1. Review for Midterm 2
OPSM 301

2. Practice Problems Problem 1:
A major drug store chain wishes to build a new warehouse to serve the whole Midwest. At the moment, it is looking at three possible locations. The factors, weights, and ratings being considered are given below:
Ratings
Factor Weights Peoria Des Moines Chicago
Nearness to markets
Labor cost
Taxes
Nearness to suppliers
Which city should they choose?

3. Practice Problems Problem 1:
A major drug store chain wishes to build a new warehouse to serve the whole Midwest. At the moment, it is looking at three possible locations. The factors, weights, and ratings being considered are given below:
Based upon the weights and rating, Des Moines should be chosen.
Weighted Ratings
Peoria Des Moines Chicago
Total
Ratings
Factor Weights Peoria Des Moines Chicago
Nearness to markets
Labor cost
Taxes
Nearness to suppliers
Which city should they choose?

4. Practice Problems Problem 2:
Balfour’s is considering building a plant in one of three possible locations. They have estimated the following parameters for each location:
Location Fixed Cost Variable Cost
Waco, Texas $300,000 $5.75
Tijuana, Mexico $800,000 $2.75
Fayetteville, Arkansas $100,000 $8.00
For what unit sales volume should they choose each location?

5. Practice Problems Problem 2: Transition between Waco and Tijuana
300, x = 800, x
3x = 500,000
x = 166,000
Problem 2:
Balfour’s is considering building a plant in one of three possible locations. They have estimated the following parameters for each location:
Location Fixed Cost Variable Cost
Waco, Texas $300,000 $5.75
Tijuana, Mexico $800,000 $2.75
Fayetteville, Arkansas $100,000 $8.00
Transition between Waco and Fayetteville
300, x = 100, x
2.25x = 200,000
x = 88,888
For what unit sales volume should they choose each location?

6. Practice Problems Problem 2: Transition between Waco and Tijuana
Locate in Fayetteville
Transition between Waco and Tijuana
300, x = 800, x
3x = 500,000
x = 166,000
Transition between Waco and Fayetteville
300, x = 100, x
2.25x = 200,000
x = 88,888
Problem 2:
Balfour’s is considering building a plant in one of three possible locations. They have estimated the following parameters for each location:
Location Fixed Cost Variable Cost
Waco, Texas $300,000 $5.75
Tijuana, Mexico $800,000 $2.75
Fayetteville, Arkansas $100,000 $8.00
For what unit sales volume should they choose each location?

7. Practice Problems Problem 3:
Our main distribution center in Phoenix, AZ is due to be replaced with a much larger, more modern facility that can handle the tremendous needs that have developed with the city’s growth. Fresh produce travels to the seven store locations several times a day making site selection critical for efficient distribution. Using the data in the following table, determine the map coordinates for the proposed new distribution center.

8. Practice Problems Problem 3:
Our main distribution center in Phoenix, AZ is due to be replaced with a much larger, more modern facility that can handle the tremendous needs that have developed with the city’s growth. Fresh produce travels to the seven store locations several times a day making site selection critical for efficient distribution. Using the data in the following table, determine the map coordinates for the proposed new distribution center.
Truck Round Trips
Store Locations Map Coordinates (x, y) per Day
Mesa (10, 5) 3
Glendale (3, 8) 3
Camelback (4, 7) 2
Scottsdale (15, 10) 6
Apache Junction (13, 3) 5
Sun City (1, 12) 3
Pima (5, 5) 10

9. Practice Problems Problem 3: Cx = = = 7.97 Cy = = = 6.69
(10*3) + (3*3) + (4*2) + (15*6) + (13*5) + (1*3) + (5*10)
255 32
Cy = = = 6.69
(5*3) + (8*3) + (7*2) + (10*6) + (3*5) + (12*3) + (5*10)
214
Practice Problems
Problem 3:
Our main distribution center in Phoenix, AZ is due to be replaced with a much larger, more modern facility that can handle the tremendous needs that have developed with the city’s growth. Fresh produce travels to the seven store locations several times a day making site selection critical for efficient distribution. Using the data in the following table, determine the map coordinates for the proposed new distribution center.
Truck Round Trips
Store Locations Map Coordinates (x, y) per Day
Mesa (10, 5) 3
Glendale (3, 8) 3
Camelback (4, 7) 2
Scottsdale (15, 10) 6
Apache Junction (13, 3) 5
Sun City (1, 12) 3
Pima (5, 5) 10

10. Practice Problems Problem 4:
John Galt Shipping wishes to ship a product that is made at two different factories to three different warehouses. They produce 18 units at Factory A and 22 units at Factory B. They need 10 units in warehouse #1, 20 units in warehouse #2, and 10 units in warehouse #3. Per unit transportation costs are shown in the table below. How many units should be shipped from each factory to each warehouse?
Warehouse #1 Warehouse #2 Warehouse #3
Plant A $4 $2 $3
Plant B $3 $2 $1

