Question

A manager receives a forecast for next year. Demand is projected to be 600 units for the first half of the year and 900 units for the second half. The monthly holding cost is $2 per unit, and it costs an estimated $55 to process an order.

a. Assuming that monthly demand will be level during each of the six-month periods covered by the forecast (e.g., 100 per month for each of the first six months), determine an order size that will minimize the sum of ordering and carrying costs for each of the six-month periods. (Round your answers to the nearest whole number.)

Period Order Size 1 – 6 months units

7 – 12 months units

b. If the vendor is willing to offer a discount of $10 per order for ordering in multiples of 50 units (e.g., 50, 100, 150), would you advise the manager to take advantage of the offer in either period? If so, what order size would you recommend? (Round intermediate calculations to 2 decimal places.)

Period Order Size

1 – 6 months units

7 – 12 months units

Answer 1

Ans a)

First six months period

Demand (D)= 600

Monthly Demand (D)= 600/6 = 100 units

Ordering Cost (S) = $55

Holding Cost (H) = $ 2 /unit/month

Economic Order Qty = Q*

Second Six months period

Demand (D)= 900

Monthly Demand (D)= 900/6 = 150 units

Ordering Cost (S) = $55

Holding Cost (H) = $ 2 /unit/month

Economic Order Qty = Q*

Order Size: Period 1 - 74 , Period 2 - 91

Ans b)

First Six month period

Q* = 74

Total Cost = Ordering Cost + Holding Cost = (d/Q*)*S + 6*(Q*/2)*H = (600/74)* 55 + 6*(74/2)*2 = 445.95 + 444 = $ 889.95

If order in multiple of 50 then ordering cost will become 45. Then either Order qty could be 50 or 100 .

For Q = 50

Total Cost = Ordering Cost + Holding Cost = (600/50)*45 + 6*(50/2)*2 = 540 + 300 = 840

For Q = 100

Total Cost = Ordering Cost + Holding Cost = (600/100)*45 + 6*(100/2)*2 = 270 + 600 = 870

Total cost for Q = 50 is less than Q* = 74 and Q =100 as per new order policy, so It will be beneficial to order Q = 50 units per order.

Second Six month period

Q* = 91

Total Cost = Ordering Cost + Holding Cost = (d/Q*)*S + 6*(Q*/2)*H = (900/91)* 55 + 6*(91/2)*2 = 543.95 + 546 = $ 1089.95

If order in multiple of 50 then ordering cost will become 45. Then either Order qty could be 50 or 100 .

For Q = 50

Total Cost = Ordering Cost + Holding Cost = (900/50)*45 + 6*(50/2)*2 = 810 + 300 = 1110

For Q = 100

Total Cost = Ordering Cost + Holding Cost = (900/100)*45 + 6*(100/2)*2 = 405 + 600 = 1005

Total cost for Q = 100 is less than Q* = 91 and Q = 50 as per new order policy, so It will be beneficial to order Q = 100 units per order.

Order Size: Period 1 - 50 , Period 2 - 100