Lecture Introduction to Management Science with Spreadsheets: Chapter 8 - Stevenson, Ozgur

Chapter 8 Network optimization models, after completing this chapter, you should be able to: State why network models are important tools for problem solving, describe the kinds of problems that can be solved using the shortest-route algorithm and use the algorithm to solve typical shortest-route problems, formulate the shortest-route problem as a linear programming problem,...

Introduction to Management Science with Spreadsheets Stevenson and Ozgur First Edition Part Deterministic Decision Models Chapter 8 Network Optimization  Models McGraw­Hill/Irwin Copyright © 2007 by The McGraw­Hill Companies, Inc. All rights reserved Learning Objectives After completing this chapter, you should be able to: State why network models are important tools for problem solving Describe the kinds of problems that can be solved using the shortest-route algorithm and use the algorithm to solve typical shortest-route problems Formulate the shortest-route problem as a linear programming problem Solve the shortest-route problem using Excel Copyright © 2007 The McGraw­Hill  Companies. All rights reserved.   McGraw­ Hill/Irwin  8–2 Learning Objectives (cont’d) After completing this chapter, you should be able to: Describe the kinds of problems that can be solved using the minimal-spanning-tree algorithm and use the algorithm to solve typical minimal-spanning-tree problems Describe the kinds of problems that can be solved using the maximal-flow algorithm and use the algorithm to solve typical maximal-flow problems Formulate the maximal-flow problem as a linear programming problem Solve the maximal-flow problem using Excel Copyrightâ2007TheMcGrawưHill McGrawư Companies.Allrightsreserved. Hill/Irwin83 Networks Networks ã Network – A set of nodes and connecting arcs or branches Can be useful in representing various systems, such as distribution systems, production systems, and transportation systems • Network models are an important approach for problem solving because: – They can be used to model a wide range of problems – They are relatively simple to work with – They provide a visual portrayal of a problem Copyright © 2007 The McGraw­Hill  Companies. All rights reserved.   McGraw­ Hill/Irwin  8–4 Frequently Frequently Used Used Algorithms Algorithms • Shortest-Route Algorithm – Used for determining the shortest time, distance, or cost from an origin to a destination through a network • Minimum Spanning Tree Algorithm – Used in determining the minimum distance (cost, time) needed to connect a set of locations into a single system • Maximal Flow Algorithm – Used for determining the greatest amount of flow that can be transmitted through a system in which various branches, or connections, have specified flow capacity limitations Copyright © 2007 The McGraw­Hill  McGraw­ Companies. All rights reserved.   Hill/Irwin  8–5 Figure Figure8–1 8–1 AASimple SimpleNetwork NetworkDiagram Diagram Copyright © 2007 The McGraw­Hill  Companies. All rights reserved.   McGraw­ Hill/Irwin  8–6 Example Example8-1 8-1 Labeling Procedure A label is developed for each node The labels consist of two numbers separated by a comma: The first number refers to the distance from Node to the labeled node along a certain path, while the second number refers to the node that immediately precedes this node along that path Copyright © 2007 The McGraw­Hill  Companies. All rights reserved.   McGraw­ Hill/Irwin  8–7 Example Example8-1 8-1(cont’d) (cont’d) Copyright © 2007 The McGraw­Hill  Companies. All rights reserved.   McGraw­ Hill/Irwin  8–8 Example Example8-1 8-1(cont’d) (cont’d) Copyright © 2007 The McGraw­Hill  Companies. All rights reserved.   McGraw­ Hill/Irwin  8–9 Figure Figure8–2 8–2 Network Networkfor forTri-State Tri-StateShipping ShippingCompany CompanyShortest-Route Shortest-Route Problem Problem Copyright © 2007 The McGraw­Hill  Companies. All rights reserved.   McGraw­ Hill/Irwin  8–10 Figure Figure8–7 8–7 Third ThirdRevision Revisionof ofFlow FlowNetwork Network Copyright © 2007 The McGraw­Hill  Companies. All rights reserved.   