Exam 10: Distribution and Network Problems

Write the LP formulation for this transportation problem.

Consider the following shortest-route problem involving six cities with the distances given.Draw the network for this problem and formulate the LP for finding the shortest distance from City 1 to City 6. Path Distance 1 to 2 3 1 to 3 2 2 to 4 4 2 to 5 5 3 to 4 3 3 to 5 7 4 to 6 6 5 to 6 2

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

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.

The number of units shipped from origin i to destination j is represented by

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

The maximal flow problem can be formulated as a capacitated transshipment problem.

In the general assignment problem,one agent can be assigned to several tasks.

The objective of the transportation problem is to

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

A foreman is trying to assign crews to produce the maximum number of parts per hour of a certain product.He has three crews and four possible work centers.The estimated number of parts per hour for each crew at each work center is summarized below.Solve for the optimal assignment of crews to work centers.

A beer distributor needs to plan how to make deliveries from its warehouse (Node 1)to a supermarket (Node 7),as shown in the network below.Develop the LP formulation for finding the shortest route from the warehouse to the supermarket.

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. a.Given the costs below,draw a network representation for this problem. b.Formulate this problem as a transshipment linear programming model.

A network of railway lines connects the main lines entering and leaving a city.Speed limits,track reconstruction,and train length restrictions lead to the flow diagram below,where the numbers represent how many cars can pass per hour.Formulate an LP to find the maximal flow in cars per hour from Node 1 to Node F.

Consider the network below.Formulate the LP for finding the shortest-route path from node 1 to node 7.

In a transshipment problem,shipments

The capacitated transportation problem includes constraints which reflect limited capacity on a route.

If a transportation problem has four origins and five destinations,the LP formulation of the problem will have

In the LP formulation of a maximal flow problem,a conservation-of-flow constraint ensures that an arc's flow capacity is not exceeded.

Peaches are to be transported from three orchard regions to two canneries.Intermediate stops at a consolidation station are possible. Shipment costs are shown in the table below.Where no cost is given,shipments are not possible.Where costs are shown,shipments are possible in either direction.Draw the network model for this problem.