Review for Midterm 2 OPSM 301. Practice Problems Problem 1: A major drug store chain wishes to build a new warehouse to serve the whole Midwest. At the

Review for Midterm 2

OPSM 301

Practice ProblemsProblem 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:

RatingsFactor Weights Peoria Des Moines ChicagoNearness to markets 20 4 7 5Labor cost 5 8 8 4Taxes 15 8 9 7Nearness to suppliers 10 10 6 10

Which city should they choose?


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:

RatingsFactor Weights Peoria Des Moines ChicagoNearness to markets 20 4 7 5Labor cost 5 8 8 4Taxes 15 8 9 7Nearness to suppliers 10 10 6 10

Which city should they choose?

Based upon the weights and rating, Des Moines should be chosen.

Weighted RatingsPeoria Des Moines Chicago

80 140 10040 40 20120 135 105100 60 100

Total 340 375 325

Problem 2:

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

Practice Problems

Location Fixed Cost Variable CostWaco, Texas $300,000 $5.75Tijuana, Mexico $800,000 $2.75Fayetteville, Arkansas $100,000 $8.00

For what unit sales volume should they choose each location?

Problem 2:


Practice Problems



Transition between Waco and Tijuana

300,000 + 5.75x = 800,000 + 2.75x3x = 500,000x = 166,000

Transition between Waco and Fayetteville

300,000 + 5.75x = 100,000 + 8.00x2.25x = 200,000

x = 88,888

Problem 2:


Practice Problems



Transition between Waco and Tijuana

300,000 + 5.75x = 800,000 + 2.75x3x = 500,000x = 166,000

Transition between Waco and Fayetteville

300,000 + 5.75x = 100,000 + 8.00x2.25x = 200,000

x = 88,888

Locate in Fayetteville


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 TripsStore Locations Map Coordinates (x, y) per DayMesa (10, 5) 3Glendale (3, 8) 3Camelback (4, 7) 2Scottsdale (15, 10) 6Apache Junction (13, 3) 5Sun City (1, 12) 3Pima (5, 5) 10



Truck Round TripsStore Locations Map Coordinates (x, y) per DayMesa (10, 5) 3Glendale (3, 8) 3Camelback (4, 7) 2Scottsdale (15, 10) 6Apache Junction (13, 3) 5Sun City (1, 12) 3Pima (5, 5) 10

Cx = = = 7.97(10*3) + (3*3) + (4*2) + (15*6) + (13*5) + (1*3) + (5*10)3 + 3 + 2 + 6 + 5 + 3 + 10

25532

Cy = = = 6.69(5*3) + (8*3) + (7*2) + (10*6) + (3*5) + (12*3) + (5*10)3 + 3 + 2 + 6 + 5 + 3 + 10

21432


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 #3Plant A $4 $2 $3Plant B $3 $2 $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?



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?



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?



What are the appropriate ABC groups of inventory items?



ABC AnalysisPercent of

Stock Number Annual $ Volume Annual $ Volume J24 12,500 46.2R26 9,000 33.3L02 3,200 11.8M12 1,550 5.8P33 620 2.3T72 65 0.2S67 53 0.2Q47 32 0.1V20 30 0.1

= 100.0



ABC AnalysisPercent of

Stock Number Annual $ Volume Annual $ Volume J24 12,500 46.2R26 9,000 33.3L02 3,200 11.8M12 1,550 5.8P33 620 2.3T72 65 0.2S67 53 0.2Q47 32 0.1V20 30 0.1

= 100.0

ABC GroupsAnnual Percent of

Class Items Volume $ VolumeA J24, R26 21,500 79.5B L02, M12 4,750 17.6C P33, &72, S67, Q47, V20 800 2.9

= 100.0


Assume you have a product with the following parameters:Annual Demand = 360 unitsHolding cost per year = $1.00 per unitOrder cost = $100 per order

What is the EOQ for this product?


Assume you have a product with the following parameters:Annual Demand = 360 unitsHolding cost per year = $1.00 per unitOrder cost = $100 per order

What is the EOQ for this product?

EOQ = = =2 * Demand * Order Cost

Holding Cost2 * 360 * 100

1

72000 = 268.33 items


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?


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 yearDemand

Q360268

T = = = 224 days between ordersWorking days

Expected number of orders3001.34


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


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

TC = +Demand * Order Cost

QQuantity of Items * Holding Cost

2

= + = 134 + 134 = $268360 * 100

268268 * 1

2


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.)


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 unitsCarrying 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

1350300

1350300

1350300

Safety stock = 5 unitsCarrying 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

13503001350300


S10 = 6 * 5 * .15 * =

$20.25

Total cost = Carrying cost + Stockout cost = $50 + $20.25 = $70.25

1350300


Stockout cost = $0

Total cost = Carrying cost + Stockout cost = $75 + $0 = $75.00


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?


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


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.



a. Find the probability that the employee is idle.b. Find the proportion of the time that the employee is

busy.c. Find the average number of people receiving and

waiting to receive some information.d. Find the average number of people waiting in line to

get some information.e. Find the average time a person seeking information

spends in the system.f. Find the expected time a person spends just waiting

in line to have a question answered (time in the queue).



a. Find the probability that the employee is idle.b. Find the proportion of the time that the employee is

busy.c. Find the average number of people receiving and

waiting to receive some information.d. Find the average number of people waiting in line to

get some information.e. Find the average time a person seeking information

spends in the system.f. Find the expected time a person spends just waiting

in line to have a question answered (time in the queue).

a. P0 = 1 – / = 1 – 20 / 30 = 0.33 33%

b. p = / = 0.66 66%c. Ls = / ( – ) = 20 / (30 – 20) = 2 people

d. Lq = 2 / ( – ) = 202 / 30(30 – 20) = 1.33 people

e. Ws = 1 / ( – ) = 1 / (30 – 20) = 0.10 hours

f. Wq = / ( – ) = 20 / 30(30 – 20) = 0.0667hours


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.


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.


Three students arrive per minute at a coffee machine that dispenses exactly four cups per minute at a constant rate. Describe the system parameters.


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( – )

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Review for Midterm 2 OPSM 301. Practice Problems Problem 1: A major drug store chain wishes to build a new warehouse to serve the whole Midwest. At the