Economic Order Quantities I have already answered a good chu

Economic Order Quantities

I have already answered a good chunk of the questions. All of the other information is provided below.

The Economic Order Quantity is 250 units.

There are no safety stocks, so the inventory reaches a level of zero before the new 250-unit order arrives. This means the average inventory is 250/2 = 125 units.

The Inventory Holding Cost is $187.50.

10 orders would be made each year, at an annual order cost of $187.50.

The Total Annual Cost of managing the inventory is $375.00 per year.

The time between orders is 25 days.

With a lead time of 10 days, the reorder point will be at 100 units.

QUESTIONS REMAINING:

1. What would be the total annual inventory cost, including the cost of goods? (Assume that one bracket costs Joe Henry $10.00)

2. Joe Henry notices that the demand for the unit he is studying is not constant, but can reasonable be approximatied by a normal distribution with average weekly demand of 50 units and a standard deviation of 15 units.

(a) If the cycle service level is to be set at 99%, find the reorder point as well as the level of the safety stock.

(b) Find the total annual inventory cost of this system, including the cost of the merchandise and the holding cost of the saftey stock.

(c) The accounting department is concerned and favors a periodic review system where orders are placed regularly every four weeks. Find the level of safety stock if the cycle service level is to stay at 99%

(d) find the total annual inventory cost of this system, including the cost of the merchandise and the holding cost of the safety stock.

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Thanks in advance.

Solution

Q1) Total annual inventory cost = Cost of goods+Inventory holding cost+Ordering cost = (D*C)+(Q/2)*H+(D/Q)*S

Total cost = (2500*10)+(125)*1.5+(2500/250)*18.75 = 25375 $

Q2) Average weekly demand (d) = 50 units; Standard deviation of demand _d = 15 units

a) Service level = 99% => z = 2.33

ROP = Demand during lead time + Safety stock = nd*L+z*_d*L = (50/7)*10+(2.33*15*10) = 182

Safety stock = 111 (approx)

b) Total annual inventory cost = 25375+(safety stock holding cost) = 25375+(SS/2)*1.5 = 25459 $(approx)

c) Safety stock(Periodic Review system) = z*_d*t+L = 2.33*15*4+10 = 131(approx)

d) Total annual inventory cost = 25375+(SS/2)*1.5 = 25474 $(approx)