Inventory Management

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Please see the attached file.

1.
Suppose that the R&B Beverage Company has a soft drink product that has a constant
annual demand rate of 3600 cases. A case of the soft drink costs R&B $3. Ordering costs
are $20 per order and holding costs are 25% of the value of the inventory per year. R&B
has 250 working days per year and the lead time is 5 days. Identify the following aspects
of the inventory policy.

Notes: Demand rate is constant and given as annual demand, D = 3600 cases
Demand is deterministic.
Number of working days, N = 250
Daily demand rate, d = Annual demand/number of working days
d = D/N = 3600/250 = 14.4 cases
Cost per unit i.e. cost per case is given, c = $3
Ordering cost is given, S = $20 per order
Holding cost is given as carrying cost rate, r = 25%
Inventory carrying cost per unit per annum = cost per unit*carrying cost rate
I = c*r = $3*25% = $0.75 per case per annum
(a) Economic order quantity
Economic Order Quantity (EOQ) is given by following formula

EOQ = 2*Annual demand*Ordering cost/Inventory carrying cost per unit per annum
EOQ = 2*D*S/I = (2*3600*$20/$0.0.75 = 438.18 cases

EOQ = _438.18 or 439 cases___

(b) Reorder point
Reorder point = Expected demand during lead time + safety stock
The annual demand is deterministic, therefore safety stock = 0
Reorder point = Expected demand during lead time
Expected demand during lead time = daily demand rate*lead time
= 14.4*5 = 72 cases
Reorder point = 72 cases
Reorder Point = ______72 cases_____________

(c) Total annual cost (You don't need to include the annual purchase cost)
Total annual cost = ordering cost + inventory cost

Ordering cost = number of orders per year*ordering cost

Number of orders per year = annual demand/EOQ
= D/EOQ = 3600/438.18 = 8.216 (9 after rounding)

Ordering cost = 8.216*$20 = $164.32

Inventory cost = Average inventory*inventory carrying cost per unit per year
Average inventory = EOQ/2 = 438.18/2 = 219.09

Inventory cost = 219.09*$0.75 = $164.32

(Important points to note at this stage. First, number of orders and EOQ were rounded only to indicate the feasible numbers. In actual calculations real numbers are used. Secondly, notice that ordering cost ($164.32) is equal to inventory cost ($164.32). This proves that the EOQ and other computations are correct. Economic order quantity is the quantity at which ordering cost is equal to inventory cost. This is the point at which total cost is minimum. To show this characteristic of inventory model, the values of EOQ and number of orders were not rounded in computations. Even with rounded values the ordering cost and inventory cost are almost equal.)

Total annual cost = $164.32 + $164.32 = $293.938

Total Annual Cost = _____$328.63________

2.
The Gilbert Air-Conditioning Company is considering the purchase of a special shipment
of portable air conditioners manufactured in Japan. Each unit will cost Gilbert $80, and it
will be sold for $125. Gilbert does not want to carry surplus air conditioners over until
the following year. Thus, all surplus air conditioners will be sold to a wholesaler for $50
per unit. Assume that the air conditioner demand follows a normal probability
distribution with mean 20 units and standard deviation 8 units.

Notes: The situation described above is a Newsboy (Newsvendor) problem. This is single period and single-item scenario where the company orders quantity of air-conditioners. The air conditioners can be sold at price of $125 during the period and at $50 at the end of period at discounted price.
Price during the period, P1 = $125
Price at the end of period, P2 = $50 (also called as salvage value or discount price)
Cost of an air conditioner, C = $80
Profit or underage cost, Cu = Price during the period - cost = 125 - 80 = $45
Overage cost, Co = Cost - price at the end of period = 80 - 50 = $30
Mean demand, u = 20 units
Standard deviation of demand, s = ...