Exercise 1

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American Public University *

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5730

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Industrial Engineering

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Dec 6, 2023

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Webster University Colorado Springs SPSM 5730 EXERCISE #1 Due Friday 6/25/21 The launch campaign is a critical period for the spacecraft manufacturer to verify a spacecraft’s functionality prior to launching it into orbit for a 5 – 15 year operational life. But the campaign is also a significant commitment of personnel, equipment, and resources. In addition to maintaining a launch base team at a remote location, key equipment such as spacecraft shipping containers, Ground Support Equipment (GSE) and propellant loading equipment may be needed for other spacecraft being built at the manufacturer’s facilities or another launch campaign. As a result, the manufacturer attempts to minimize the campaign duration without jeopardizing the mission or switch out its resources as they are needed elsewhere. Various operations research (OR) techniques can be used to select launch vehicles and make resource allocation decisions to reduce operational costs. Launch campaigns follow relatively standard processes, varying slightly in logistics and schedules for the different launch vehicles and facilities. Aside from procuring just the launch service, the manufacturer’s cost to support a launch campaign includes: cost of living for the team, launch base support infrastructure (e.g. telecommunications), and transport for the team, the spacecraft, and consumable materials (e.g. propellants). If the manufacturer anticipates the need to launch a certain number of spacecraft during a given year, then the manufacturer can analyze the costs to run a campaign for each launch vehicle and select and combination that minimizes overall cost using linear programming techniques. An optimal (ie maximum or minimum) solution is found for a given function with specialized constraints on the variables of the function. You are going to compare four different launch vehicles to support a campaign to launch 10 SBIRS-Low satellites to support the geo constellation. They must all be launched in the next two years. Here is a table listing costs and other information associated with each vehicle. Cost/Rocket Cost Support Max avail/yr. Process time Launch time Antares M C 3 Q L Atlas N C 2 R L Delta O C 2 S L Falcon 9 P C 3 T L
Webster University Colorado Springs 1. Write the objective and constraints for this problem. Objective - The objective is to minimize cost to run a launch campaign to verify a spacecraft's functionality prior to launching it into orbit for a 5 - 15 year operational life Constraints- The cost of living for the team, launch base support infrastructure, transport for the team, the spacecraft and consumable materials. 2. Determine appropriate values for M, N, O, P, Q, R, S, and T. You may assume 2 months of processing time (Q, R, S, T) per stage. Also let C = $5M and L = 30 days. Find the best set of launch vehicles to satisfy the requirement. Cite your references. Antares: C = LM + 3C. Atlas: C = LN+ 3C $5,000,000 = 30M + (3 × 60) $5,000,000 = 30M + (2 × 60) $5,000,000 = 30M + 180. $5,000,000 = 30M + 120 $5,000,000 - 180 = 30M. $5,000,000 - 180 = 30M $4,999,820 ÷ 30 = 30M ÷30. $4,999,880 ÷ 30 = 30M ÷30 M = $166,661 M = $166,663 Falcon 9: C = LP+ 3C. Delta C = LO + 3C $5,000,000 = 30M + (3 × 60) $5,000,000 = 30M + (2 × 60) $5,000,000 = 30M + 180. $5,000,000 = 30M + 120 $5,000,000 - 180 = 30M. $5,000,000 - 180 = 30M $4,999,820 ÷ 30 = 30M ÷30. $4,999,880 ÷ 30 = 30M ÷30 M = $166,661 M = $166,663
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