The Washington State Legislature Is Trying to Decide on Locations

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The Answer is This is a set covering problem.The decisions to be made are whether to locate a team in each county.The requirement for each county is that there be a team nearby,where nearby is defined as in that county or an adjacent county.The data for this problem are the coverage data.In particular,in the row representing each county,there is a 1 in every column that would satisfy the coverage of the row's county if there were a team there.For example,Clallum county would be covered if there is a team in either Clallum or Jefferson county.

This is a set covering problem.The decisions to be made are whether to locate a team in each county.The requirement for each county is that there be a team nearby,where nearby is defined as in that county or an adjacent county.The data for this problem are the coverage data.In particular,in the row representing each county,there is a 1 in every column that would satisfy the coverage of the row's county if there were a team there.For example,Clallum county would be covered if there is a team in either Clallum or Jefferson county. The decisions to be made in this problem are whether or not to place a team in each county.Thus,a binary variable is defined for each county in the changing cells Team? (D44:AN44).The values in Team? (D44:AN44)will eventually be determined by Solver.For now,arbitrary values are entered.The goal is to minimize the total number of teams.Thus,the objective cell should calculate this total: Total Teams = SUM(Teams?).This formula is entered into TotalTeams (AQ44). The functional constraints in this problem are that each county must have at least one team nearby.Given Teams? (D44:AN44),we calculate the number of teams nearby in TeamsNearby(AO5:AO41).For Clallum county,this will be =SUMPRODUCT(D5:AN5,Team?).Using a range name or an absolute reference for Team?,this formula can be copied into cells AO6:AO41 to calculate the number of teams nearby for the other counties.The TeamsNearby (AO5:AO41)must be >= 1,as indicated by the >= in AP5:AP41. The Solver information and solved spreadsheet are shown below. Thus,they should locate a team in Jefferson,King,Lewis,Clark,Okanagan,Blanton,Spokane,and Whitman counties,for a total of 8 teams.(There are multiple optimal solutions for this problem.)

The decisions to be made in this problem are whether or not to place a team in each county.Thus,a binary variable is defined for each county in the changing cells Team? (D44:AN44).The values in Team? (D44:AN44)will eventually be determined by Solver.For now,arbitrary values are entered.The goal is to minimize the total number of teams.Thus,the objective cell should calculate this total: Total Teams = SUM(Teams?).This formula is entered into TotalTeams (AQ44).

The functional constraints in this problem are that each county must have at least one team nearby.Given Teams? (D44:AN44),we calculate the number of teams nearby in TeamsNearby(AO5:AO41).For Clallum county,this will be =SUMPRODUCT(D5:AN5,Team?).Using a range name or an absolute reference for Team?,this formula can be copied into cells AO6:AO41 to calculate the number of teams nearby for the other counties.The TeamsNearby (AO5:AO41)must be >= 1,as indicated by the >= in AP5:AP41.

The Solver information and solved spreadsheet are shown below.

Thus,they should locate a team in Jefferson,King,Lewis,Clark,Okanagan,Blanton,Spokane,and Whitman counties,for a total of 8 teams.(There are multiple optimal solutions for this problem.)

The Washington State Legislature Is Trying to Decide on Locations

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The Washington State Legislature Is Trying to Decide on Locations

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Correct Answer:
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