Exam 6: Distribution and Network Models

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The shortest-route problem is a special case of the transshipment problem.

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A transshipment constraint must contain a variable for every arc entering or leaving the node.

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RVW (Restored Volkswagens) buys 15 used VW's at each of two car auctions each week held at different locations. It then transports the cars to repair shops it contracts with. When they are restored to RVW's specifications, RVW sells 10 each to three different used car lots. There are various costs associated with the average purchase and transportation prices from each auction to each repair shop. Also there are transportation costs from the repair shops to the used car lots. RVW is concerned with minimizing its total cost given the costs in the table below. RVW (Restored Volkswagens) buys 15 used VW's at each of two car auctions each week held at different locations. It then transports the cars to repair shops it contracts with. When they are restored to RVW's specifications, RVW sells 10 each to three different used car lots. There are various costs associated with the average purchase and transportation prices from each auction to each repair shop. Also there are transportation costs from the repair shops to the used car lots. RVW is concerned with minimizing its total cost given the costs in the table below.

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When the number of agents exceeds the number of tasks in an assignment problem, one or more dummy tasks must be introduced in the LP formulation or else the LP will not have a feasible solution.

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Constraints in a transshipment problem

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​Define the variables and constraints necessary in the LP formulation of the maximal flow problem.

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Transshipment problem allows shipments both in and out of some nodes while transportation problems do not.

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Which of the following is not true regarding an LP model of the assignment problem?

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Find the maximal flow from node 1 to node 7 in the following network. Find the maximal flow from node 1 to node 7 in the following network.

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​How is the shortest-route problem like the transshipment problem?

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