Assignment 3: Inventory Management
Problem 1 (15pts)
A retailer sells approximately 10,000 units of a cereal bar per year, which is high in comparison to other similar products. With this fact in mind, the retailer negotiated the following purchase cost per unit with the wholesale to reduce inventory costs:
Order Quantity
Wholesaler Price Per Unit
$5.00
$4.50
$4.00
The holding costs account for 25% of each unit’s price, and placing an order costs $12 to the company. In the old contract, the company was paying $4.75 per cereal bar unit. Is this new contract worth it?
Problem 2 (15 pts)
A famous hotel chain in Toronto wishes to determine the number of rooms that it should allocate for the summer season. Every allocated incurs a daily expense of $25 to the hotel, due to cleaning and maintenance costs (regardless if the room is occupied or not). Customers pay $200 per night stay. Suppose that daily demand during summer is Normally distributed with mean 100 and variance 49. What is the optimal number of rooms to allocate per day to maximize expected revenue?
Problem 3 (18 pts)
The daily demand for ice creams at i-Scream parlor is normally distributed with a mean of 100 quarts and a standard deviation of 120 quarts. The owner has the ice cream supplied by a wholesaler who charges $2 per quart. The wholesaler charges a $90 delivery charge independent of order size. The opportunity cost of capital to i-Scream is estimated to be 25% per year. Assume 360 days in the year.
a. Assume that an order arrives instantaneously after being placed.
i. How many quarts is it optimal for i-Scream to order? (2 pts)
ii. When does i-scream need to place an order? (2 pts)
iii. What is the average length between two successive orders? (2 pts) iv. How many orders will be placed in a year on the average? (2 pts)
b. Assume now that it takes 9 days for an order to be supplied. The owners would like to ensure that, 95% of the times, they will experience no stock-outs. When does i-Scream need to place an order now? (4 points).
c. Currently the owners do not follow the EOQ and safety stock policy outlined above. Instead, they order 2000 quarts of ice cream when they have 1000 quarts on hand. Assume that it takes 9 days for an order to be supplied.
i. How much is the safety stock under the current policy? (2 pts)
ii. How much is the average inventory under the current policy? (2 pts)
iii. What is the average time spent by a quart of ice cream at the parlor? (2 pts)
Problem 4 (6x2=12 pts)
An electronic products retailer is designing its inventory of high-quality laptops for which the company is known for. After negotiations with the manufacturer, the cost for ordering products was set to a fixed amount of $450. The annual costs of maintaining the inventory in stock is $170 per unit. The estimated demand for this special type of laptop is 1,200 per year.
(a) Assuming a traditional economic order quantity model, what is the optimal quantity that the retailer should place per order?
(b) If the order you obtained is fractional, should you round it up or down?
(c) What is the resulting total inventory costs per year?
(d) How many orders will be placed every year on expectation?
(e) What is the expected interval between orders? Assume the year has 250 working days.
(f) To have a more accurate representation of the costs, the company would like to consider the extra purchase cost of $600 per laptop, based on negotiations with the manufacturer. The retailer sells each laptop for $1,500 (already accounting for taxes). What is the annual profit the retailer will have with this laptop brand?
Problem 5 (8x5=40 pts)
Answer the following multiple-choice questions and include the correct answer in the table below. No justification needed. There is only one correct answer for each question.
1. Suppose the purchase price of an item increases. However, the annual demand, the ordering/setup cost, and the percentage carrying cost remain unchanged. Then, the order quantity computed using the EOQ formula
a) Increases.
b) Decreases.
c) Does not change.
d) I need more information to answer this question.
2. Suppose the lead time for the delivery of a product increases while the service level and the distribution of the daily demand remain unchanged. Then, the (optimal) reorder point in the fixed order quantity model a) Increases.
b) Decreases.
c) Does not change.
d) I need more information to answer this question.
3. Consider the fixed order quantity model under two scenarios: Under scenario A, the price of the product is $1. Under scenario B, the price of the product for orders under 1000 units is $1. However, the
Question
Correct Answer
price for orders over 1000 is $0.9. Suppose under each decision, you compute the optimal order quantity and place orders of that size. Which of the following statements is correct?
a) The annual setup cost under scenario A is greater than or equal to that under scenario B.
b) The annual holding cost under scenario A is less than or equal to that under scenario B.
c) Choices (a) and (b). d) None of the above.
4. The operations manager of Air Canada would like to decide on the number of seats to overbook. She knows that the number of no-shows follows a uniform distribution with the minimum of 0 passengers and the maximum of 9 passengers. The price of each ticket is $200. If the manager cannot accommodate a passenger, she has to return their $200 and pay them an extra $850 for their inconvenience. How many seats should the manager overbook?
a) 0 b) 1 c) 2 d) 7 e) 8 f) 9
5. Under which of the following conditions the critical fractile (service level) is negative? a) The salvage value is greater than the purchase price.
b) The salvage value is less than the purchase price.
c) The demand is normally distributed, and the z-value is negative.
d) None of the above.
6. Consider the fixed order quantity model with random demand. Suppose we use the optimal order quantity and the optimal reorder point. Which of the following statements are correct?
a) The expected annual holding cost is less than the expected annual ordering/setup cost.
b) The expected annual holding cost is equal to the expected annual ordering/setup cost.
c) The expected annual holding cost is greater than the expected annual ordering/setup cost. d) We do not have sufficient information.
7. Consider a fixed order quantity model whose demand has a normal distribution. Assume the lead time is L days and the average daily demand rate is d. What service level does the reorder point of ������������������=������������ correspond to?
a) 0
b) 1
c) 0.5 d) 0.75
8. If the lead-time for receiving the orders from the supplier doubles, the order quantity in the fixed order quantity model
a. Halves.
b. Doubles.
c. Increase by a factor of √2. d. None of the above.
If needed, you can assume the following with regards to the normal distribution service level values: • for a 95% service level, z = 1.65
• for a 92.65% service level, z = 1.45
• for a 87.5% service level, z = 1.15
• for a 82.12% service level, z = 0.92 • for a 79.10% service level, z = 0.81 • for a 73.47% service level, z = 0.63 • for a 69.15% service level, z = 0.50 • for a 62.55% service level, z = 0.32 • for a 55.11% service level, z = 0.13 • for a 52.39% service level, z = 0.06
