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Ergonomics Inc. sells ergonomically designed office chairs. The company has the

ID: 414993 • Letter: E

Question

Ergonomics Inc. sells ergonomically designed office chairs. The company has the following information:

average demand= 20 units per day

average lead time= 30 days

Item unit cost= $50 for orders of less than 200 units

Item unit cost= $48 for orders of 200 units or more

Ordering cost= $25

Inventory carrying cost= 25%

The business year is 250 days

How many chairs should the firm order each time? Assume there is no uncertainty at all about the demand or the lead time. There are many associated questions, such as what will the firm's average inventory be under each alternative? What will be the breakdown of costs for each alternative?

Explanation / Answer

Average demand = 20 units per day

Number of days in a year = 250 days

Annual demand (D) = 20 units x 250 = 5000 units

Ordering cost (S) = $25

Order quantity price Holding cost(H)

Less than 200 $50 $12.5(25% of $50)

200 or more $48 $12(25% of $48)

The economic order quantity for unit cost of $50 is calculated as : sqrt of (2DS / H)

= sqrt of [(2 x 5000 x 25) / 12.5]

= sqrt of 20000

= 141.42 or rounded to 141 units

With the order quantity (Q) = 141 units,

Total cost = Ordering cost + Holding cost + product cost

= [(D/Q) S] + [(Q/2)H] + (price x D)

= [(5000/141)25] + [(141/2)12.5] + (50 x 5000)

= $886.52 + $881.25 + $250000

= $251767.77

The economic order quantity with an unit price of $48 is calculated as : sqrt of (2DS / H)

= sqrt of [(2x 5000 x 25) / 12]

= 144.34 or rounded to 144 units

But 144 units is not feasible as it will cost $50 instead of $48 per unit. So now we have to calculate the total cost for the minimum quantity needed to get an unit price of $48.The minimum order quantity (Q) to get an unit price of $40 is 200 units. So with Q = 200 units,

Total cost = Ordering cost + Holding cost + product cost

= [(D /Q )S] + [(Q /2)H] + (price x D)

=[(5000/200)25] + [(200/2)12] + (48 x 5000)

= $625 + $1200 + $240000

= $241825

So the firm should order 200 chairs each time as it has the lowest total cost

The firms average inventory with Q= 141 unit is Q/2 = 141/2 = 70.5.Likewise the firm's average inventory with Q= 200 units is Q/2 = 200/2 = 100 units

The break down of costs for each alternatives are calculated above as Ordering cost, Holding cost and purchase cost.