Exam 6: Distribution and Network Problems

Draw the network for this assignment problem. Min 10x_1A + 12x_1B + 15x_1C + 25x_1D + 11x_2A + 14x_2B + 19x_2C + 32x_2D + 18x_3A + 21x_3B + 23x_3C + 29x_3D + 15x_4A + 20x_4B + 26x_4C + 28x_4D s.t. x_1A + x_1B + x_1C + x_1D = 1 x_2A + x_2B + x_2C + x_2D = 1 x_3A + x_3B + x_3C + x_3D = 1 x_4A + x_4B + x_4C + x_4D = 1 x_1A + x_2A + x_3A + x_4A = 1 x_1B + x _2B + x_3B + x_4B = 1 x_1C + x _2C + x_3C + x_4C = 1 x_1D + x_2D + x_3D + x_4D = 1

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

In the general linear programming model of the assignment problem,

The direction of flow in the shortest-route problem is always out of the origin node and into the destination node.

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. $\text { a. Given the costs below, draw a network representation for this problem. }$ Repait Shops Used Car Lots 1 2 Auction 1 550 500 Auction 2 600 450 1 2 3 1 250 300 500 2 350 650 450 $\text { b. Formulate this problem as a transshipment linear programming model. }$ $$

Converting a transportation problem LP from cost minimization to profit maximization requires only changing the objective function; the conversion does not affect the constraints.

Explain how the general linear programming model of the assignment problem can be modified to handle problems involving a maximization function, unacceptable assignments, and supply not equally demand.

The assignment problem is a special case of the

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.

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

Write the LP formulation for this transportation problem.

Draw the network for this transportation problem. Min 2+3+5+9+12+10 s.t. ++\leq500 ++\leq400 +=300 +=300 +=300 \geq0

The parts of a network that represent the origins are

The assignment problem constraint x₃₁ + x₃₂ + x₃₃ + x₃₄ $\le$ 2 means