Operations MGT Practice Questions Exam 2

C&A has monthly turns of 4, cost of goods sold of $12 million, and revenue of $36 million. What is its average inventory?

$0.25 million Average inventory = Cost of goods sold/Turns. Cost of goods sold = $12 million per year = $12/12 = $1 million per month. Average inventory = $1/4 = $0.25 million.

C&A has annual turns of 10, cost of goods sold of $9 million, and revenue of $20 million. What is its average inventory?

$0.9 million Turns = R/I; R = annual flow rate or COGS. Solve for I. Average inventory = Cost of goods sold/Turns = ($9 million)/10 = $0.9 million.

Firm A's demand for a product is 15 units per month. Its supplier charges an ordering cost of $5 per order and $10 per unit with a 10% discount for orders of 15 units or higher. Firm A incurs a 25% annual holding cost. Firm A orders at a quantity of 28 units. What is its annual total cost?

$1,684 With an order quantity of 28, the firm receives the discount. The holding cost at the discount price = $10 × (1 - 10%) × 25% = $2.25. Annual ordering cost if it orders at 28 units = (15 × 12)/28 × $5 = $32.14. Annual holding cost when ordering at 28 units with discount = 28/2 × $2.25 = $31.50. Annual purchasing cost when ordering at 28 units = (15 × 12) × $9 = $1,620. The total annual cost = $1,620 + $31.50 + $32.14 = $1,683.64, or $1,684.

C&A purchases fertilizer for its lawn-care business from a supplier who charges $30 per order and $50 per case. Each case consists of five bags of fertilizer. C&A needs 2,000 bags of fertilizer a year. C&A's annual holding costs are 30%. What is C&A's holding cost per bag per year?

$3 Holding cost per bag per year = $50/5 × 30% = $3

C&A has four months-of-supply, cost of goods sold of $12 million, and revenue of $36 million. What is its average inventory?

$4 million Average Inventory = Cost of goods sold x Months of supply. CoGS = $12/12 = $1 million per month AvgIn = ($1 mill) x 4 month supply = $4 million

Company C&A sells 600 bottles of a dietary supplement per week at $100 per bottle. The supplement is ordered from a supplier who charges Company C&A $30 per order and $50 per bottle. Company C&A's annual holding cost percentage is 40%. Assume Company C&A operates 50 weeks in a year. What is Company C&A's total ordering and holding cost per year if the order quantity is 200?

$6,500 Annual holding cost per bottle = 40% × $50 = $20. Annual demand = 600 × 50 = 30,000. Total ordering and holding cost at 200 = (200/2 × $20) + (30,000/200 × $30) = $6,500.

Store A uses the newsvendor model to manage its inventory. Demand for its product is normally distributed with a mean of 500 and a standard deviation of 250. Store A purchases the product for $10 each unit and sells each for $30. Inventory is salvaged for $5. What is its expected profit if Store A's order quantity is 400 units?

$6560 z = (400 − 500) / 250 = −0.4. Use Table 13.4 to find I(z = −0.4) = 0.23. Expected inventory = σ × I(z) = 250 × 0.23 = 57.6. Expected sales = Order quantity − Expected inventory = 400 − 57.6 = 342.4. Expected profit = (Price × Expected sales) + (Salvage value × Expected inventory) − (Cost × Order quantity) = ($30 × 342.4) + ($5 × 57.6) − ($10 × 400) = $6,560.

Store A uses the newsvendor model to manage its inventory. Demand for its product is normally distributed with a mean of 500 and a standard deviation of 300. Store A purchases the product for $10 each unit and sells each for $25. Inventory is salvaged for $5. What is its maximum profit?

$7500 Maximum profit = Expected demand × (Price − Cost) = 500 × ($25 − $10) = $7,500.

Bakery A uses 60 bags of flour each month. The flour is purchased from a supplier for a price of $80 per bag and an ordering cost of $20 per order. Bakery A's annual inventory holding cost percentage is 40%. If Bakery A chooses to use the economic order quantity for flour purchases, what will be the total of its holding and ordering costs per year?

