Question

1. A large producer of household products purchases a glyceride used in one of its deodorant soaps from outside of the company at a cost of $1.5 per pound. It uses the glyceride at a fairly steady rate of 40 pounds per month, and the company uses a 23 percent annual interest rate to compute holding costs. The chemical can be purchased from a supplier who charges a delivery fee that varies on the ordering quantity as follows:

Order Size	Delivery Fee
0≤Q≤700	$15
701≤Q≤1,500	$25
1,501≤Q	$30

Assume that the cost of order processing is $150. What is the optimal order quantity and the corresponding annual total cost?

Answer 1

Answer: 700, $938.40

Annual Demand D = Monthly Demand *12 = 12*40 = 480 pounds

Total Cost per Order (S) = Cost per order + Delivery Fee

Holding Cost per unit(G) = Unit Cost * Annual Holding Cost %

If EOQ > higher limit of the range

Feasible EOQ = Higher limit of the range

If EOQ < lower limit of the range

Feasible EOQ = lower limit of the range

Ordering Cost = (Annual Demand/Feasible EOQ)*Total cost per order (S)

Holding Cost = (Feasible EOQ/2)*Holding Cost per unit

Purchasing Cost = Annual Demand (D) *Unit Cost

Total Cost = Ordering Cost + Holding Cost + Purchasing Cost

Total Cost for Q = 700 is the least among all three scenario. Optimal Order Qty is 700 and total cost for the same is $938.14