1. CitiSavings Bill Processing Operations CitiSavings operates three bill-processing centers as a part of its credit card business. These centers are located in the Los Angeles, Chicago, and New York areas, and they can process the following numbers of bills each day: Los Angeles Chicago New York 60,000 105,000 100,000 Daily bill processing capacity an average payment is approximately 10 cents per day. CitiSavings would like to determine to which processing center customers from the different regions should mail their payments in order to minimize the float, i.e., the interest income lost due to the in-transit time of the payments. a. (10 points) Formulate and solve the decision model CitiSavings is facing. Under the optimal mailing plan, what is the daily float? b. (5 points) The USPS is changing its delivery network, and CitiSavings has discovered that the average number of days that a bill spends in transit from the West to Chicago will increase from 6 to 7 days. How will this change your recommended assignment plan and the associated daily float? Can this question be answered without re- solving the model? Explain. c (5 points) By how much would the bill-processing capacity in New York have to decrease before your recommended solution would change? Explain your answer. d. (5 points) CitiSavings realizes that it can expand the processing capacity in Los Angeles center by 15,000 units at a total cost of $3,000 per day. Should this be done? Explain. CitiSavings intends to merge with BankZero, which has its own set of processing centers for credit card bills. BankZero's processing centers are in Toledo, OH and Atlanta, GA. The processing capabilities of the full set of processing centers are as follows: Customers from around the country mail payments on their credit card bills to one of the three centers. The average number of bills to be processed, daily, is specified for each of four regions, as follows: Number of bills to be processed West 70,000 Midwest 50,000 East 80,000 South 40,000 Chicago New York Toledo Atlanta Los Angeles When a bill is mailed from a region to a processing center, it spends time in the U.S. Postal Service (USPS) delivery system. The table below shows the average number of days a bill spends in transit between each region and processing center: 60,000 105,000 100,000 135,000 155,000 Daily processing capacity Los Angeles Chicago New York West 2 6 8 Midwest 6 2 5 By region, the daily number of bills to be processed for the two companies' combined customer bases, and the transit times are as follows: Bills to be Los Chicago New Toledo Atlanta processed Angeles York West 100,000 2 6 8 8 East 8 5 2 6 South 8 5 5 Midwest 150,000 6 2 5 2 5 Each day a bill spends in transit is a day's worth of interest CitiSavings loses on the payment received. At a 5% annual interest rate, the interest lost on Prof. Joern Meissner, PhD Prof. Joern Meissner, PhD East 2 100,000 8 5 5 5 South 100,000 8 5 5 5 2 CitiSavings recognizes that the combined operations would have significant excess capacity and contemplates saving money by closing some of the processing centers. CitiSavings estimates that the cost of closing down a facility is negligibly small, while the daily fixed costs of operating the five facilities are as follows: Los Chicago New York Toledo Atlanta Angeles Fixed daily $12,000 $21,000 $20,000 $40,000 $30,000 operating cost CitiSavings would like to minimize the sum of the operating costs of the facilities, plus the float. e. (5 points) Formulate and solve this new decision model. According to your analysis, which facilities should be closed down? f. (5 points) CitiSavings' management would like to consider the expansion of the capacity at the Los Angeles processing center as another option within an overall consolidation plan. That is, in addition to either closing the center or leaving it at the current capacity, they want to consider adding the option of expanding LA's capacity by 15,000 bills-per-day. The additional cost would be $3,000 per day. Extend the formulation of your problem in e) to include this additional option and solve the resulting model. Will this extra-capacity option be exercised? 1. CitiSavings Bill Processing Operations CitiSavings operates three bill-processing centers as a part of its credit card business. These centers are located in the Los Angeles, Chicago, and New York areas, and they can process the following numbers of bills each day: Los Angeles Chicago New York 60,000 105,000 100,000 Daily bill processing capacity an average payment is approximately 10 cents per day. CitiSavings would like to determine to which processing center customers from the different regions should mail their payments in order to minimize the float, i.e., the interest income lost due to the in-transit time of the payments. a. (10 points) Formulate and solve the decision model CitiSavings is facing. Under the optimal mailing plan, what is the daily float? b. (5 points) The USPS is changing its delivery network, and CitiSavings has discovered that the average number of days that a bill spends in transit from the West to Chicago will increase from 6 to 7 days. How will this change your recommended assignment plan and the associated daily float? Can this question be answered without re- solving the model? Explain. c (5 points) By how much would the bill-processing capacity in New York have to decrease before your recommended solution would change? Explain your answer. d. (5 points) CitiSavings realizes that it can expand the processing capacity in Los Angeles center by 15,000 units at a total cost of $3,000 per day. Should this be done? Explain. CitiSavings intends to merge with BankZero, which has its own set of processing centers for credit card bills. BankZero's processing centers are in Toledo, OH and Atlanta, GA. The processing capabilities of the full set of processing centers are as follows: Customers from around the country mail payments on their credit card bills to one of the three centers. The average number of bills to be processed, daily, is specified for each of four regions, as follows: Number of bills to be processed West 70,000 Midwest 50,000 East 80,000 South 40,000 Chicago New York Toledo Atlanta Los Angeles When a bill is mailed from a region to a processing center, it spends time in the U.S. Postal Service (USPS) delivery system. The table below shows the average number of days a bill spends in transit between each region and processing center: 60,000 105,000 100,000 135,000 155,000 Daily processing capacity Los Angeles Chicago New York West 2 6 8 Midwest 6 2 5 By region, the daily number of bills to be processed for the two companies' combined customer bases, and the transit times are as follows: Bills to be Los Chicago New Toledo Atlanta processed Angeles York West 100,000 2 6 8 8 East 8 5 2 6 South 8 5 5 Midwest 150,000 6 2 5 2 5 Each day a bill spends in transit is a day's worth of interest CitiSavings loses on the payment received. At a 5% annual interest rate, the interest lost on Prof. Joern Meissner, PhD Prof. Joern Meissner, PhD East 2 100,000 8 5 5 5 South 100,000 8 5 5 5 2 CitiSavings recognizes that the combined operations would have significant excess capacity and contemplates saving money by closing some of the processing centers. CitiSavings estimates that the cost of closing down a facility is negligibly small, while the daily fixed costs of operating the five facilities are as follows: Los Chicago New York Toledo Atlanta Angeles Fixed daily $12,000 $21,000 $20,000 $40,000 $30,000 operating cost CitiSavings would like to minimize the sum of the operating costs of the facilities, plus the float. e. (5 points) Formulate and solve this new decision model. According to your analysis, which facilities should be closed down? f. (5 points) CitiSavings' management would like to consider the expansion of the capacity at the Los Angeles processing center as another option within an overall consolidation plan. That is, in addition to either closing the center or leaving it at the current capacity, they want to consider adding the option of expanding LA's capacity by 15,000 bills-per-day. The additional cost would be $3,000 per day. Extend the formulation of your problem in e) to include this additional option and solve the resulting model. Will this extra-capacity option be exercised