$960 Holding cost per bag per year = $80 × 40% = $32. EOQ = {SQRT ((2x60x12x20)/32) } = 30 bags. Annual holding and ordering cost = 30/2 x $32 + 20 x 60 x 12/30 = $960

Demand for a company's product is normally distributed with a mean of 50 and a standard deviation of 10. What is the coefficient of variation of its demand forecast?

0.2 Coefficient of variation = Standard deviation/Mean = 10/50 = 0.2.

C&A has on average $6,000 in inventory and its daily sales are $200. What are C&A's weekly inventory turns (assuming demand occurs seven days a week)?

0.23 Inventory turns = Weekly demand/Inventory = 7 × 200/6,000 = 0.23 turn.

Firm C's demand for a product is 60 units per month. Its supplier charges an ordering cost of $40 per order and $35 per unit with a 20% discount for orders of 100 units or more. Orders must be placed in integer multiples of 100 units. Firm C incurs a 20% annual holding cost. What is the optimal order quantity that minimizes the total purchasing, ordering, and holding cost?

100 EOQ at regular price = {SQRT (2×60×12×40)/(0.2×35)} = 90. Total purchasing, ordering, and holding cost at 90 = (60 × 12 × $35) + (90/2 × $35 × 0.2) + (60 × 12)/90 × $40) = $25,835. Minimum quantity to get discount = 100. Purchasing cost with discount = $35 × (1 - 20%) = $28. Holding cost per unit per year with discount = 0.2 × $28 = $5.60. EOQ at discount price = {SQRT 2×60×12×40/5.6 } =101. It needs to order at multiple of 100. Therefore, the order quantity should be 100. Total cost at 100 = (60 × 12 × $28) + (100/2 × $5.6) + [(60 × 12/100) × $40] = $20,728. The optimal order quantity is 100.

Firm C's demand for a product is 60 units per month. Its supplier charges an ordering cost of $40 per order and $35 per unit with a 20% discount for orders of 100 units or more. Firm C incurs a 20% annual holding cost. What is the optimal order quantity that minimizes the total purchasing, ordering, and holding cost?

101 EOQ at regular price = { SQRT (2×60×12×40)/(0.2×35) }= 90. Total purchasing, ordering, and holding cost at 90 = (60 × 12 × $35) + (90/2 × $35 × 0.2) + (60 × 120/90 × $40) = $25,835. Minimum quantity to get discount = 100. Purchasing cost with discount = $35 × (1 - 20%) = $28. Holding cost per unit per year with discount = 0.2 × $28 = $5.60. EOQ = { SQRT (2×60×12×$40)/$5.6 } = 101 Since the EOQ at the discounted price is feasible, it is also optimal. Total costs at 101 = (60 × 12 × $28) + (101/2 × $5.6) + [(60 × 12/101) × $40] = $20,728. The optimal order quantity is 101.

Store A uses the newsvendor model to manage its inventory. Demand for its product is normally distributed with a mean of 500 and a standard deviation of 300. How many units should be ordered to achieve a 99.7% in-stock probability? Use Table 13.4.

1340 The z value for 0.997 is 2.748 (from Excel) or 2.8 (Table 13.4). Order quantity = µ + zσ = 500 + (2.8 × 300) = 1,340.

Bakery A uses 60 bags of flour each month. The flour is purchased from a supplier for a price of $80 per bag and an ordering cost of $20 per order. Bakery A's annual inventory holding cost percentage is 40%. If Bakery A chooses to use the economic order quantity for flour purchases, what will be its average inventory?

15 Holding cost per bag per year = $80 × 40% = $32. EOQ={ SQRT ((2×60×12×20)/32) } = 30 Bags. Average inventory = 30/2 = 15.

Firm B's demand for a product is 100,000 units per year.. It has a holding cost of $50 per unit per year and an ordering cost of $10 per order. If the firm is required to order an integer multiple of 150 units, what order quantity should it use to minimize ordering and holding costs?

150 EOQ = { SQRT (2×100,000×$10)/$50 } = 200, which is not an integer multiple of 150. Total costs if order is 150 = (150/2 × $50) + (100,000/150 × $10) = $10,417. Total costs if order is 300 = (300/2 × $50) + (100,000/300 × $10) = $10,833. Therefore, it is cheaper to order 150 units each time.

