MODULE FIVE: INVENTORY ANALYSIS
Instructions
1.
2.
Read the scenarios presented and answer the related questions.
Submit your work as a pdf through the appropriate link in Blackboard.
Scenario 1: I-Scream Parlor
Daily demand for ice cream at the I-Scream parlor has a mean of 220 quarts per day. The owner has the ice cream
supplied by a wholesaler who charges $5 per quart. The wholesaler charges a $50 delivery charge independent of
order size. The opportunity cost of capital to I-Scream is estimated to be 20% per year, and the additional storage
cost of keeping the ice cream frozen and in stock is another 5% per year. Assume 360 days in a year.
1.
What is the optimal order size for quarts of ice cream?
Formula:
Daily demand of quarts (mean) = 220
Days in a year = 360
D = Annual demand = 220 x 360 = 79,200
S = Ordering cost = $50
H = Annual inventory holding cost = (20% + 5%) × $5 = $1.25
Optimal order size (EOQ) = ( 2 × D × S / H ) ½
= ( 2 × 79,200 × 50 / 1.25 ) ½
= ( 6,336,000) ½
= 2,517.14 units
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Scenario 2: Parts-R-Us
Parts-Are-Us is an auto parts supplier launched in 2015. Annual sales have increased by a factor of 10 over the last 5
years. After reviewing inventory levels, the president of the company finds that system wide inventories have
increased by a factor of 5 over that period. The president views this as a signal that the company has been managing its
inventories well. Assume that the company uses an Economic Order Quantity model to place orders and has no lead
time or safety stock. Also assume that the setup cost and holding cost have not changed over this period – in other
words, all that has changed is demand.
1.
Do you agree with the company president’s view that the firm is managing its inventory well based on the
information presented?
Formula:
EOQ = Economic order quantity
D = Annual demand
S = Cost per order
H = Annual holding cost per unit
Annual sales have increased by a factor of 10
EOQ = √2(10D)S / H
= 3.16 √2DS/H
Average inventory = EOQ/2 or 50% of EOQ
Since the EOQ increased by 3.16, the inventory must also increase by the same factor, 3.16.
However, the rise is 5 times instead of a 3.16 increment. Therefore, given all of the assumptions, if the
company were managing the inventory well, the inventory would have increased by a factor of 3.16 (the
square root of 10) and not by a factor of 5. Hence, we disagree with the President's view.
Scenario 3: Parts-R-Us
A supplier to Toyota stamps out parts using a press. Changing a part type requires the supplier to change a die on the
press. This changeover currently takes two hours. The supplier estimates that each hour spent on the changeover
costs $250. Demand for parts is 1,000 per month. Each part costs the supplier $100, and the supplier incurs an
annual holding cost of 20%.
1.
Determine the optimal production batch size for the supplier.
This changeover currently takes = 2 hours
Hour spent on the changeover costs = $250
Demand for parts = 1,000 per month
Each part costs the supplier = $100
Supplier incurs an annual holding cost = 20%.
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D = Annual demand = 1000 x 12 = 12,000
S = Fixed setup cost = 2 x $250 = $500
H = Annual holding cost = $100 x 20% = $20 per year
EOQ = √2(D)S / H
EOQ = √2(12,000 x 500) / 20
EOQ = 774.6 = 775
The optimal production batch size for the supplier is 775.
2.
Toyota wants the supplier to reduce its batch size by a factor of 4; that is, if the supplier currently
produces Q parts per batch, Toyota would like them to produce Q/4 parts per batch. What should the
supplier do in order to achieve this result? In other words, what setup time (in minutes) creates a scenario
in which the optimal batch size drops to ¼ of its current level?
Target batch size = Q/4 = 775/4 = 194
In the equation of EOQ, the Batch size (Q) is directly proportional to the square root of the setup cost.
