Introduction to Management Science

Key words: network flow models, branches 5) The values assigned to branches typically represent distance, time, or cost. Dif. 1 page Ref: 282 6) Flows in a network can only be in one direction. Answer: FALSE Dif. 1 page Ref: 294 7) The shortest route problem is to find the shortest distance between an origin and various destination points. Answer: TRUE Dif;. 1 Page Ref: 282 Main Heading: The Shortest Route Problem 8) The shipping company manager wants to determine the best routes for the trucks to take to reach their destinations. This problem can be solved using the minimal pning tree.

Answer: FALSE Key words: shortest route problem ) The shortest route network problem could help identify the best route for pizza delivery drivers from the pizza parlor to a specific customer. Answer: TRUE Dif. Page Ref: 282 Key words: network flow models, shortest route 10) The minimal pning tree problem is to connect all nodes in a network so that the total branch lengths are minimized. Answer: TRUE Dif. 1 page Ref: 289 Main Heading: The Minimal Spanning Tree Problem Key words: minimal pning tree problem 1 1) The first step of the minimal pning tree solution to compute the distance of any path through the network.

Answer: FALSE Dif. Page Ref: 291-293 2) The last step of the minimal pning tree solution method is to make sure all nodes have Joined the pning tree. Answer: TRUE 13) In a minimal pning tree, the source and destination nodes must be connected along a single path. Answer: FALSE Dif. 1 page Ref: 291-293 14) The choice of the initial node in the minimal pning tree technique must be the first node. Answer: FALSE backtracking. Answer: FALSE 16) The shortest route network problem could help identify the best plan for running cables for televisions throughout a building.

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Answer: FALSE Key words: network flow models, shortest route, minimal pning tree 7) The goal of the maximal flow problem is to maximize the amount of flow of items from an origin to a destination. Answer: TRUE Main Heading: The Maximal Flow Problem Key words: maximal flow problem 18) For a directed branch, flow is possible in only one direction. Answer: TRUE 19) To determine the maximum possible flow of railroad cars through the rail system they should first select the longest path from origin to destination and ship as much as possible on that path.

Answer: FALSE 20) The shortest route problem requires that there be a branch from each destination to every other destination. Answer: FALSE 1) The maximal flow algorithm may end with capacity remaining at the source. Dif. Page Ref: 294-297 22) The source node is the input node in a maximal flow problem. Answer: TRUE Dif. 1 page Ref: 294-297 23) The direction of the flow is not critical in the maximal flow problem. Answer: FALSE 24) A traffic system could be represented as a network in order to determine bottlenecks using the maximal flow network algorithm.

Answer: TRUE Key words: network flow models, maximal flow 25) In a network flow problem, branches. Answer: nodes Main Heading: Network Models 26) In a network flow problem, to another. Answer: branches present Junction points connecting connect nodes and show flow from one point 27) In a network flow problem, the values assigned to distance, time, or cost. Answer: branches typically represent 28) The shipping company manager wants to determine the best routes for the trucks to take to reach their destinations. This problem can be solved using the solution technique.

Answer: shortest route 29) The connects all nodes in a network so that the total branch lengths are minimized. Answer: minimal pning tree Main Heading: Minimal Spanning Tree Problem an origin to a destination. Answer: maximal flow Main Heading: Maximal Flow Problem 1)A network model could be used to represent the capacity of a series of dams for flood control. Answer: maximal flow Dif. Page Ref: 294 32) A company plans to use an automatic guided vehicle for delivering mail to ten departments. The vehicle will begin from its docking area, visit each department, and return to the docking area.

Cost is proportional to distance traveled. The type of network model that best represent this situation is Main Heading: Shortest Route Problem . Answer: Shortest route 33) Determining where to build roads at the least cost within a park that reaches every popular sights represents a pning tree outwork model. Answer: minimal Key words: network flow models, minimal pning tree 34) Determining where to build one way roads at the least cost within a park that takes visitors to every popular sight and returns them to the entrance represents a network model.

Answer: Shortest route 35) Determining where capacity needs to be added within a series of one way roads within a park represents a model. Answer: maximal flow [pica] Figure 1 . Delivery Routes branch is the distance in miles between the respective nodes. What is the shortest route from the source node (node 1) to nodes 2, 3, and 4. Indicate the total distance for each route. Answer: (node 1) - (node 2): 6 miles (node 1) - (node 2) - (node 3): 8 miles (node 1) - (node 2)- (node 4): 11 miles Dif. Page Ref: 283-286 Key words: shortest route problem, shortest route problem solution 37) Consider the network diagram given in Figure 1 . Assume that the amount on each route from the source node (node 1) to nodes 5 and 6. Indicate the total distance for each route. Answer: (node 1) - (node 2)- (node 3)- (node 5) : 13 miles (node 1) - (node 2) - (node 4) - (node 6): 13 miles 38) Consider the network diagram given in Figure 1 . Assume that the amount on each branch is the distance in miles between the respective nodes. Also assume that it is not possible to travel from a node with a higher number to a node with a lower number.

