Question

Holding Cost	10
Order Cost (Per Order)	100
Order Quantity	130
Optimal Order Quantity	51.0

B) As stated in this case, if the products have to be ordered at a minimum of amount of 130 units, how much should of the products have to be ordered? Please explain your reasons either by calculation or logical statements.

If Alex decides to order 130 units per time, he calculates that the total cost will increase by 67%, which is obtained by ((3+1/3)/2)-1. This calculation method is very quick although it is a rough calculation. Please write down the formula Alex uses for this quick rough calculation. (hint: in other words, given the optimal Q* and an arbitrary Q, people can know the percentage of total cost increases if ordering Q units per time instead of Q*).

Do you think the above calculation method is rough? Please explain using calculation.

Answer 1

The optimal quantity coming from calculation is 51 whereas minimum order quantity is 130. So, we should go with minimum order quantity as it may be due to following reasons:

• Lower price of material in case of placing orders more than 130
• The run size for the supplier is such that 130 units must be taken
• It is minimum possible quantity that can be supplied due to packaging or logistics constraint

Total cost = Total demand/Order quantity*Order cost + Order quantity/2*Holding cost + Price*Total demand

Assuming price is same for 51 units or 130 units, then Price*Total demand factor can be removed

Total cost for Q as 130 = Demand/130*100 + 130/2*10 = Demand*0.77 + 650

Total cost for Q as 51 = Demand/51*100 + 51/2*10 = Demand*1.97 + 255

So, it is not possible to calculate the % change without knowing Pricing and Total Demand