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PART>MBA 540 Homework Set 2
Question 1. 30 points, each part is worth 5 points.
We have the following information about weekly demand for ai6 cell phones at a Best Purchase store:
TB>Average weekly demand:
300 phones
Standard deviation of weekly demand:
50 phones
Order lead time:
2 weeks
Standard deviation of order lead time:
1.5 weeks
Item cost:
$600 per phone
Cost to place an order:
$100 per orde
Yearly holding cost per phone:
40% of item cost
Solution:
Some of the data provided above is in weeks while the other is yearly. Therefore converting all of the data to annual time units, the data is as below:
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INST>a.
INST>What is the economic order quantity for this phone? What is the resulting total annual relevant cost?
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Based on the given data and plugging in the values of D, Co and Ch,
EOQ = Q = SQRT ( 2 x 15600 x 100 / 240) = XXXXXXXXXX
Total Annual Cost TC = (D/Q)*Co + (Q/2)*Ch=(15600/ XXXXXXXXXXx XXXXXXXXXX/2)x240 =
= $27,364.21
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INST>Suppose Best Purchase cu
ently orders a week’s demand at a time (i.e., the order quantity is 300). How does the annual relevant cost of this policy compare with the cost you obtained in part (a)? Show your work.
If Best Purchase cu
ently orders a week’s demand => Q = 300.
Then Total Annual Cost = TC = (D/Q)*Co + (Q/2)*Ch.
Plugging in all D, Co and Ch from the problem description, we get
TC = (15600/300) x XXXXXXXXXX/2) x 250 = $41,200.
The total annual cost is ($41,200 - $27,364.21) = $ XXXXXXXXXXmore than when the EOQ was ordered at 114 phones per order when compared to 300 phones per order. This increase in cost is probably because of the holding cost.
c.. Suppose the store places an order every time the inventory level drops to 1200. What is the probability of no stock-out achieved under this policy?
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Since the order is placed every time the inventory level drops to 1200, Reorder Point = 1200.
Using the formula Rp = D x L + Safety Stock, we can get the safety stock. Plugging in the values we know in this formula, we get
Safety Stock = Rp – (DxL) = 1200 – XXXXXXXXXXx XXXXXXXXXX) = 600.
Now that we know the safety stock value, we can calculate the probability of no stock-out by using the formula : Safety Stock = z x sigma-D x √?̅
Solving for z , z = Safety Stock / (sigma-D x √?̅) = 600 / (2600 * √ XXXXXXXXXX) = 1.1766
· NORMSDIST(z) NORMSDIST(1.1766) = 88%
Therefore, the probability of no stock-out if the reorder point = 1200 is 88%
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INST>d. Now assume that the store wants to achieve a probability of no stock-out of 99% (z=2.33).
INST>What is the new reorder point for the phone? How much of the reorder point consists of safety stock?
Calculating for safety stock using Safety Stock = z x sigma-D x √?̅,
Safety Stock = 2.33 x 2600 x √ XXXXXXXXXX = XXXXXXXXXX
Re-order point to get 99% probability of no stock-out using RP = (DxL)+SafetyStock =
RP = XXXXXXXXXXx XXXXXXXXXX.07 = XXXXXXXXXXTherefore the new re-order point to achieve 99% probability of no stock-out = XXXXXXXXXX.
The safety stock is XXXXXXXXXX/ XXXXXXXXXX% of the re-order point.
e. Using the economic order quantity from part (a) and the safety stock level from part (d), compute the annual inventory holding cost this store incurs.e.
Total annual cost = TC = (D/Q)*Co + (Q/2+safety stock)*Ch
The annual Holding cost from the anove Equation = (Q/2+safety stock)*Ch
= XXXXXXXXXX/ XXXXXXXXXXx 240 = $298,819.28
· Annual Holding Costs = $298,819.28
f. Because electronics becomes obsolete so quickly, Best Purchase is thinking about raising holding cost from 40% of item cost to a higher percentage. What will be the impact on the economic order quantity? Briefly explain your answer.
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Increase in the annual holding cost will reduce the EOQ. As the holding cost increases, to retain the economic benefit to the company, ordering lesser inventory on each order is the right thing to do.
For example: The holding cost as per the problem description is 40% of the item cost. At this price, the EOQ in 1A is XXXXXXXXXXunits. If the holding cost is increased to 50%, the EOQ then becomes = Squareroot ( 2 x XXXXXXXXXXx $100) / $300 = XXXXXXXXXXThe new EOQ = 101.98
Question 2. 14 points, 7 points for each part
SkiForever is planning orders for its 2022 winter catalog. One order will be placed at their supplier nine months ahead of the selling season. The demand forecast for one of the jackets is normally distributed with mean 4000 and standard deviation 1200. The company plans to sell the jackets at a price of $300. SkiForever pays their supplier $150 per jacket and unsold jackets will be moved to the outlet store at the end of the selling season and will be priced at $100. It is assumed that at that price all remaining jackets will sell. It costs $20 to hold a jacket in inventory until the end of the season and move it to the outlet store.
Solution:
a. How many jackets should SkiForever order?
The number of jacket to be ordered can be calculated by the formula Q = D+z*sigma-D.
Based on the data, D = 4000; sigma-D = 1200.
z can be calculated by NORMSINV(F(Q*)).
F(Q*) = Cu/(Cu+Co).
Cu (Understocking cost) = p – c = $300 - $150 = $150
Co (Overstocking cost) = c – s. Here salvage cost is $100. However, there is a holding cost of $20 for each item. Therefore, the salvage cost (s) = $100 - $20 = $80.
Therefore Co = $150 - $80 = $70
F(Q*) = Cu / (Cu + Co) = $150 / ($150 + $70) = 0