# 1. No Tell Motel operates 52 weeks per year, 6 days per week, and uses a continuous review inventory system. It purchases bath soap for \$5.65 per box. The following information is available about these boxes of soap. Demand = 132 boxes/week Order cost =\$74/order Annual holding cost = 24 percent of cost Desired cycle-service level = 95 percent Lead time = 3 weeks Standard deviation of weekly demand = 25 boxes Current on-hand inventory is 159 boxes, with no open orders or backorders. a. What is the EOQ? What would be the average time between orders (in weeks)? b. What should ROP be? c. An inventory withdrawal of 18 boxes was just made. Is it time to reorder? d. The motel currently uses a lot size of 600 boxes (i.e., Q = 600). What is the annual holding cost of this policy? Annual ordering cost? Without calculating the EOQ, how can you conclude from these two calculations that the current lot size is too large? e. What would be the annual cost saved by shifting from the 600-box lot size to the EOQ?

Weekly demand, d = 132
So, Annual demand, D = 132 boxes per week * 52 weeks = 6,864
Order cost, K = \$74
Unit holding cost, h = 24% of 5.65 = \$1.356
Average lead time, L = 3 weeks
CSL = 95%, So, z = 1.645
Std.Dev. of weekly demand, σ = 25 boxes

(a)

EOQ = (2.D.K / h)1/2 = SQRT(2*6864*74 / 1.356) = 866 boxes

Average time betwwen orders = EOQ / weekly demand = 866 / 132 = 6.56 weeks

(b)

ROP = d.L + z.σ.√L = 132*3 + 1.645*25*√3 = 467 boxes

(c)

The inventory level becomes 159 – 18 = 141 boxes which is less than the ROP. So, it is time order (even befire the inventory withdrawal, the inventory level of 159 is below ROP).

(d)

Q = 600

Annual holding cost = (Q/2) * h = (600/2)*1.356 = \$406.8

Annual ordering cost = (D/Q) * K = (6864/600) * 74 = \$846.56

Since the ordering cost is more than the holding cost, the order size is too less (not large!). If it were EOQ, then they would have been equal.

(e)

Q = EOQ = 866

Annual holding cost = (866/2)*1.356 = \$587.1

Annual ordering cost = (6864/866) * 74 = \$596.5

So,

Savings = (\$406.8 + \$846.56) – (\$587.1 + \$596.5) = \$69.76

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