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Review for Midterm 2

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Review for Midterm 2

OPSM 301

Ratings

FactorWeightsPeoriaDes MoinesChicago

Nearness to markets20475

Labor cost5884

Taxes15897

Nearness to suppliers1010610

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:

Which city should they choose?

Weighted Ratings

PeoriaDes MoinesChicago

80140100

404020

120135105

10060100

Total340375325

Ratings

FactorWeightsPeoriaDes MoinesChicago

Nearness to markets20475

Labor cost5884

Taxes15897

Nearness to suppliers1010610

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.

Which city should they choose?

LocationFixed CostVariable Cost

Waco, Texas$300,000$5.75

Tijuana, Mexico$800,000$2.75

Fayetteville, Arkansas$100,000$8.00

Problem 2:

Balfour’s is considering building a plant in one of three possible locations. They have estimated the following parameters for each location:

For what unit sales volume should they choose each location?

LocationFixed CostVariable Cost

Waco, Texas$300,000$5.75

Tijuana, Mexico$800,000$2.75

Fayetteville, Arkansas$100,000$8.00

Transition between Waco and Tijuana

300,000 + 5.75x = 800,000 + 2.75x

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:

Transition between Waco and Fayetteville

300,000 + 5.75x = 100,000 + 8.00x

2.25x = 200,000

x = 88,888

For what unit sales volume should they choose each location?

Locate in Fayetteville

LocationFixed CostVariable Cost

Waco, Texas$300,000$5.75

Tijuana, Mexico$800,000$2.75

Fayetteville, Arkansas$100,000$8.00

Transition between Waco and Tijuana

300,000 + 5.75x = 800,000 + 2.75x

3x = 500,000

x = 166,000

Transition between Waco and Fayetteville

300,000 + 5.75x = 100,000 + 8.00x

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:

For what unit sales volume should they choose each location?

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 LocationsMap 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

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.

(10*3) + (3*3) + (4*2) + (15*6) + (13*5) + (1*3) + (5*10)

3 + 3 + 2 + 6 + 5 + 3 + 10

(5*3) + (8*3) + (7*2) + (10*6) + (3*5) + (12*3) + (5*10)

3 + 3 + 2 + 6 + 5 + 3 + 10

Cx = = = 7.97

Cy = = = 6.69

255

32

214

32

Truck Round Trips

Store LocationsMap 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

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.

Warehouse #1Warehouse #2Warehouse #3

Plant A$4$2$3

Plant B$3$2$1

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 #1Warehouse #2Warehouse #3

Plant A$4$2$3

Plant B$3$2$1

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 #1Warehouse #2Warehouse #3

Plant A$4$2$3

Plant B$3$2$1

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 #1Warehouse #2Warehouse #3

Plant A$4$2$3

Plant B$3$2$1

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?

Problem 6:

What are the appropriate ABC groups of inventory items?

ABC Analysis

Percent of

Stock NumberAnnual $ VolumeAnnual $ Volume

J2412,50046.2

R269,00033.3

L023,20011.8

M121,5505.8

P336202.3

T72650.2

S67530.2

Q47320.1

V20300.1

= 100.0

Problem 6:

What are the appropriate ABC groups of inventory items?

ABC Analysis

Percent of

Stock NumberAnnual $ VolumeAnnual $ Volume

J2412,50046.2

R269,00033.3

L023,20011.8

M121,5505.8

P336202.3

T72650.2

S67530.2

Q47320.1

V20300.1

= 100.0

ABC Groups

AnnualPercent of

ClassItemsVolume$ Volume

AJ24, R2621,50079.5

BL02, M124,75017.6

CP33, &72, S67, Q47, V208002.9

= 100.0

Problem 1:

What are the appropriate ABC groups of inventory items?

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?

2 * Demand * Order Cost

Holding Cost

2 * 360 * 100

1

EOQ = = =

72000 = 268.33 items

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?

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?

300

1.34

N = = = 1.34 orders per year

360

268

Demand

Q

Working days

Expected number of orders

T = = = 224 days between orders

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?

Problem 9:

What is the total cost for the inventory policy used in Problem 7?

Demand * Order Cost

Q

TC = +

268 * 1

2

360 * 100

268

= + = 134 + 134 = $268

Quantity of Items * Holding Cost

2

Problem 9:

What is the total cost for the inventory policy used in Problem 7?

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 = 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

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

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

1350

300

1350

300

1350

300

1350

300

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

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?

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) + 180 = 66 + 180 = 246 Ceiling Lamps

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.

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).

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) = 0.0667hours

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.

Problem 2:

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 0.0667 hours and there are

160 (20 arrivals * 8 hours) arrivals per day.

Therefore: Total waiting time = 160 x 0.0667 = 10.67 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.

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 = = 1.125 people in the queue on average

Wq = = 0.375 minutes in the queue waiting

Ls = Lq + = 1.87 people in the system

Ws= Wq + = 0.625 minutes in the system

2

2( – )

2( – )

1

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.