Exam 10: Distribution and Network Models

The difference between the transportation and assignment problems is that

The shortest-route problem finds the shortest-route

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

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.

The objective of the transportation problem is to

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 Demand 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 \ldots\ldots\ldots \ldots \ldots \ldots \ldots 1 0 10 45 45 2 100 0 0 0 3 50 50 0 0 TOTAL TRANSPORTATION COST OR REVENUE IS 1755

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

Write the LP formulation for this transportation problem.

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

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

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

A plant manager for a sporting goods manufacturer is in charge of assigning the manufacture of four new aluminum products to four different departments.Because of varying expertise and workloads,the different departments can produce the new products at various rates.If only one product is to be produced by each department and the daily output rates are given in the table below,which department should manufacture which product to maximize total daily product output? (Note: Department 1 does not have the facilities to produce golf clubs.) Department Baseball Bats Tennis Rackets Golf Clubs Racquetball Rackets 1 100 60 X 80 2 100 80 140 100 3 110 75 150 120 4 85 50 100 75 Formulate this assignment problem as a linear program.

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 the following shortest-route problem involving seven cities.The distances between the cities are given below.Draw the network model for this problem and formulate the LP for finding the shortest route from City 1 to City 7. Path Distance 1 to 2 6 1 to 3 10 1 to 4 7 2 to 3 4 2 to 5 5 3 to 4 5 3 to 5 2 3 to 6 4 4 to 6 8 5 to 7 7 6 to 7 5

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

Find the maximal flow from node 1 to node 7 in the following network.

Show both the network and the linear programming formulation for this assignment problem. Task Person A B C D 1 9 5 4 2 2 12 6 3 5 3 11 6 5 7

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

We assume in the maximal flow problem that

Which of the following is NOT a characteristic of assignment problems?