Exam 6: Distribution and Network Problems

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

Explain what adjustments are made to the transportation linear program when there are unacceptable routes.

Write the linear program for this transshipment problem.

The difference between the transportation and assignment problems is that

Whenever total supply is less than total demand in a transportation problem, the LP model does not determine how the unsatisfied demand is handled.

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

How is the assignment linear program different from the transportation model?

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

A professor has been contacted by four not-for-profit agencies that are willing to work with student consulting teams. The agencies need help with such things as budgeting, information systems, coordinating volunteers, and forecasting. Although each of the four student teams could work with any of the agencies, the professor feels that there is a difference in the amount of time it would take each group to solve each problem. The professor's estimate of the time, in days, is given in the table below. Use the computer solution to see which team works with which project. Projects Team Budgeting Information Volunteers Forecasting A 32 35 15 27 B 38 40 18 35 C 41 42 25 38 D 45 45 30 42 ASSIGNMENT PROBLEM *********************** OBJECTIVE: MINIMIZATION SUMMARY OF UNIT COST OR REVENUE DATA TASK AGENT 1 2 3 4 \@cdots \@cdots \@cdots \@cdots \@cdots 1 32 35 15 27 2 38 40 18 35 3 41 42 25 38 4 45 45 30 42 OPTIMAL ASSIGNMENTS COST/REVENUE ************ ********** ASSIGN AGENT 3 TO TASK 1 41 ASSIGN AGENT 4 TO TASK 2 45 ASSIGN AGENT 2 TO TASK 3 18 ASSIGN AGENT 1 TO TASK 4 27 TOTAL COST/REVENUE 131

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.

When a route in a transportation problem is unacceptable, the corresponding variable can be removed from the LP formulation.

Is it a coincidence to obtain integer solutions to network problems? Explain.

The objective of the transportation problem is to

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

The shortest-route problem finds the shortest-route

Consider a maximal flow problem in which vehicle traffic entering a city is routed among several routes before eventually leaving the city. When represented with a network,

The following table shows the unit shipping cost between cities, the supply at each source city, and the demand at each destination city. The Management Scientist solution is shown. Report the optimal solution. Destination Source Terre Haute Indianapolis Ft. Wayne South Bend Supply St. Louis 8 6 12 9 100 Evansville 5 5 10 8 100 Bloomington 3 2 9 10 100 Dem and 150 60 45 45 TRANSPORTATION PROBLEM *************************** OBJECTIVE: MINIMIZATION SUMMARY OF ORIGIN SUPPLIES ****************************** ORIGIN SUPPLY 1 100 2 100 3 100 SUMMARY OF DESTINATION DEMANDS ************************************* DESTINATION DEMAND 1 150 2 60 3 45 4 45 SUMMARY OF UNIT COST OR REVENUE DATA ******************************************* FROM TO DESTINATION ORIGIN 1 2 3 4 1 8 6 12 9 2 5 5 10 8 3 3 2 9 10 OPTIMAL TRANSPORTATION SCHEDULE ************************************** SHIP FROM TO DESTINATION ORIGIN 1 2 3 4 1 0 10 45 45 2 100 0 0 0 3 50 50 0 0 TOTAL TRANSPORTATION COST OR REVENUE IS 1755

The problem which deals with the distribution of goods from several sources to several destinations is the

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

Canning Transport is to move goods from three factories to three distribution centers. Information about the move is given below. Give the network model and the linear programming model for this problem. Source Supply Destination Demand A 200 50 B 100 125 C 150 125 Shipping costs are: Destination Source A 3 2 5 B 9 10 - C 5 6 4 (Source B cannot ship to destination Z)