In the classical EOQ models, the demand rate of an item was assumed to be constant where shortages were not allowed. However, in the real market, the demand rate of any product is always in a dynamic state. In reality, models are developed not only considering the variation of demand rate with time, but also the cost that is affected by shortage. While developing the model, the researchers usually take the demand rate to be either a linear demand rate or an exponential demand rate.
The linear demand rate implies steady increase or decrease in demand. These cases are rarely seen to obtain for any product. On the other hand, an exponential demand rate implies an exponential increase or decrease in demand. Due to high exponential rate, it is doubtful whether the real market demand of any product can really rise or fall exponentially. Therefore, a better alternative is either accelerated rise or precipitated fall in demand. Accelerated growth in demand rate takes place in case of the state-of-the-art aircrafts, super computers, machines and their spare parts.
On the other hand, the precipitated decline in the demand rate is thought to occur in the case of obsolete aircrafts, super computers, machines and their spare parts. The demand rate of seasonal product of showing a rapid rise to a peak in the mid season and witnessing a sudden fall when the season wanes out can also be taken care of in this proposed model. The proposed model is based on the quadratic demand rate which can be represented as .
The different cases of quadratic demand rate are as follows: Case I: When , the demand rate increases which is called the accelerated growth in demand.
Case II: When , the demand rate is called the retarded growth in demand rate.
Case III: When , the demand rate is called the accelerated decline in demand rate.
Case IV: When , the demand rate is called the retarded decline in demand rate.
This advantage of quadratic demand rate has motivated the authors to adopt the proposed model. The deterioration rate is taken to be constant. The holding cost is also a quadratic function of time. The shortages are allowed and partially backlogged. The backlogging rate is a variable and it depends on the length of the waiting time for the next replenishment. The objective of the model is to determine the shortage time point, the length of the cycle, the optimal order quantity and the optimal total average cost.
The proposed model can be modified in numerous ways. For example, it may be modified from quadratic demand to a more generalized demand pattern and stochastic demand pattern. Also, it could be modified to include the variable deterioration rates such as the two-parameter Weibull distribution deterioration, the three-parameter Weibull distribution deterioration and gamma distribution. Finally, it could be generalized to a model which would allow an economic production lot size model.
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