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Exam 10: Distribution and Network Problems

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Question 1

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Which of the following is not true regarding the linear programming formulation of a transportation problem?

A) Costs appear only in the objective function.
B) The number of variables is (number of origins) x (number of destinations) .
C) The number of constraints is (number of origins) x (number of destinations) .
D) The constraints' left-hand side coefficients are either 0 or 1.

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Question 2

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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. 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

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Team A works with the forecast...

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Question 3

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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. 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

Write the linear program for this transshipment problem.

The shortest-route problem finds the shortest-route

A transportation problem with 3 sources and 4 destinations will have 7 decision variables.

We assume in the maximal flow problem that

The assignment problem is a special case of the

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

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

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

Arcs in a transshipment problem

Flow in a transportation network is limited to one direction.

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

In a transportation problem with total supply equal to total demand,if there are four origins and seven destinations,and there is a unique optimal solution,the optimal solution will utilize 11 shipping routes.

A transshipment problem is a generalization of the transportation problem in which certain nodes are neither supply nodes nor destination nodes.

Consider a shortest route problem in which a bank courier must travel between branches and the main operations center.When represented with a network,

Fodak must schedule its production of camera film for the first four months of the year.Film demand (in 1,000s of rolls)in January,February,March and April is expected to be 300,500,650 and 400,respectively.Fodak's production capacity is 500 thousand rolls of film per month.The film business is highly competitive,so Fodak cannot afford to lose sales or keep its customers waiting.Meeting month i 's demand with month i +1's production is unacceptable. Film produced in month i can be used to meet demand in month i or can be held in inventory to meet demand in month i +1 or month i +2 (but not later due to the film's limited shelflife).There is no film in inventory at the start of January. The film's production and delivery cost per thousand rolls will be $500 in January and February.This cost will increase to $600 in March and April due to a new labor contract.Any film put in inventory requires additional transport costing $100 per thousand rolls.It costs $50 per thousand rolls to hold film in inventory from one month to the next. a.Modeling this problem as a transshipment problem,draw the network representation. b.Formulate and solve this problem as a linear program.

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,

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. Shipping costs are: