Question

Demand for a certain product is 25,000 units/yr. Unit cost is $10.00. Holding cost rate is 30%/yr. Changeove5r (setup) time between products is 10.0 hr, and downtime cost during changeover is $150/hr. Determine (a) economic order quantity, (b) total inventory costs, and (c) total inventory cost per year as a proportion of total production costs.

Answer 1

a) EOQ = square root of (2 *Annual demand* set up cost / holding cost per unit annually)

EOQ= square root of 2*25,000 *$150/hr *10hr / $10* 30% = 5000 units

b) Total inventory costs = holding cost+ setup cost

Total setup cost = (10 hours*$150/ hr) * (annual demand / EOQ i.e. 25000/ 5000) = $7500

Total holding cost = (Average Inventory i.e. 5000units / 2) * (holding cost per unit annually i.e. $10 * 30%) = $7500

Total inventory cost =7500 +7500 = $15000

c) Total inventory cost per year as a proportion of total production costs

First we compute Total production costs = (Purchase cost i.e. unit cost * annual demand) + Inventory cost

{25,000 units/yr * Unit cost is $10.00}+ $15000

=$ 265000

Total inventory cost per year as a proportion of total production costs = Inventory cost / total production cost

15000/ 265000$ = .0566