Exam 6: Optimization Models With Integer Variables
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The binary variables in the fixed cost models correspond to:
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Solver may be unable to solve some integer programming problems,even when they have an optimal solution.
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Exhibit 6-3
PharmaCo wants to determine how to deploy sales representatives across its Western U.S. region to support a new drug for obesity. Sales representatives will be located in a "home city", which they serve, in addition to cities with feasible commuting distance, with the objective that all cities must be served by at least one sales representative. The feasible connections between each city in the region are listed below (1 indicates a feasible connection):
-Refer to Exhibit 6-3.Formulate an integer programming model to identify a feasible deployment plan to the sales representatives.What is the minimum number of representatives that can cover this region
What are their home cities
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The branching part of the branch and bound algorithm that Solver uses to solve integer programming models means that the algorithm:
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Exhibit 6-2
Sinclair Plastics operates two chemical plants which produce polyethylene; the Ohio Valley plant which can produce up to 10,000 tons per month and the Lakeview plant which can produce up to 7,000 tons per month. Sinclair sells its polyethylene to three different auto manufacturing plants, Grand Rapids (demand = 3000 tons per month), Blue Ridge (demand = 5000 tons per month), and Sunset (demand = 4000 tons per month). The variable unit cost of shipping a ton is $1 per mile. The number of miles between the respective plants is shown in the table below:
In addition to the variable unit costs of shipping, Sinclair incurs a fixed handling cost (of pickup and delivery) for any shipping routes it uses. These costs are discounted for longer routes, as shown below:
Grand Rapids Blue Ridge Sunset Ohio Valley 50 40 100 Lakeview 60 50 75
Fixed Cost Levels Distance (mi) Fixed Cost <=25 \ 100,000 <=50 \ 60,000 <=75 \ 20,000 <=100 \ 0
-Refer to Exhibit 6-2.What problem will occur if we use an IF statement to model the fixed handling costs
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Exhibit 6-2
Sinclair Plastics operates two chemical plants which produce polyethylene; the Ohio Valley plant which can produce up to 10,000 tons per month and the Lakeview plant which can produce up to 7,000 tons per month. Sinclair sells its polyethylene to three different auto manufacturing plants, Grand Rapids (demand = 3000 tons per month), Blue Ridge (demand = 5000 tons per month), and Sunset (demand = 4000 tons per month). The variable unit cost of shipping a ton is $1 per mile. The number of miles between the respective plants is shown in the table below:
In addition to the variable unit costs of shipping, Sinclair incurs a fixed handling cost (of pickup and delivery) for any shipping routes it uses. These costs are discounted for longer routes, as shown below:
Grand Rapids Blue Ridge Sunset Ohio Valley 50 40 100 Lakeview 60 50 75
Fixed Cost Levels Distance (mi) Fixed Cost <=25 \ 100,000 <=50 \ 60,000 <=75 \ 20,000 <=100 \ 0
-Refer to Exhibit 6-2.This problem is an example of what type of integer programming model
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Complete enumeration of all possible solutions in many integer programming problems is impractical.
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Any integer program involving 0 − 1 variables with ____ constraint(s)is called a knapsack problem.
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Problems with a fixed cost that is incurred only if an activity is undertaken at a positive level are inherently nonlinear.
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Exhibit 6-3
PharmaCo wants to determine how to deploy sales representatives across its Western U.S. region to support a new drug for obesity. Sales representatives will be located in a "home city", which they serve, in addition to cities with feasible commuting distance, with the objective that all cities must be served by at least one sales representative. The feasible connections between each city in the region are listed below (1 indicates a feasible connection):
-Refer to Exhibit 6-3.This problem is an example of what type of integer programming model
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