Write the constraint associated with the second node (node 2) for the 0-1 integer linear programming formulation of the shortest route problem. Answer: EX. - EX.-EX.=o Dif. Page Ref: 287-289 Key words: short route prop, integer linear prop form of the short route prop 39) Consider the network diagram given in Figure 1 . Assume that the amount on each number. Write the constraint associated with the fifth node (node 5) for the 0-1 integer linear programming formulation of the shortest route problem. Answer: EX. - EX.=o 40) Consider the network diagram given in Figure 1 .

Assume that he numbers on the branches indicate the length of cable (in miles) six nodes on a telecommunication network. What is the minimum number of miles of cable to be used to connect all six nodes? Answer: 17 miles Key words: minimal p tree prop, solution of minimal p tree prop Pro-carpet company manufactures carpets in Northwest Indiana and delivers them to warehouses and retail outlets. The network diagram given in the Figure below shows the possible routes and travel times (in minutes) from the carpet plant to the various warehouses or retail outlets.

V = Valparaiso, P=Portage, G=Gary, Ha=Hammond, Hi=Highland, M = Marseille, L -? Lansing 41) Determine the shortest route for a carpet delivery truck from the carpet plant in Valparaiso, Indiana to warehouses in Hammond - IN, Gary - IN and Marseille - IN. State the total completion time in minutes or each route Answer: Valparaiso - Portage - Marseille: 19 minutes Valparaiso - Portage - Gary: 25 minutes Valparaiso - Portage - Marseille - Hammond: 30 minutes 42) Determine the shortest route for a carpet delivery truck from the carpet plant in Valparaiso, Indiana to retail outlets in Portage - IN, Highland - IN, and Lansing, Illinois.

Portage: 13 minutes Valparaiso - Portage - Marseille - Hammond - Highland: 35 minutes Valparaiso - Portage - Marseille - Hammond - Lansing: 37 minutes Dif:2 Page Ref: 283-286 43) Write the constraint associated with the Valparaiso (source) node for the 0-1 integer linear programming formulation of the shortest route problem. Answer: XV + XV=I 44) Write the constraint associated with the Lansing (destination) node for the 0-1 integer linear programming formulation of the shortest route problem. Answer: Xii- 45) Draw the network associated with the following constraints for a shortest route robber.

EX.+EX. EX.- EX. EX. + EX. EX. = 1 Answer: - EX. = O Dif. Space Ref: 287-289 Key words: network flow problem, shortest route Consider the following network, which shows the location of various facilities within a youth camp and the distances (in tens of yards) between each facility. 46) Walking trails will be constructed to connect all the facilities. In order to preserve the natural beauty of the camp (and to minimize the construction time and cost), the directors want to determine which paths should be constructed.

Use this network to determine which paths should be built. Answer: Minimal pning tree shown in bold. Key words: minimal pning tree 47) The camp nurse is stationed at Facility B. What is the shortest route from B to C? Answer: B to G to E to C for a total of 30. Dif. 1 page Ref: 283-286 youth camp and the distances (in tens of yards) between each facility. There is a swampy area between facility A and E. 48) Walking trails will be constructed to connect all the facilities. In order to preserve determine which paths should be built.

Answer: Minimal pning tree shown in bold. 49) A clean up crew visits is stationed at facility D and wants to take the shortest out to each site. They usually clean up facilities C, E, A and F on the same day and therefore want the shortest route from D to each facility.. Recommend a route for the crew to leave from D, clean up each facility one after the other, and return to facility D. (Assume all paths are accessible. ) Answer: D to E to F to C to A to D. Total distance = 47. This is really a small version of the traveling salesman problem.

Doing the minimal pning tree prior to this problem may be helpful. Dif 2 Page Ref: 283-286 50) A clean up crew is stationed at facility F and wants to take the shortest route to each site. They usually clean up facilities B and A on the same day and therefore want the shortest route from F to each facility. Recommend a route for the crew to leave from F, clean up each facility A and B, and then return to facility D. (Assume all paths are accessible. ) Answer: F-E-G-B-D-A-C-F for a total of 77. This is a small version of the traveling salesmen problem. Doing the minimal pning tree prior to this problem may be helpful. ). The clean up crew may want to add additional facilities on the days they clean up A and B if they have time. Dif 2 Page Ref: Refer to the figure below to answer the following questions. Figure 3 51) Consider the network diagram given in Figure 3 with the indicated flow capacities along each branch. Determine the maximal flow from source node 1 to destination Dif. Page Ref: 294-297 Key words: maximal flow problem, solution of the maximal flow problem 52) Consider the network diagram given in Figure 3 with the indicated flow capacities along each branch. Determine the maximal flow on the following path: node 1 to node 2 to node 7 to destination node 9. Answer: maximum flow: 5 53) Consider the network diagram given in Figure 3 with the indicated flow capacities along each branch. What is the objective function for the 0-1 integer linear programming formulation of the maximal flow problem?

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