Linear programming
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The city of Spring View is taking bids from six bus companies on the eight routes that must be driven in the surround school district. Each company enters a bid on how much it will charge to drive selected routes, although not all companies bit on all routes. The data are contained in the Excel file attached. If the company does not bid on a route, the corresponding cell is blank. The city must decide which companies to assign to which routes with the specifications that (1) if a company does not bid on a route, it cannot be assigned to that route, (2) exactly one company must be assigned to each route, and (3) a company can be assigned to at most two routes. The objective is to minimize the total cost of covering all routes.
in the optimal solution to the bus route assignment problem (provided in the Excel file), company 2 is assigned to bus routes 6 and 7. Support these two routes are far enough apart that is infeasible for one company to service both of them.
(a) Write down algebraic constraint in terms of the decision variables defined during lecture to accommodate this restriction.
(b) Add the constraint to the existing model and comment on the new optimal solution.
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a) Let the decision variable be , where i=1,2,...,31, since there are 31 different routes, displayed below. For example, is the route from origin 1 to destination 2, is the route from origin 1 to destination 3, and ...
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