McGraw­ Hill/Irwin  8–23 Figure Figure8–8 8–8 Final FinalSolution Solutionfor forFlow FlowNetwork NetworkExample Example Copyright © 2007 The McGraw­Hill  Companies. All rights reserved.   McGraw­ Hill/Irwin  8–24 Figure Figure8–9 8–9 Flow FlowNetwork Networkfor forDemonstration DemonstrationofofReverse ReverseFlow Flow Copyright © 2007 The McGraw­Hill  Companies. All rights reserved.   McGraw­ Hill/Irwin  8–25 Figure Figure8–10 8–10 Flow FlowNetwork Networkfor forDemonstration DemonstrationofofReverse ReverseFlow Flow Copyright © 2007 The McGraw­Hill  Companies. All rights reserved.   McGraw­ Hill/Irwin  8–26 Figure Figure8–11 8–11 Revised RevisedFlow FlowNetwork Network Copyright © 2007 The McGraw­Hill  Companies. All rights reserved.   McGraw­ Hill/Irwin  8–27 Table Table8–1 8–1 Branches Branchesofofthe theNetwork Networkand andFlow FlowCapacities Capacitiesofofthe theBranches Branches for forthe theTurkmen TurkmenOil OilLtd Ltd.Maximal MaximalFlow FlowProblem Problem Copyright © 2007 The McGraw­Hill  Companies. All rights reserved.   McGraw­ Hill/Irwin  8–28 Figure Figure8–12 8–12 Network NetworkDiagram Diagramfor forthe theMaximal MaximalFlow FlowProblem Problemfor forTurkmen Turkmen Oil OilLtd Ltd Copyright © 2007 The McGraw­Hill  Companies. All rights reserved.   McGraw­ Hill/Irwin  8–29 Exhibit Exhibit8–6 8–6 Input InputWorksheet Worksheetfor forthe theTurkmen TurkmenOil OilLtd Ltd.Maximal MaximalFlow FlowProblem Problem Copyright © 2007 The McGraw­Hill  Companies. All rights reserved.   McGraw­ Hill/Irwin  8–30 Exhibit Exhibit8–7 8–7 Parameter ParameterSpecification SpecificationScreen Screenfor forthe theTurkmen Turkmen Oil OilLtd Ltd.Maximal MaximalFlow FlowProblem Problem Copyright © 2007 The McGraw­Hill  Companies. All rights reserved.   McGraw­ Hill/Irwin  8–31 Exhibit Exhibit8–8 8–8 Output OutputWorksheet Worksheetfor forthe theTurkmen TurkmenOil OilLtd Ltd.Maximal MaximalFlow Flow Problem Problem Copyright © 2007 The McGraw­Hill  Companies. All rights reserved.   McGraw­ Hill/Irwin  8–32 Table Table8–2 8–2 Summary Summaryofofthe theOptimal OptimalFlow FlowQuantities Quantitiesfor forTurkmen TurkmenOld OldLtd Ltd Copyright © 2007 The McGraw­Hill  Companies. All rights reserved.   McGraw­ Hill/Irwin  8–33 Exhibit Exhibit88–9 –9 Worksheet Worksheetfor forSolved SolvedProblem Problem1,1,the theShortest-Route Shortest-RouteProblem Problem (Beginning (BeginningNode Node1,1,Ending EndingNode Node5) 5) Copyright © 2007 The McGraw­Hill  Companies. All rights reserved.   McGraw­ Hill/Irwin  8–34 Exhibit Exhibit88–10 –10 Parameter ParameterSpecification SpecificationScreen Screenfor forSolved SolvedProblem Problem1,1,the theShortestShortestRoute RouteProblem Problem(Beginning (BeginningNode Node1,1,Ending EndingNode Node5) 5) Copyright © 2007 The McGraw­Hill  Companies. All rights reserved.   McGraw­ Hill/Irwin  8–35 Exhibit Exhibit88–11 –11 Worksheet Worksheetfor forSolved SolvedProblem Problem3,3,the theMaximal MaximalFlow FlowProblem Problem Copyright © 2007 The McGraw­Hill  Companies. All rights reserved.   McGraw­ Hill/Irwin  8–36 Exhibit Exhibit88–12 –12 Parameter ParameterSpecification SpecificationScreen Screenfor forSolved SolvedProblem Problem3,3,the the Maximal MaximalFlow FlowProblem Problem Copyright © 2007 The McGraw­Hill  Companies. All rights reserved.   McGraw­ Hill/Irwin  8–37 ... McGraw­ Hill/Irwin ? ?8? ??7 Example Example 8-1 8- 1(cont’d) (cont’d) Copyright © 2007 The McGraw­Hill  Companies. All rights reserved.   McGraw­ Hill/Irwin ? ?8? ? ?8 Example Example 8-1 8- 1(cont’d) (cont’d)... Hill/Irwin ? ?8? ??17 Example Example 8-3 8- 3(cont’d) (cont’d) Copyright © 2007 The McGraw­Hill  Companies. All rights reserved.   McGraw­ Hill/Irwin ? ?8? ?? 18 Example Example 8-3 8- 3(cont’d) (cont’d) Copyright © 2007 The McGraw­Hill ... Hill/Irwin ? ?8? ??11 Exhibit Exhibit 8-2 8- 2 Parameter ParameterSpecification SpecificationScreen Screenfor forthe theTri-State Tri-StateShipping Shipping Company CompanyShortest-Route Shortest-RouteProblem