Question

International Diesel Machine (IDM) purchases 38,000 premium oil filters each year at a price of $4.00 per unit. The ordering cost is $9.00 per order, and the annual holding cost is estimated at 25% of the unit value. The supplier to IDM will increase his unit price from $4.00 to $4.50 on 1 July. How long will this order last in years? What would be the economic order quantity once parts from this order end? What cost savings would result from this order?

Answer 1

Current order is at a price of $4

Other relevant details :

Annual demand = D = 38000 FILTERS

Ordering Cost = C = $9

Annual unit holding cost = I = 25% of $4 = $1

Therefore, Current economic order quantity = Square root ( 2 x D x C/I) = Square root ( 2 x 38000 x 9/1) = 827.04 ( 827 rounded to nearest whole number)

Duration this order of 827 filters will last = 827/38000 year = 0.02176 year

THIS ORDER WILL LAST 0.02176 YEARS

Revised economic order quantity at parts price of $4.5 per unit :

Annual demand = 38000 filters

Ordering cost = C = $9

Annual unit holding cost = I = 25% of $4.5 =$1.125

Revised economic order quantity = Square root ( 2 x 38000 x 9/1.125) = 779.74 ( 780 units rounded to nearest whole number )

ECONOMIC ORDER QUANTITY ONCE PARTS FROM PREVIOUS ORDER ENDS = 780 UNITS

Total cost

= Annual value of items + annual ordering cost + annual holding cost

= Price unit x 38000 ( demand) + ordering cost x 38000 ( annual demand)/EOQ + Annual unit holding cost x EOQ/2

Thus,

Total cost when price is $4 / unit

= $38000 x 4 + $9x 38000/827 +$ 1 x 827/2

= $152000 + $413.54 + $413.50

=$152827.04

Total cost when price is $4.5/ unit

= $38000 x 4.5 + $9 x 38000/780 + 1.125 x 780/2

= $171000 + $ 438.46 + $438.75

= $171876.92

Cost savings from current order = $171876.92 - $152827.04 = $19049.88