A company turns its inventory six times a year. What is its months-of-supply?

2 (12 months/6 times)

Demand is modeled with a normal distribution that has a mean of 300 and a standard deviation of 50. What is the probability that demand is 400 or more? Use Table 13.4

2.3% The z-value = (400 − 300)/50 = 2. Look up z of 2 in Table 13.4. Or use Excel's NORM.S.DIST(2,TRUE). The probability that demand is 400 or less is 0.9772. Subtract this result from 1 to get the probability of z ≥ 2, which is 2.3%.

Firm B's demand for a product is 10 units per month. Its supplier charges an ordering cost of $5 per order and $10 per unit with a 10% discount for orders of 15 units or higher. Firm B incurs a 30% annual holding cost. What is the optimal order quantity for Firm B (i.e., the order quantity that minimizes the total purchasing, ordering, and holding cost)?

21 EOQ at regular price = { SQRT (2×10×12×5)/(10×0.3)(2×10×12×5)/(10×0.3) } = 20 units. This EOQ is higher than the threshold of 15 units to get the discount. Therefore, the optimal order quantity is the EOQ at the discount price. The holding cost at the discount price = $10 × (1 - 10%) × 30% = $2.70. EOQ at discount price = { SQRT (2×10×12×5)/(9×0.3) } =21 units.

C&A sells two kinds of sandwiches: regular and deluxe. Each regular sandwich costs $1 to make and each deluxe sandwich costs $2 to make. On average, C&A has 5 regular and 10 deluxe sandwiches in inventory and 0.5 days-of-supply. How many sandwiches does C&A expect to sell each day?

30 Average Inventory = 5+10=15. Days of Supply = 0.5 Flow rate = 15/0.5 = 30

Bakery A uses 60 bags of flour each month. The flour is purchased from a supplier for a price of $80 per bag and an ordering cost of $20 per order. Bakery A's annual inventory holding cost percentage is 40%. What is its economic order quantity?

30 Holding cost per bag per year = $80 × 40% = $32. EOQ={ SQRT ((2×60×12×20)/32) } =30bags.

Company C&A sells 600 bottles of a dietary supplement per week at $100 per bottle. The supplement is ordered from a supplier who charges Company C&A $30 per order and $50 per bottle. Company C&A's annual holding cost percentage is 40%. Assume Company C&A operates 50 weeks in a year. What order quantity minimizes Company C&A's total ordering and holding cost per year?

300 Annual holding cost per bottle = 40% × $50 = $20. Annual demand = 600 × 50 = 30,000. EOQ={ SQRT (2×30,000×$30)/$20} =300.

C&A purchases cases of fertilizer for its lawn-care business from a supplier who charges C&A $30 per order and $50 per case. Each case consists of five bags of fertilizer. C&A needs 2000 bags of fertilizer a year. C&A's annual holding costs are 30%. How many cases of fertilizer should C&A order from its supplier with each order to minimize the total ordering and holding cost?

40 Holding cost per case per year = $50 × 30% = $15. Annual demand = 2,000 bags/5 bags = 400 cases. EOQ={SQRT (2×30,000×$40)/$15 } =400cases.

Company A purchases cases of fertilizer for its lawn-care business from a supplier who charges Company A $30 per order and $50 per case. Each case consists of five bags of fertilizer and the order size must be an integer multiple of five bags. Company A needs 2,000 bags of fertilizer a year. Company A's annual holding costs are 30%. What would be the order quantity that minimizes annual ordering and holding costs?

40 cases Holding cost per case per year = $50 × 30% = $15. Annual demand = 2,000 bags/5 bags = 400 cases. EOQ = {SQRT (2×400×$30)/$15 } = 40 cases. This is feasible because 40 cases is equivalent to 200 bags, an integer multiple of 5 bags.

Demand is modeled with a normal distribution that has a mean of 300 and a standard deviation of 50. What is the probability that demand is 400 or less? Use Table 13.4

97.7% The z-value = (400 − 300)/50 = 2. Look up z in Table 13.4. Or use Excel'sNORM.S.DIST(2,TRUE). The probability of z ≤ 2 is 97.7%.

