutions towards different nature of demand is also presented graphically.

Highlights

The traditional inventory model considers the ideal case in which depletion of inventory is caused by a constant demand rate
The mathematical models are developed under the following notations and assumptions: Notations: (i) R(t): Demand rate. (ii) θ (t) : Time-varying deterioration rate. (iii) T: The fixed length of each production cycle. (iv) HC: Holding cost per unit time (v) C1 : The unit cost of an item. (vi) DC: Deterioration cost per unit per unit time. (vii) Ordering Cost (OC): Ordering cost per order. (viii)Salvage Cost (SV): Salvage value per unit per unit time (ix) C2 : Shortage cost unit per unit time. (x) I(t): The inventory level at time t. (xi) Q: The maximum inventory level during the cycle. (xii) T: The length of cycle time. (xiii)TC: Average total cost per unit time
Solving the equation (10) with the help of computer using the above parameter values, we find the following optimum outputs

Summary

Introduction

The traditional inventory model considers the ideal case in which depletion of inventory is caused by a constant demand rate. Poonam Mishra and Shah [9] studied an EOQ model for inventory management of time dependent deteriorating items with salvage value. Karthikeyan et al [12] developed a model to determine the optimum order quantity for constant deteriorating items with cubic demand and salvage value. Their model does not allow for time-varying deterioration and shortages, which would not make applicable in real. Many researchers like Sharma et al [13], Santhi et al [14], Pakhira et al [15] etc are noteworthy For these sort of situations, efforts have been made to develop a realistic inventory model with time-varying deterioration rate. The model is illustrated with the help of a numerical example, some particular cases are derived and a comparative study of the optimal solutions towards different nature of demand is presented graphically

Notations and Assumptions

Formulation and Solution of the Model

Concluding Remarks