a- What is the optimal order quantity and the optimal total ordering and holding cost? b.If the order quantity is 50% less than the optimal order quantity, what is the percentage of the additional holding and ordering cost incurred compared to the optimal cost of holding and ordering? c-If the order quantity is 50% more than the optimal order quantity, what is the percentage of the additional holding and ordering cost incurred compared to the optimal cost of holding and ordering?

Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter2: Introduction To Spreadsheet Modeling
Section: Chapter Questions
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EOQ formula gives the order quantity that minimizes the total ordering and inventory holding cost. Although it may be thought that the simplifying assumptions of the EOQ model limits the applicability of this concept to a variety of cases, in practice, it provides satisfactory results. The reason for this is the robustness of the total cost function with respect to the choice of Q. In other words, if another order quantity is used instead of the optimal one, the overall effect of this choice on the total cost function is not that much. The objective of this question is to investigate the robustness of EOQ.

The purchase price of an electronic component is $100 per unit. The holding cost is calculated directly from the opportunity cost of the money tied up according to a market interest rate of 10% per year. The annual demand is 6000 units per year and the ordering cost is $12 per order.

a- What is the optimal order quantity and the optimal total ordering and holding cost?

b.If the order quantity is 50% less than the optimal order quantity, what is the percentage of the additional holding and ordering cost incurred compared to the optimal cost of holding and ordering?

c-If the order quantity is 50% more than the optimal order quantity, what is the percentage of the additional holding and ordering cost incurred compared to the optimal cost of holding and ordering? 

d-In general, what would be the percentage of the additional holding and ordering cost compared to the optimal cost of holding and ordering if the order quantity is, say, k times the economic order quantity?

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