Abstract
The classical economic production quantity (EPQ) assumes that the replenishments are instantaneous. As a manager of a factory, there is a problem must be taken into consideration. If the establishment buys all of the raw materials at the beginning, the stock-holding cost for the raw materials should be counted into the relevant costs. So the main purpose of this paper will add the raw materials stock-holding cost to the EPQ model and take the time value of money into consideration. Therefore, we will calculate the present value and compare the difference between take and does not take the time value of money into consideration. From these procedures of calculating, we found some interesting results: 1) the present value of total stock-holding cost of raw materials plus products from the beginning to time t is the same as the stock-holding cost of classical economic order quantity (EOQ) model; 2) the present value of total relevant cost is independent of the production rate (if the production rate is greater than the demand rate); 3) the optimal cycle time of total relevant cost not taking the time value into consideration is the same the optimal cycle time of classical EOQ model; 4) the purchasing cost per unit time is irrelevant to time.
Highlights
Harris (1915) is the first one to use the idea of mathematical way to model the EOQ model
If the establishment buys all of the raw materials at the beginning, the stock-holding cost for the raw materials should be counted into the relevant costs
We will calculate the present value and compare the difference between take and does not take the time value of money into consideration. From these procedures of calculating, we found some interesting results: 1) the present value of total stock-holding cost of raw materials plus products from the beginning to time t is the same as the stock-holding cost of classical economic order quantity (EOQ) model; 2) the present value of total relevant cost is independent of the production rate; 3) the optimal cycle time of total relevant cost not taking the time value into consideration is the same the optimal cycle time of classical EOQ model; 4) the purchasing cost per unit time is irrelevant to time
Summary
Harris (1915) is the first one to use the idea of mathematical way to model the EOQ model. The EPQ model is a well-known and commonly used inventory control technique. E.W. Taft ([1]) did not consider the stock-holding cost for the raw materials in EPQ system. The EPQ is a well-known and commonly used inventory control technique. Teng ([3]) uses the discount cash-flow approach to establish the models, and obtain the optimal ordering policies to the problem. The classical EPQ assumes that the replenishments are instantaneous and the relevant costs only contain ordering cost, stock-holding cost of products and cost of buying raw materials. The main purpose of the inventory model will add the raw materials’ stockholding cost to the EPQ model and compute the total relevant costs. Using the upper and lower bounds, an algorithm to compute the optimal cycle time is developed. We hope the model will be more reasonable and practical
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