BUS 381: Additional Optimization Problems 1. Chawdhry Cloud Services operates several data centers across the United States that contain servers which store and process the data on the Internet. Suppose that Galaxy Cloud Services currently has five outdated data centers: one each in Michigan, Ohio, and California and two in New York. Management is considering increasing the capacity of these data centers to keep up with increasing demand. Each data center contains servers that are dedicated to "Secure" data and to "Super Secure" data. The cost to update each data center and the resulting increase in server capacity for each type of server is as follows: Data Center Cost ($ millions) Secure Servers Super Secure Servers Michigan 2.5 50 30 New York 1 3.5 80 40 New York 2 3.5 40 80 Ohio 4.0 90 60 California 2.0 20 30 OBJECTIVE: The projected needs are for a total increase in capacity of 90 Secure servers and 90 Super Secure servers. Management wants to determine which data centers to update to meet projected needs and, at the same time, minimize the total cost of the added capacity. ANSWER: Model New York Michigan 1 Upgrade Data Center Min Cost ($M) 0 6 New York 2 0 Ohio 0 California 1 1 Solution 2 Model New York Michigan 1 Upgrade Data Center Min Cost ($M) 1 6 0 New York 2 Ohio 1 California 0 0 Problem 2 1. Chawdhry Co. provides paper to smaller companies whose volumes are not large enough to warrant dealing directly with the paper mill. STAR receives 100-feet-wide paper rolls from the mill and cuts the rolls into smaller rolls of widths 12, 15, and 30 feet. The demands for these widths vary from week to week. The following cutting patterns have been established: Number of: Pattern 12ft. 15ft. 30ft. Trim Loss 1 0 6 0 10 ft. 2 0 0 3 10 ft. 3 8 0 0 4 ft. 4 2 1 2 1 ft. 5 7 1 0 1 ft. Trim loss is the leftover paper from a pattern (for example, for pattern 4, 2(12) + 1(15) + 2(30) = 99 feet used resulting in 100-99 = 1 foot of trim loss). Demands this week are 5,670 12-foot rolls, 1,680 15-foot rolls, and 3,350 30-foot rolls. OBJECTIVE: Develop an all-integer model that will determine how many 100-foot rolls to cut into each of the five patterns in order to meet demand and minimize trim loss (leftover paper from a pattern). ANSWER: Problem 3 Problem 2: 50 Points Your Manufacturing company has been tasked with building Televisions, computers, and microwaves. To make these products, there are three sub components: Capacitors, Resistors, and Processors. Below shows the maximum number of Televisions, computers, and microwaves we can make along with the maximum number of capacitors, resistors, and processors available to make them. Your Revenue function is determined as $2 for every capacitor used, $3 for every resistor, and $25 for each processor. However, there are FIXED costs if you decide to use the these. If you use Capacitors, it will have a fixed cost of $50, Resistors will have a fixed cost of $60, and Processors have a fixed cost of $250. The total profit is Revenue – Cost. Objective: Determine how many Capacitors, resisters, and processors to use in order to maximize profit. You will also need to capture if you choose to use Capacitors (SC), Resistors (SR), and Processors (SP). (NOTE: The profit is made up of 6 numbers: First three for Revenue and last three for cost, thus why they are negative) Also, note SC, SR, SP are 1 or 0, so you will need to add a constraint in the solver for “BIN” instead of > or < just like you did Integer. Lastly, you will need three constraints that show if SC, SR, or SP are 0, then the Available for Capacitor , Resistor, and Processors, is 0 Ie: Constraint Capacitor 159
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