11. Practice Problems Problem 1:
John Galt Shipping wishes to ship a product that is made at two different factories to three different warehouses. They produce 18 units at Factory A and 22 units at Factory B. They need 10 units in warehouse #1, 20 units in warehouse #2, and 10 units in warehouse #3. Per unit transportation costs are shown in the table below. How many units should be shipped from each factory to each warehouse?
Warehouse #1 Warehouse #2 Warehouse #3
Plant A $4 $2 $3
Plant B $3 $2 $1

12. Practice Problems Problem 5:
Assume that in Problem 1 the demand at each warehouse is increased by 4 units. Now how many units should be shipped from each factory to each warehouse?
Warehouse #1 Warehouse #2 Warehouse #3
Plant A $4 $2 $3
Plant B $3 $2 $1

13. Practice Problems Problem 2:
Assume that in Problem 1 the demand at each warehouse is increased by 4 units. Now how many units should be shipped from each factory to each warehouse?
Warehouse #1 Warehouse #2 Warehouse #3
Plant A $4 $2 $3
Plant B $3 $2 $1

14. Practice Problems Problem 6:
What are the appropriate ABC groups of inventory items?

15. Practice Problems Problem 6: ABC Analysis Percent of
Stock Number Annual $ Volume Annual $ Volume
J24 12,
R26 9,
L02 3,
M12 1, P T S Q V
 = 100.0
Problem 6:
What are the appropriate ABC groups of inventory items?

16. Practice Problems Problem 1: ABC Groups Annual Percent of
ABC Analysis
Percent of
Stock Number Annual $ Volume Annual $ Volume
J24 12,
R26 9,
L02 3,
M12 1, P T S Q V
 = 100.0
Problem 1:
What are the appropriate ABC groups of inventory items?
ABC Groups
Annual Percent of
Class Items Volume $ Volume
A J24, R26 21,
B L02, M12 4,
C P33, &72, S67, Q47, V
 = 100.0

17. Practice Problems Problem 7:
Assume you have a product with the following parameters:
Annual Demand = 360 units
Holding cost per year = $1.00 per unit
Order cost = $100 per order
What is the EOQ for this product?

18. Practice Problems Problem 7:
Assume you have a product with the following parameters:
Annual Demand = 360 units
Holding cost per year = $1.00 per unit
Order cost = $100 per order
What is the EOQ for this product?
EOQ = = =
2 * Demand * Order Cost
Holding Cost
2 * 360 * 100 1
= items

19. Practice Problems Problem 8:
Given the data from Problem 7, and assuming a 300-day work year, how many orders should be processed per year? What is the expected time between orders?

20. Expected number of orders
Practice Problems
Problem 8:
Given the data from Problem 3, and assuming a 300-day work year, how many orders should be processed per year? What is the expected time between orders?
N = = = 1.34 orders per year
Demand Q
360
268
T = = = 224 days between orders
Working days
Expected number of orders
300
1.34

21. Practice Problems Problem 9:
What is the total cost for the inventory policy used in Problem 7?

22. Quantity of Items * Holding Cost
Practice Problems
Problem 9:
What is the total cost for the inventory policy used in Problem 7?
TC =
Demand * Order Cost Q
Quantity of Items * Holding Cost 2
= = = $268
360 * 100
268
268 * 1

23. Practice Problems Problem 10:
Litely Corp sells 1,350 of its special decorator light switch per year and places orders for 300 of these switches at a time. Assuming no safety stocks, Litely estimates a 50% chance of no shortages in each cycle and the probability of shortages of 5, 10, and 15 units as 0.2, 0.15, and 0.15 respectively. The carrying cost per unit per year is calculated as $5 and the stockout cost is estimated at $6 ($3 lost profit per switch and another $3 loss of goodwill or future sales). What level of safety stock should Litely use for this product? (Consider safety stock of 0, 5, 10, and 15 units.)

24. Practice Problems Problem 10:
Safety stock = 0 units
Carrying cost = $0
Total Stockout Costs = (stockout costs * possible units of shortage * probability of shortage * number of orders per year)
S0 = 6 * 5 * .2 *
6 * 10 * .15 *
6 * 15 * .15 * =
$128.25
1350
300
Practice Problems
Safety stock = 5 units
Carrying cost = $5/unit * 5 units
S5 = 6 * 5 * .15 *
6 * 10 * .15 * =
$60.75
Total cost = Carrying cost + Stockout cost =
$25 + $60.75 = $85.75
1350
300
Safety stock = 10 units
Carrying cost = $5/unit * 10 units
S10 = 6 * 5 * .15 * =
$20.25
Total cost = Carrying cost + Stockout cost =
$50 + $20.25 = $70.25
1350
300
Problem 10:
Litely Corp sells 1,350 of its special decorator light switch per year and places orders for 300 of these switches at a time. Assuming no safety stocks, Litely estimates a 50% chance of no shortages in each cycle and the probability of shortages of 5, 10, and 15 units as 0.2, 0.15, and 0.15 respectively. The carrying cost per unit per year is calculated as $5 and the stockout cost is estimated at $6 ($3 lost profit per switch and another $3 loss of goodwill or future sales). What level of safety stock should Litely use for this product? (Consider safety stock of 0, 5, 10, and 15 units.)
Safety stock = 15 units
Carrying cost = $5/unit * 15 units
Stockout cost = $0
Total cost = Carrying cost + Stockout cost =
$75 + $0 = $75.00

