Question

A regional distributor deals with a product ABC that has an annual demand of 3000 unit. It costs $23 per unit and holding the unit in the warehouse cost $ .02 each day. Each time when the distributor places an order from the manufacturer, it need to pay $500 fixed ordering fee. Assuming each year has 365 days. Please answer following questions based the information provided.

1. What is the total cost under the optimal ordering quantity?
2. How frequently the distributor will be placing an order (hint: think about arrival rate and inter-arrival time)?
3. It turns out that the analyst who provided those cost estimates under-estimated the holding cost of the inventory by .01 each day (that is holding costs $ .03 each day). What is the penalty in the total cost because of this estimation mistake? Considering the total cost, would you say the penalty is relatively large or small?

Answer 1

Annual Demand D = 3000 units

Holding Cost H = 0.02*365 = 7.3 per unit per year

Ordering Cost S = 500

Purchase cost P = 23

EOQ = (2DS/H)^(1/2)

EOQ = (2*3000*500/7.3)^(1/2) = 641.06

EOQ = 641 units

Time between order = (EOQ/D)*365

Time between order = (641/3000)*365

Time between order = 77.99 days = 78 days

Total Cost = (D/EOQ)*S + (EOQ/2)*H + D*P

Total Cost = (3000/641)*500 + (641/2)*7.3 + 3000*23

Total Cost = 73679.74 (including purchase cost (D*P))

Total Cost = 4679.74 (Excluding purchase cost)

__________________________________________________________________________

New Holding Cost = 0.03*365 = 10.95

EOQ = (2*3000*500/10.95)^(1/2) = 523.42

EOQ = 523 units

Total Cost = (D/EOQ)*S + (EOQ/2)*H + D*P

Total Cost = (3000/523)*500 + (523/2)*10.95 + 3000*23

Total Cost = 74731.49 (including purchase cost (D*P))

Total Cost = 5731.49 (Excluding purchase cost)

Increase in Cost (Excluding purchase cost) = 5731.49 - 4679.74 = 1051.75

Increase is quite significant.