Bobby's Bagels has four locations in the city. Each of them sell fresh bagels daily. Bagels cannot be stored overnight. As a result, each store forecasts its demand for the day and prepares certain number of bagels in the store. Any unsold bagels at the end of the day is donated to charity.

The daily demand for bagels at each of the four locations is normally distributed, with the following details:

• Uptown: Mean 100, standard deviation 20
• Midtown: Mean 150, standard deviation 30
• Downtown: Mean 200, standard deviation 40
• College town: Mean 50, standard deviation 10

Answer the following questions using this information.

Question 1

Suppose Bobby's Bagels decided to maintain 97.7% Service Level at each of the four locations by holding bagels in opening inventory at each location.

How many bagels, at least, should Bobby's decide to hold every day at the four locations Uptown (U), Midtown (M), Downtown (D), and College town (C) that would meet or exceed the 97.7% SL?

Answers should be in whole numbers only.

(Hint: 97.7% corresponds to a z value of 2)

Group of answer choices

1. U 100, M 150, D 200, C 50
2. U 140, M 210, D 280, C 70
3. U 150, M 200, D 300, C 75
4. U 145, M 205, D 275, C 75

Question 2

By holding inventory separately at each of the four locations, how much total opening inventory of bagels will Bobby's hold every day?

Group of answer choices

1. 500
2. 600
3. 700
4. 800

Question 3

By holding the (lowest possible) inventory every day at each location that guarantees 97.7% SL at each location, what is Bobby's Bagels expected daily sales, taken across the four locations?

Answer up to two decimal places.

Hint: since it is not 100% SL, expected sales at each location will not equal the mean demand. Find the Expected Sales at each location, and then sum over the four locations.

Question 4

By holding the (lowest possible) inventory every day at each location that guarantees 97.7% SL at each location, what is Bobby's Bagels expected leftover inventory, taken across the four locations?

Answer up to two decimal places.

Hint: Find the Expected Leftover Inventory at each location, and then sum over the four locations.

Note that it will also be equal to opening inventory - Expected Sales.

Question 5

Bobby's Bagels is in the process of determining an alternate inventory holding policy.

Instead of each of the four locations holding inventory to provide its own SL guarantee of 97.7%, Bobby's Bagels is planning to set up a mini warehouse at its Midtown location.

Then, this mini warehouse will stock bagels daily for the four locations, and in regular intervals, delivery personnel will replenish bagels at the individual stores at little to no lead time from this mini warehouse.

Bobby's needs to determine how much inventory to hold at this mini warehouse. This information will be useful for Bobby's Bagels to decide whether consolidating inventory at the mini warehouse will be cost-efficient or not.

If this mini warehouse has to meet the demand at the four stores mentioned above, what is the mean and standard deviation of the daily demand that the mini warehouse will face?

Group of answer choices

1. Mean: 500, Std Dev: 100
2. Mean: 500, Std. Dev: 3,000
3. Mean: 500, Std. Dev: 54.77
4. Mean: 75,000, Std. Dev: 3,000

Question 6

At this mini warehouse, Bobby's needs to achieve 97.7% service level (z = 2).

How much inventory at least should the mini warehouse hold every day to meet or exceed this SL requirement?

Answers should be in whole numbers only.

Group of answer choices

1. 500
2. 565
3. 610
4. 700

Question 71

By holding all inventory of bagels in the mini warehouse, what is Bobby's Bagels' expected leftover inventory at the end of the day?

Answer up to 2 decimal places.

Question 8

By consolidating inventory for all locations in the mini warehouse, will Bobby's Bagels reduce the amount of inventory to hold and the amount of expected leftover inventory, while maintaining the same 97.7% service level guarantee?

Group of answer choices

1. No, there will be no reduction.
2. Amount to hold will be reduced by 90, but expected leftover inventory will not be reduced
3. Expected leftover inventory will be reduced by approximately 90, but the amount to hold will not reduce
4. Both the amount to hold and the expected leftover inventory will be reduced by approximately 90

Question 9

Bobby's Bagels is wondering if consolidating inventory will have similar results if the service level guarantee is lower.

Bobby's wants to see what would happen to the total inventory to hold, at a service level guarantee of 84%.

In that case, by changing from holding inventory at each store independently, to holding inventory centrally at the mini warehouse, the total inventory to hold will:

Group of answer choices

1. remain the same
2. increase by 35
3. decrease by 45
4. cannot be determined

Question 10

Bobby's Bagels wants to reevaluate its service level strategy.

The bagels sell at $5, while they cost $2 to make.

For each lost customer, there is no additional goodwill loss. Excess inventory donated to charity earns no salvage value.

What is the optimal service level for Bobby's Bagels stores?