25. Practice Problems Problem 11:
Presume that Litely carries a modern white kitchen ceiling lamp that is quite popular. The anticipated demand during lead-time can be approximated by a normal curve having a mean of 180 units and a standard deviation of 40 units. What safety stock should Litely carry to achieve a 95% service level?

26. Practice Problems Problem 11:
Presume that Litely carries a modern white kitchen ceiling lamp that is quite popular. The anticipated demand during lead-time can be approximated by a normal curve having a mean of 180 units and a standard deviation of 40 units. What safety stock should Litely carry to achieve a 95% service level?
To find the safety stock for a 95% service level it is necessary to calculate the 95th percentile on the normal curve. Using the standard Normal table from the text, we find the Z value for 0.95 is 1.65 standard units. The safety stock is then given by:
(1.65 * 40) = = 246 Ceiling Lamps

27. Practice Problems Problem 12:
A new shopping mall is considering setting up an information desk manned by one employee. Based upon information obtained from similar information desks, it is believed that people will arrive at the desk at a rate of 20 per hour. It takes an average of 2 minutes to answer a question. It is assumed that the arrivals follow a Poisson distribution and answer times are exponentially distributed.

28. Practice Problems Problem 1:
A new shopping mall is considering setting up an information desk manned by one employee. Based upon information obtained from similar information desks, it is believed that people will arrive at the desk at a rate of 20 per hour. It takes an average of 2 minutes to answer a question. It is assumed that the arrivals follow a Poisson distribution and answer times are exponentially distributed.
Find the probability that the employee is idle.
Find the proportion of the time that the employee is busy.
Find the average number of people receiving and waiting to receive some information.
Find the average number of people waiting in line to get some information.
Find the average time a person seeking information spends in the system.
Find the expected time a person spends just waiting in line to have a question answered (time in the queue).

29. Practice Problems Problem 12:
A new shopping mall is considering setting up an information desk manned by one employee. Based upon information obtained from similar information desks, it is believed that people will arrive at the desk at a rate of 20 per hour. It takes an average of 2 minutes to answer a question. It is assumed that the arrivals follow a Poisson distribution and answer times are exponentially distributed.
Find the probability that the employee is idle.
Find the proportion of the time that the employee is busy.
Find the average number of people receiving and waiting to receive some information.
Find the average number of people waiting in line to get some information.
Find the average time a person seeking information spends in the system.
Find the expected time a person spends just waiting in line to have a question answered (time in the queue).
P0 = 1 –  /  = 1 – 20 / 30 = 0.33  33%
p =  /  = 0.66  66%
Ls =  / ( – ) = 20 / (30 – 20) = 2 people
Lq = 2 / ( – ) = 202 / 30(30 – 20) = 1.33 people
Ws = 1 / ( – ) = 1 / (30 – 20) = 0.10 hours
Wq =  / ( – ) = 20 / 30(30 – 20) = hours

30. Practice Problems Problem 13:
Assume that the information desk employee in Problem 12 earns $5 per hour. The cost of waiting time, in terms of customer unhappiness with the mall, is $12 per hour of time spent waiting in line. Find the total expected costs over an 8-hour day.

31. Practice Problems Problem 2: From the solution to Problem 12:
Assume that the information desk employee in Problem 1 earns $5 per hour. The cost of waiting time, in terms of customer unhappiness with the mall, is $12 per hour of time spent waiting in line. Find the total expected costs over an 8-hour day.
From the solution to Problem 12:
The average person waits hours and there are
160 (20 arrivals * 8 hours) arrivals per day.
Therefore: Total waiting time = x = hours
Total cost for waiting = Total waiting time * Cost per hour =
10.67 * $12 = $128 per day.
Salary cost = 8 hours * $5 = $40
Total cost = Salary cost + Waiting cost = $40 + $128 =
$168 per day.

32. Practice Problems Problem 14:
Three students arrive per minute at a coffee machine that dispenses exactly four cups per minute at a constant rate. Describe the system parameters.

33. Practice Problems Problem 14:
Three students arrive per minute at a coffee machine that dispenses exactly four cups per minute at a constant rate. Describe the system parameters.
Lq = = people in the queue on average
Wq = = minutes in the queue waiting
Ls = Lq = 1.87 people in the system
Ws = Wq = minutes in the system 2
2( – )   1