Exam 10: Distribution and Network Models

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

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

The network flows into and out of demand nodes are what makes the production and inventory application modeled in the textbook a

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

Constraints in a transshipment problem

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

Draw the network for this assignment problem. Min 10+12+15+25+11+14+19+32 +18+21+23+29+15+20+26+28 s.t. +++=1 +++=1 +++=1 +++=1 +++=1 +++=1 +++=1 +++=1

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

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

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.

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 parts of a network that represent the origins are

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. Work Center WC1 WC2 WC3 WC4 Crew A 15 20 18 30 Crew B 20 22 26 30 Crew C 25 26 27 30

Arcs in a transshipment problem

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

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 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

Write the linear program for this transshipment problem.

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

A transportation problem with 3 sources and 4 destinations will have 7 variables in the objective function.