Read the description of the following three optimization problems. Consider then the components of these problems that are itemized. For each of these components, identify whether it belongs to the data, the variables, the constraints or the objectives. (Note: all situations described below are inspired by practical applications of optimization detailed in the journal IJAA (Informs Journal on Applied Analytics).) 1. National Science Foundation (NSF) scheduler: The NSF provides a significant amount of funding for scientific research in the United States. In 2014, NSF's budget allocated over seven billion US dollars to research and related activities. The NSF receives about 55,000 research proposals every year across all directorates. Of these, about twenty percent are funded. Staff at NSF select advisors from relevant academic communities to serve on panels to review most proposals. NSF hosted approximately 1,600 panels between October 2012 and September 2013, which means that many panels might be meeting simultaneously on any given day. Determining which meeting room to use for each panel and on what day to run each panel is a challenging scheduling problem. NSF has approximately 60 meeting rooms that it uses for hosting panel discussions at its headquarters. Each room has a number of properties that impact its suitability for a specific panel; these properties include the room's size, the technology available in the room (e.g., projectors), and whether the room is associated with a specific directorate. Additionally, panels that meet for multiple consecutive days must remain in the same room for the duration of the panel. (a) Capacity of each room. (b) Each room should not be used by more than one panel on each date on which the room is available. (c) Size, or number of panelists, for each panel. (d) NSF wants to schedule as many panels as possible. (e) Each panel should be assigned to at most one room and one beginning date. (f) Beginning date for each panel. (g) If a panel begins on a given date in a given room, it also uses or occupies that room for the duration of the panel. (h) Duration, or number of days, for each panel.

Read the description of the following three optimization problems. Consider then the components of these problems that are itemized. For each of these components, identify whether it belongs to the data, the variables, the constraints or the objectives. (Note: all situations described below are inspired by practical applications of optimization detailed in the journal IJAA (Informs Journal on Applied Analytics).) 1. National Science Foundation (NSF) scheduler: The NSF provides a significant amount of funding for scientific research in the United States. In 2014, NSF's budget allocated over seven billion US dollars to research and related activities. The NSF receives about 55,000 research proposals every year across all directorates. Of these, about twenty percent are funded. Staff at NSF select advisors from relevant academic communities to serve on panels to review most proposals. NSF hosted approximately 1,600 panels between October 2012 and September 2013, which means that many panels might be meeting simultaneously on any given day. Determining which meeting room to use for each panel and on what day to run each panel is a challenging scheduling problem. NSF has approximately 60 meeting rooms that it uses for hosting panel discussions at its headquarters. Each room has a number of properties that impact its suitability for a specific panel; these properties include the room's size, the technology available in the room (e.g., projectors), and whether the room is associated with a specific directorate. Additionally, panels that meet for multiple consecutive days must remain in the same room for the duration of the panel. (a) Capacity of each room. (b) Each room should not be used by more than one panel on each date on which the room is available. (c) Size, or number of panelists, for each panel. (d) NSF wants to schedule as many panels as possible. (e) Each panel should be assigned to at most one room and one beginning date. (f) Beginning date for each panel. (g) If a panel begins on a given date in a given room, it also uses or occupies that room for the duration of the panel. (h) Duration, or number of days, for each panel.