Which of the following is NOT a possible complication that prevents a firm from ordering at the economic order quantity level?

A supplier charges a fixed cost to place an order.

Which of the following is NOT a subjective forecasting method?

Arrive at a forecast through time series extrapolation.

To evaluate inventory turns for a publicly traded company, data on average inventory can be found in which one of the following financial reports?

Balance sheet

Expected profit is a direct measure of how well a company serves its customers.

False

Incentive alignment is a subjective forecasting bias committed by the forecaster without his/her awareness of it.

False

Measuring inventory in terms of dollars tells us whether the amount of inventory is large or not.

False

When solving for an optimal order quantity in the presence of a quantity discount, the best approach is to select an order quantity which takes advantage of the discount.

False

Which of the following is a reason for batching?

Fixed costs associated with starting the process

Which of the following is TRUE regarding the economic order quantity (EOQ) model?

Holding cost per unit per year is independent of order quantity.

Which of the following statements concerning the economic order quantity (EOQ) model is FALSE?

If the order quantity is large, the ordering cost dominates the EOQ cost.

Which of the following is TRUE regarding evaluating the quality of a forecast?

In the mean squared error evaluation, one single observation can make a very large difference.

Which of the following is NOT a way to manage a newsvendor product that has substantial mismatch costs?

Increase product variety

Which consequence of stockouts is the most costly?

Loss of the sale and loss of the customer

Which of the following is not an input to the forecasting process?

New techniques of optimization

A(n) ___________ tag is a small electronic device that transmits a unique radio signal to identify the object to which it is attached.

RFID

_________ protects a firm against unpredictable demand.

Safety stock

Bread expires at the end of the day and cannot be sold. This is an example of which component of the store's inventory holding cost?

Spoilage cost

A critical ratio of 0.8 means there is an 80% chance that demand is less than or equal to the optimal order quantity.

True

A newsvendor earns a high percentage of the maximum profit if its critical ratio is close to one.

True

Expanding product variety does not always result in an increase in profit.

True

Manufacturers usually carry work-in-process inventory.

True

When solving for an optimal order quantity in the presence of order quantity restrictions, the best approach is to order at a feasible quantity closest to the economic order quantity.

True

The assumptions behind the economic order quantity (EOQ) model include all of the following EXCEPT __________.

a fixed ordering cost per year

Average inventory is reported as an _____________ in a publicly traded company's ____________.

asset, balance sheet

The days-of-supply of a process is the amount of time it takes for the _________ to flow through the system at the ___________.

average inventory, average flow rate

The factors that influence mismatch costs are __________ and __________.

critical ratio, coefficient of variation of demand

Expected profit __________ as the critical ratio __________.

decreases, decreases

The __________ function provides the probability that an uncertain outcome is a certain level or __________.

distribution, lower

Demand forecasting is the process of creating statements about ____________ of demand that are ______________.

future realizations, currently uncertain

___________ is a phenomenon when all experts __________ though the outcome is fundamentally wrong or unlikely.

groupthink, agree

Inventory turns and days-of-supply measure _______ items remain in __________.

how long, inventory

Higher days of supply means _________ inventory. Higher turns means ______ inventory.

more, less

Product pooling is more effective with products whose demands are __________.

negatively correlated

Inventory can be measured in many ways EXCEPT in ______.

profit

A wide and short density function has a large __________ relative to the __________.

standard deviation, mean

The __________ is the cost of ordering one unit __________.

underage cost, too few

C&A sells T-shirts for $20 that cost $5 to produce. The annual holding cost percentage is 10% and the T-shirts turn 25 times a year. What holding cost does C&A incur for each T-shirt?

$0.02 The annual holding cost = $5 × 10% = $0.50. The T-shirt spends 1/25 of a year in inventory, so each T-shirt incurs $0.50/25 = $0.02 in holding cost.

Bakery A sells bread for $2 per loaf that costs $0.50 per loaf to make. Bakery A gives an 80% discount for its bread at the end of the day. What is the overage cost?

$0.10 The salvage value is $2 × (1 − 0.8) = $0.40. The loss of making one too many = $0.50 − $0.40 = $0.10.