MBA 540 Homework Set 2Question 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:Average weekly...

MBA 540 Homework Set 2
Question 1:
a. The economic order quantity (EOQ) can be calculated using the formula:
EOQ = sqrt((2 * demand per year * order cost) / holding cost per unit)
where demand per year = 52 * average weekly demand = 1,560 bags order cost = $20 holding cost per unit = 30% of $25 = $7.50
By substituting the values we will get
EOQ = sqrt((2 * 1560 * 20) / 7.5) = 128.7
Therefore, the store should order 128 bags each time to minimize its relevant costs. The total annual relevant cost can be computed by adding the ordering cost of annual and holding cost of annual:
Annual ordering cost = (demand per year / EOQ) * order cost = (1560 / 128.7) * 20 = $243.15 Annual holding cost = (EOQ / 2) * holding cost per unit = (128.7 / 2) * 7.5 = $483.38
Total relevant cost = ordering cost annual + holding cost annual = $726.53
b. The annual relevant cost of the current policy of ordering 100 bags at a time can be computed using the same formula as in part (a):
Annual ordering cost = (demand per year / order quantity) * order cost = (1560 / 100) * 20 = $312 Annual holding cost = (order quantity / 2) * holding cost per unit = (100 / 2) * 7.5 = $375
Total relevant cost = ordering cost annual + holding cost annual = $687
Comparing this with the total annual relevant cost obtained in part (a), we can see that the current policy of ordering 100 bags at a time is less optimal.
c. The store places an order every time the inventory level drops to 75 bags, which means that the maximum inventory level is 75 + EOQ = 203.7 bags. The probability of no stock-out can be calculated using the normal distribution:
Probability of no stock-out = P(z > (lead time demand - inventory level) / lead time demand standard deviation)
where lead time demand = average weekly demand * lead time = 30 * 2 = 60 bags lead time demand standard deviation = standard deviation of weekly demand * sqrt(lead time) = 5 * sqrt(2) = 7.07 bags z = (lead time demand - inventory level) / lead time demand standard deviation = (60 - 203.7) / 7.07 = -21.5
Using a standard normal distribution table or a calculator, we find that the probability of no stock-out is essentially zero.
d. To achieve a probability of no stock-out of 95%, the store needs to set the reorder point at the demand during lead time plus the safety stock
Safety stock = z * lead time demand standard deviation
where z = 1.645 (corresponding to a 95% service level)
Reorder point = lead time demand + safety stock = 60 + 1.645 * 7.07 = 71.6
Therefore, the store should reorder when the inventory level drops to 71.6 bags. The safety stock is 1.645 * 7.07 = 11.63 bags.
e. The annual inventory holding cost with the EOQ from part (a) and the safety stock level from part (d) can be calculated as: Holding cost = (111.39 + 5.23) / 2 x $7.5 = $842.59
f. If the holding cost per unit per year is increased, the EOQ will decrease. This is because a higher holding cost per unit per year will increase the cost of carrying inventory, making it more expensive to order larger quantities. As a result, the optimal order quantity will decrease to balance the cost of ordering against the cost of holding...