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 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 20 4 7 5 Labor cost 5 8 8 4 Taxes 15 8 9 7 Nearness to suppliers 10 10 6 10 Which city should they choose?

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 80 140 100 40 40 20 120 135 105 100 60 100 Total 340 375 325 Ratings Factor Weights Peoria Des Moines Chicago Nearness to markets 20 4 7 5 Labor cost 5 8 8 4 Taxes 15 8 9 7 Nearness to suppliers 10 10 6 10 Which city should they choose?

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?

Practice Problems Problem 2: 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: 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 300,000 + 5.75x = 100,000 + 8.00x 2.25x = 200,000 x = 88,888 For what unit sales volume should they choose each location?

Practice Problems Problem 2: Transition between Waco and Tijuana Locate in Fayetteville 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: 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?

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.

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

Practice Problems Problem 3: Cx = = = 7.97 Cy = = = 6.69 (10*3) + (3*3) + (4*2) + (15*6) + (13*5) + (1*3) + (5*10) 3 + 3 + 2 + 6 + 5 + 3 + 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

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

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

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

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

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

Practice Problems Problem 6: ABC Analysis Percent of Stock Number Annual $ Volume Annual $ Volume J24 12,500 46.2 R26 9,000 33.3 L02 3,200 11.8 M12 1,550 5.8 P33 620 2.3 T72 65 0.2 S67 53 0.2 Q47 32 0.1 V20 30 0.1  = 100.0 Problem 6: What are the appropriate ABC groups of inventory items?

Practice Problems Problem 1: ABC Groups Annual Percent of ABC Analysis Percent of Stock Number Annual $ Volume Annual $ Volume J24 12,500 46.2 R26 9,000 33.3 L02 3,200 11.8 M12 1,550 5.8 P33 620 2.3 T72 65 0.2 S67 53 0.2 Q47 32 0.1 V20 30 0.1  = 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 21,500 79.5 B L02, M12 4,750 17.6 C P33, &72, S67, Q47, V20 800 2.9  = 100.0

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?

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 72000 = 268.33 items

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?

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

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

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 = + = 134 + 134 = $268 360 * 100 268 268 * 1

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.)

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

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?

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) + 180 = 66 + 180 = 246 Ceiling Lamps

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.

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).

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) = 0.0667hours

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.

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 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.

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.

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 = = 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( – )   1