Question

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.
b. why is it important to be able to assume that demand will be level during each six-month period?
c. 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

Answer 1

A)First six month, monthly demand = 560 / 6 =93.33
1-6 months order size:= Sqrt( 2 x A x O / C )
Where:
O = Ordering cost per order
C = Carrying cost per order
= Sqrt ( 2 x 93.33 x 55 / 2 )= 71.65 or 72
7-12 months, monthly demand= 900 / 6= 150
7-12 months order size:
= Sqrt( 2 x A x O / C )
= Sqrt( 2 x 150 x 55 / 2)
= 90.83 or 91
B)First six month period:Monthly total cost = (Q/2) x H + (d/Q) x S= (72 / 2) x 2 + (93.33 / 72) x 5 = $143.30With discount of $ 10, S = $ 55 - $10 = $ 45
Monthly TC at Q = 50= (50/2) x 2 + (93.33 / 50)x 45 = $134.0 Monthly TC at Q = 100 = (100/2) x 2 + (93.33 / 100) x 45 = $142.00
Monthly TC at Q = 150 = (150/2) x 2 + (93.33 / 150) x 45 = $178.00 
C)
Yes, the manager should take gain of the proposal and order Q = 50 units during this six-month period. Second six-month period:d = monthly demand= 900 / 6
= 150,

H = $2.00 per unit per month,S = $55, & EOQ = 91.
Monthly TC (Q = 91):
= (91/2) x 2 + (150/91) x 55
= $181.66
Monthly TC (Q = 50):= (50/2)x2 + (150/50)x 45= $185Monthly TC (Q = 100) = (100/2) x 2 + (150/100) x 45= $167.50
Monthly TC (Q = 150)= (150/2) x 2 + (150/150) x 45= $195