BACKGROUND: CreditMаster is а nаtiоnal credit card cоmpany with thоusands of cardholders located across the United States. Every day throughout the month, CreditMaster sends out statements to different customers summarizing their charges for the previous month. Customers then have 30 days to remit a payment for their bills. CreditMaster includes a pre-addressed envelope with each statement for customers to use in making their payments. One of the critical problems facing CreditMaster involves determining what address to put on the pre-addressed envelopes sent to various parts of the country. The amount of time that elapses between when a customer writes his or her check and when CreditMaster receives the cash for the check is referred to as float. Checks can spend several days floating in the mail and in processing before being cashed. This float time represents lost revenue to CreditMaster because if the company could receive and cash these checks immediately, it could earn additional interest on these funds. To reduce the interest being lost from floating checks, CreditMaster would like to implement a lockbox system to speed the processing of checks. Under such a system, CreditMaster, for example, might have all its customers on the West Coast send their payments to a bank in Sacramento which, for a fee, processes the checks and deposits the proceeds in a CreditMaster account. Similarly, CreditMaster might arrange for a similar service with a bank on the East Coast for its customers there. Such lockbox systems are a common method companies use to improve their cash flows. Question: CreditMaster has identified six different cities as possible lockbox sites. The annual fixed cost of operating a lockbox in each of the possible locations is given in the following table. Table 1: Annual Lockbox Operating Costs Sacramento Denver Chicago Dallas New York Atlanta 25,000 30,000 35,000 35,000 30,000 35,000 An analysis was done to determine the average number of days a check floats when sent from seven different regions of the country to each of these six cities. The results of this analysis are summarized in the following table. This table indicates, for instance, that a check sent from the central region of the country to New York spends an average of three days in the mail and in processing before CreditMaster actually receives the cash for the check. Table 2: Average Days of Float Between Regions and Possible Lockbox Locations Sacramento Denver Chicago Dallas New York Atlanta Central 4 2 2 2 3 3 Mid-Atlantic 6 4 3 4 2 2 Midwest 3 2 3 2 5 4 Northeast 6 4 2 5 2 3 Northwest 2 3 5 4 6 7 Southeast 7 4 3 2 4 2 Southwest 2 3 6 2 7 6 Further analysis was done to determine the average amount of payments being sent from each region of the country. These results are given next: Table 3: Average Daily Payments by Region Payments Central 45,000 Mid-Atlantic 65,000 Midwest 50,000 Northeast 90,000 Northwest 70,000 Southeast 80,000 Southwest 60,000 Thus, if payments from the Central region are sent to New York, on any given day, there is an average of $135,000 in undeposited checks from the Central region. Because CreditMaster can earn 15% on cash deposits, it would be losing $20,250 per year in potential interest on these checks alone. CreditMaster would like you to make an LP to determine which of the six potential lockbox locations should be used, and to which lockbox location should each region be assigned if a maximum of four regions can be assigned to any lockbox location.
Burnt Beаns (Medium Versiоn) is а fаst-grоwing East Cоast coffee company based in Charleston, SC where they currently have their only production facility. Due to increased demand for its cold brew products, the company is exploring expansion options. They currently have warehouses from which they supply retailers in 4 cities (Charlston, Atlanta, Raleigh, and Jacksonville). It is considering activating up to three additional regional roasting centers (new production) this year to better serve markets in the Southeast. The initial proposal is to is to collocate up to three new production facilities in cities where they have warehouses. Your goal is to help them determine which of the 3 facilities they should open in the coming year. Your Task Formulate and solve a linear program to minimize the total cost of production, shipping, plant tooling, and new facility fixed cost (i.e. insurance, taxes, facility maintenance). While meeting customer demand in each region. Which plants to activate Demand Forecast (Units) Region Demand Atlanta 4150 Charleston 4400 Jacksonville 3000 Raleigh 3300 Plant Capacities and Costs Plant Capacity/Quarter Fixed buildout cost (one time) New Quartey Fixed ($/Qtr.) Prod. Cost Atlanta 1500 $5,000 $3,500 $1.90 Charleston 2000 $0 $0 $2.00 Jacksonville 1000 $3,500 $2,500 $2.00 Raleigh 1200 $6,500 $4,000 $2.10 Shipping Costs per Unit From To Atlanta Charleston Jacksonville Raleigh Atlanta $0.00 $0.25 $0.20 $0.20 Charleston $0.25 $0.00 $0.35 $0.30 Jacksonville $0.20 $0.35 $0.00 $0.25 Raleigh $0.20 $0.30 $0.25 $0.00
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