(Hint: this is given by the Critical Ratio)

Group of answer choices

1. 60%
2. 70%
3. 80%
4. 90%

Question 11

In order to achieve the service level that is optimal for Bobby's (matching the critical ratio), how much opening inventory should be carried at each store, if each store manages inventory individually? Write down whole numbers only (no decimal values), and remember to choose the lowest inventory level that matches or exceeds the SL requirement.

Uptown store:

Midtown store:

Downtown store:

Collegetown store:

Question 12

By holding these inventories that result in the optimal service level at each store independently, how much will Bobby's Bagels make in total expected profits every day across the four stores?

Answer: $ _________

(Choose the closest answer)

Group of answer choices

1. 1,500.00
2. $1,237.75
3. $1,306.74
4. $1,795,46

Question 13

By holding these inventories that result in the optimal service level at each store independently, how much will be the expected daily sales for Bobby's Bagels, across the four different stores? What will be the overall fill rate?

Group of answer choices

1. 500, 100%
2. 472.55, 94.51%
3. 450, 90%
4. 460.80, 92.16%

Question 14

Now, in the consolidated mini warehouse, how much inventory should be held to achieve the optimal service level?

Group of answer choices

1. 500
2. 514
3. 520
4. 550

Question 15

What is the expected daily profit that Bobby's Bagels will earn by holding this inventory in the consolidated mini warehouse?

Answer: $ ________.

Group of answer choices

1. 1,394.20
2. 1,300.10
3. 1,494.50
4. 1,324.40

Question 16

By holding this inventory that result in the optimal service level in the consolidated mini warehouse, how much will be the expected daily sales for Bobby's Bagels? What will be the overall fill rate?

Group of answer choices

1. 484.44, 96.89%
2. 450.00, 90%
3. 477.77, 95.55%
4. 491.25, 98.25%

Bobby's Bagels is now planning raw material inventory for the four stores.

As previously noted, the daily demand for bagels at each of the four locations is normally distributed, with the following details:

• Uptown: Mean 100, standard deviation 20
• Midtown: Mean 150, standard deviation 30
• Downtown: Mean 200, standard deviation 40
• College town: Mean 50, standard deviation 10

All locations are served by the same supplier. For each location, the lead time is normally distributed, with mean of 3 days and standard deviation of 1 day.

For the raw material to make one bagel, the supplier charges $1 to Bobby's, as material cost.

For each delivery to a store, the supplier charges $100 as ordering, shipping, and handling costs.

However, if Bobby's decide to operate a mini-warehouse instead of holding inventory at each store, the supplier is willing to make a larger delivery for a $150 fee per delivery. The raw material cost and lead time (mean and standard deviation) to deliver to the mini warehouse will remain the same as shipping to individual stores.

Bobby's inventory carrying cost is 18.25% of the material cost per year, and the business operates 365 days a year.

Answer the following questions with this information.

Question 17

Bobby's Bagels wants to maintain a service level of 95% for the raw material, and inventory is monitored continuously.

Suppose Bobby's decides to order independently for each store.

Determine the following (to two decimal places):

• EOQ for Uptown - call it EOQ(U)
• EOQ for Midtown - call it EOQ(M)
• EOQ for Downtown - call it EOQ(D)
• EOQ for Collegetown - call it EOQ(C)

Add these four EOQs = EOQ(U) + EOQ(M) + EOQ(D) + EOQ(C). What is the total quantity ordered?

Answer to two decimal places.

Question 18

Determine the following (to two decimal places):

• Safety Stock for Uptown - call it SS(U)
• SS for Midtown - call it SS(M)
• SS for Downtown - call it SS(D)
• SS for Collegetown - call it SS(C)

Add these four SS = SS(U) + SS(M) + SS(D) + SS(C). What is the total quantity in safety stock across the four locations?

Answer to two decimal places.

Question 19

Without changing the 95% SL requirement, if Bobby's Bagels moves to a consolidated mini warehouse model, where the supplier would make one consolidated delivery, what would be the EOQ and the SS?

Note that the supplier's mean and standard deviation of lead time does not change; however, the ordering cost changes.

Group of answer choices

1. EOQ 25,000.00; SS 800.00
2. EOQ 17,320.51; SS 837.10
3. EOQ 27,486.93; SS 870.37
4. EOQ 17,888.54; SS 348.15

Question 20

By consolidating the inventory of the raw material in the mini warehouse, what is the impact on the total average inventory and the total relevant cost, TRC?

Group of answer choices

1. Both increase after consolidation, by about 20%
2. Both decrease after consolidation, by about 20%
3. Both increase after consolidation, by about 35%
4. Both decrease after consolidation, by about 35%