Therefore, if Q is reduced by a factor of 4, then the setup cost should decrease by a factor of 16
Target setup cost = 500/16 = $31.25
Each hour of setup costs $ 250
Therefore, target setup time = 31.25/250 = 0.125 hours or 7.5 minutes
The supplier should achieve a setup time of 7.5 minutes so that the optimal batch size drops to 1/4 of its
current level.
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Scenario 4: Dresses-We-Sell
Dresses-We-Sell offers a line of upscale evening dresses in a boutique. The store charges $500 per dress and sales
average 20 units per week. Currently, they order 80 dresses at a time from the manufacturer and pay $200 per dress.
Lead-time is 2 weeks. The store estimates the administrative cost of placing each order to be $200. Adding the cost
of capital and related costs the store manager believes that each dollar’s worth of idle inventory cost $0.30 per year.
1.
Compute the total annual cost of ordering and carrying inventory.
Wd = Average weekly demand = 20 units
Annual demand = 20 units x 52 weeks = 1040 units
Cost of dress = 200 per unit
Administrative cost of placing each order = 200
Order size = 80 units
Annual carrying cost = 0.30 per dollar 0.3 x 200 = 60
= (1040/80) x 200 + (80/2) x 60 = $5000
The total annual cost of ordering and carrying inventory is $5000
2.
If they wish to minimize cost, when and how much should the store order in each batch? (Assume that
the store will order enough units to cover demand for some number of weeks – n, so the question is to
find the value of the integer n yielding the lowest total cost.)
EOQ = √2(D)S / H
EOQ = √2 (1040 x 200) / 60 = 83 units
Q/wd = 83/20 = 4.15 = 4 weeks
Optimal order = #weeks x demand per week = 4 x 20 = 80 units
Leadtime = 2 weeks
Weekly demand = 20 units
Re order point = leadtime x weekly demand
Re order point = 2 x 20 = 40 units
The store will order 80 units when the inventory level is 40 units.
3.
Find the number of inventory turns per year given the old and the new policy.
The old and the optimal policy has the order size Q=80
In both cases, the weeks of supply will be = 4.
Therefore, Number of weeks/weeks of supply = 52/ 4 = 13 turns per year
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Scenario 5: Dresses-We-Make (Supplier to Dresses-We-Sell)
The supplier from Scenario 4 offers Dresses-We-Sell a volume based discount. The supplier will drop the price to
$195 per dress, but for only order sizes above 200. The store is also considering an alternate supplier that has an
electronic ordering system. Because of the nature of the software, ordering from this supplier drops the
administrative cost to $100 per order and the store can select any order size up to (but not more than) 200 units per
order.
1.
Which deal should the store accept? (Assume they must accept one of these deals.)
Volume discount deal
Order quantity, Q = 200 units
Item cost, C = $195 per unit
Order cost = 200
Annual demand = 52 x 20 = 1040
Unit carrying cost, h = 0.3 of 195 = $58.5 per annum
Total annual ordering cost = (annual demand/quantity ordered ) x order cost = (1040/200) x 200 = 1040
Annual carrying cost = (order quantity/ 2) x 58.5 = (200/2) x 58.5 = 5850
Total cost of the item = (annual demand x cost per item) = 1040 x 195 = 202,800
Total annual Ordering cost + total annual carrying cost + total cost of the item
= 1040 + 5850 + 202,800 = $209,690
The deal of alternate supplier with electronic ordering
Order cost, K = $100 per order
Item cost, C = $200 per unit
Unit carrying cost, h = $60 per annum
EOQ = (2.D.K / h)1/2 = (2 * 1040 * 100 / 60)^0.5 = 59 units
Total annual ordering cost = (1040/59) * 100 = 1762.71
Total annual carrying cost = (EOQ/2) * annual carrying cost = (59/2)* 60 = 1770
Total cost of the item = Annual demand * cost of the item = 1040 * 200 = 208,000
1763 +1770 + 208,000 = 211,533
The volume-discount deal is the best as it offers the least annual total cost of $209,690 among all the
possible alternatives.
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