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The network below shows the flows possible between pairs of six locations. Formulate an LP to find the maximal flow possible from Node 1 to Node 6. The network below shows the flows possible between pairs of six locations. Formulate an LP to find the maximal flow possible from Node 1 to Node 6.

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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. 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 ********************************************* OPTIMAL ASSIGNMENTS COST/REVENUE ************************ *************** ASSIGNMENT PROBLEM ************************ OBJECTIVE: MINIMIZATION SUMMARY OF UNIT COST OR REVENUE DATA ********************************************* 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 ********************************************* OPTIMAL ASSIGNMENTS COST/REVENUE ************************ *************** OPTIMAL ASSIGNMENTS COST/REVENUE ************************ *************** 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 ********************************************* OPTIMAL ASSIGNMENTS COST/REVENUE ************************ ***************

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Team A works with the forecast...

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Arcs in a transshipment problem


A) must connect every node to a transshipment node.
B) represent the cost of shipments.
C) indicate the direction of the flow.
D) All of the alternatives are correct.

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

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The parts of a network that represent the origins are


A) the capacities
B) the flows
C) the nodes
D) the arcs

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The assignment problem constraint x31 + x32 + x33 + x34 ≤\le 2 means


A) agent 3 can be assigned to 2 tasks.
B) agent 2 can be assigned to 3 tasks.
C) a mixture of agents 1, 2, 3, and 4 will be assigned to tasks.
D) there is no feasible solution.

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Constraints in a transshipment problem


A) correspond to arcs.
B) include a variable for every arc.
C) require the sum of the shipments out of an origin node to equal supply.
D) All of the alternatives are correct.

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B

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,


A) the nodes represent stoplights.
B) the arcs represent one way streets.
C) the nodes represent locations where speed limits change.
D) None of the alternatives is correct.

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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.

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Draw the network for this transportation problem. Draw the network for this transportation problem.

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11eb7fec_db5f_574c_8992_f3af70a246b1_TB8643_00

The objective of the transportation problem is to


A) identify one origin that can satisfy total demand at the destinations and at the same time minimize total shipping cost.
B) minimize the number of origins used to satisfy total demand at the destinations.
C) minimize the number of shipments necessary to satisfy total demand at the destinations.
D) minimize the cost of shipping products from several origins to several destinations.

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The difference between the transportation and assignment problems is that


A) total supply must equal total demand in the transportation problem
B) the number of origins must equal the number of destinations in the transportation problem
C) each supply and demand value is 1 in the assignment problem
D) there are many differences between the transportation and assignment problems

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Show both the network and the linear programming formulation for this assignment problem. Show both the network and the linear programming formulation for this assignment problem.

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

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True

In a transshipment problem, shipments


A) cannot occur between two origin nodes.
B) cannot occur between an origin node and a destination node.
C) cannot occur between a transshipment node and a destination node.
D) can occur between any two nodes.

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


A) maximal flow problem
B) transportation problem
C) assignment problem
D) shortest-route problem

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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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The assignment problem is a special case of the


A) transportation problem.
B) transshipment problem.
C) maximal flow problem.
D) shortest-route problem.

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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. 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.

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Write the LP formulation for this transportation problem. Write the LP formulation for this transportation problem.

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