Determine the annual holding and order costs. (Do not round any intermediate cal

Question

Determine the annual holding and order costs. (Do not round any intermediate calculations. Round your final answers to 2 decimal places.)

Assume a price break of $60 per order was offered for purchase quantities of 2,100 units per order. If you took advantage of this price break, how much would you save annually? (Do not round any intermediate calculations (including number of setups per year). Round your final answer to 2 decimal places.)

rev: 02_29_2016_QC_CS-29489, 03_02_2016_QC_CS-29489, 03_08_2016_QC_CS-29489

  Item cost $ 10.00   Standard deviation of weekly demand 20 per week   Order cost $ 207.00   Lead time 3 weeks   Annual holding cost (%) 24 % of item cost   Service probability 90 %   Annual demand 24,300   Average demand 486 per week

Explanation / Answer

D = annual demand = 24,300
S = ordering cost = $207
H = carrying cost per unit per annum = $10 x 24% = $2.4

EOQ = Q* = (2.D.S / H)1/2 = SQRT(2*24300*207/2.4) = 2047

L = average lead time = 3 weeks
s = std. dev. of weekly demand = 20
d = average weekly demand = 486
Z = NORMSDIST(0.90) = 0.816

Safety stock = Z. s. SQRT(L) = 0.816*20*SQRT(3) = 28

Holding cost for cycle stock = (Q*/2) x H = (2047/2)*2.4 = $2456.4
Holding cost for safety stock = 28 x 2.4 = $67.2

Total holding cost = $2456.4+$67.2 = $2523.6

Total ordering cost = (D/Q*) x S = (24300/2047) x 207 = $2457.3

So, the naswer for (b)

Annual holding cost (without considering safety stock) = $2456.4
Annual holding cost (with safety stock) = $2523.6
Annual ordering cost = $2457.3

Total cost (without safety stock) = $2456.4 + $2457.3 = $4913.7

(c)

S = $207 - $60 = $147
Q = 2100

Holding cost (without safety stock) = (Q/2) x H = (2100/2) x 2.4 = $2520
Ordering cost = (D/Q) x S = (24300/2100) x 147 = $1701

Total cost = $2520+$1701 = $4221

So, savings = $4913.7 - $4221 = $692.7

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