Question

Consider the all-units quantity discount schedule below. 

Which of the following sets of order quantities is guaranteed to contain the optimal solution (i.e., best order quantity)? 

A) {205, 400, 600, 800} 

B) {600, 800} 

C) {210, 400, 600}  

D) {210, 400, 600,800} 

E) {805} 

Answer 1

ANSWER: E) {805}

Explanation: This is an EOQ with discount model. In this model, we determine EOQ for each price, if the EOQ is within the order quantity interval for that price level, then EOQ is considered, otherwise Minimum order quantity for that price is considered for total cost evaluation. In this case, we see that, for the lowest price , i.e.  18, the feasible quantity is EOQ of 805, rather than minimum order quantity of 800. This means that the holding cost and ordering cost are equal for order quantity of 805, and hence the total inventory related cost is the lowest for this quantity of 805. Unit cost is already the lowest, i.e 18, for this quantity. Hence, the best order quantity is 805.