Lecture Introduction to Management Science with Spreadsheets: Chapter 6 - Stevenson, Ozgur

Chapter 6 - Supplement Transportation and assignment solution procedures, after completing this chapter, you should be able to: Use the transportation method to solve problems manually, deal with special cases in solving transportation problems, use the assignment (Hungarian) method to solve problems manually. deal with special cases in solving assignment problems.

Introduction to Management Science with Spreadsheets Stevenson and Ozgur First Edition Part Deterministic Decision Models Chapter 6 Transportation,  Transshipment, and  Assignment Problems McGraw­Hill/Irwin Copyright © 2007 by The McGraw­Hill Companies, Inc. All rights reserved Learning Objectives After completing this chapter, you should be able to: Describe the nature of transportation, transshipment, and assignment problems Formulate a transportation problem as a linear programming model Use the transportation method to solve problems with Excel Solve maximization transportation problems, unbalanced problems, and problems with prohibited routes Solve aggregate planning problems using the transportation model Copyright © 2007 The McGraw­Hill  McGraw­ Companies. All rights reserved.   Hill/Irwin  6–2 Learning Objectives (cont’d) After completing this chapter, you should be able to: Formulate a transshipment problem as a linear programming model Solve transshipment problems with Excel Formulate an assignment problem as a linear programming model Use the assignment method to solve problems with Excel Copyright © 2007 The McGraw­Hill  Companies. All rights reserved.   McGraw­ Hill/Irwin  6–3 Transportation Transportation Problems Problems • Transportation Problem – A distribution-type problem in which supplies of goods that are held at various locations are to be distributed to other receiving locations – The solution of a transportation problem will indicate to a manager the quantities and costs of various routes and the resulting minimum cost – Used to compare location alternatives in deciding where to locate factories and warehouses to achieve the minimum cost distribution configuration Copyright © 2007 The McGraw­Hill  Companies. All rights reserved.   McGraw­ Hill/Irwin  6–4 Formulating Formulating the the Model Model • A transportation problem – Typically involves a set of sending locations, which are referred to as origins, and a set of receiving locations, which are referred to as destinations – To develop a model of a transportation problem, it is necessary to have the following information: Supply quantity (capacity) of each origin Demand quantity of each destination Unit transportation cost for each origin­destination route Copyright © 2007 The McGraw­Hill  Companies. All rights reserved.   McGraw­ Hill/Irwin  6–5 Transshipment Transshipment Problems Problems • Transshipment Problems – A transportation problem in which some locations are used as intermediate shipping points, thereby serving both as origins and as destinations – Involve the distribution of goods from intermediate nodes in addition to multiple sources and multiple destinations Copyright © 2007 The McGraw­Hill  Companies. All rights reserved.   McGraw­ Hill/Irwin  6–6 Assignment Assignment Problems Problems • The Assignment-type Problems – Involve the matching or pairing of two sets of items such as jobs and machines, secretaries and reports, lawyers and cases, and so forth – Have different cost or time requirements for different pairings Copyright © 2007 The McGraw­Hill  Companies. All rights reserved.   McGraw­ Hill/Irwin  6–7 Figure Figure6–1 6–1 Schematic SchematicofofaaTransportation TransportationProblem Problem Copyright © 2007 The McGraw­Hill  Companies. All rights reserved.   McGraw­ Hill/Irwin  6–8 Table Table6–1 6–1 Transportation TransportationTable Tablefor forHarley’s Harley’sSand Sandand andGravel Gravel Copyright © 2007 The McGraw­Hill  Companies. All rights reserved.   McGraw­ Hill/Irwin  6–9 Special Special Cases Cases of of Transportation Transportation Problems Problems • Maximization – Transportation-type problems that concern profits or revenues rather than costs with the objective to maximize profits rather than to minimize costs • Unacceptable Routes – Certain origin-destination combinations may be unacceptable due to weather factors, equipment breakdowns, labor problems, or skill requirements that either prohibit, or make undesirable, certain combinations (routes) Copyright © 2007 The McGraw­Hill  Companies. All rights reserved.   McGraw­ Hill/Irwin  6–10 Table Table6–4 6–4 Transportation TransportationTable Tablefor forAggregate AggregatePlanning PlanningPurposes Purposes Copyright © 2007 The McGraw­Hill  Companies. All rights reserved.   McGraw­ Hill/Irwin  6–25 Example Example6-3 6-3 Copyright © 2007 The McGraw­Hill  Companies. All rights reserved.   McGraw­ Hill/Irwin  6–26 Table Table6–5 6–5 Transportation TransportationTable Tablefor forthe theAggregate AggregatePlanning PlanningProblem Problemof of Example Example6-3 6-3 Copyright © 2007 The McGraw­Hill  Companies. All rights reserved.   McGraw­ Hill/Irwin  6–27 Using Using the the Transportation Transportation Problem Problem to to Solve Solve Location Location Planning Planning Problems Problems • Location Analysis – Comparing transportation costs for alternative locations for new facilities to minimize total cost – Provides planners an opportunity to assess the impact of each warehouse location on the total distribution costs for the system Copyright © 2007 The McGraw­Hill  Companies. All rights reserved.   McGraw­ Hill/Irwin  6–28 Table Table6–6 6–6 System Systemwith withChicago ChicagoWarehouse Warehouse Table Table6–7 6–7 System Systemwith withDetroit DetroitWarehouse Warehouse Copyright © 2007 The McGraw­Hill  Companies. All rights reserved.   McGraw­ Hill/Irwin  6–29 Example Example6-4 6-4 A manager has prepared a table that shows the cost of performing each of five jobs by each of five employees (see Table 6-8) According to this table, job I will cost $15 if done by Al $20 if it is done by Bill, and so on The manager has stated that his goal is to develop a set of job assignments that will minimize the total cost of getting all four jobs done It is further required that the jobs be performed simultaneously, thus requiring one job being assigned to each employee In the past, to find the minimum-cost set of assignments, the manager has resorted to listing all of the different possible assignments (i.e., complete enumeration) for small problems such as this one But for larger problems, the manager simply guesses because there are too many possibilities to try to list them For example, with a 5X5 table, there are 5! = 120 different possibilities; but with, say, a 7X7 table, there are 7! = 5,040 possibilities Copyright © 2007 The McGraw­Hill  Companies. All rights reserved.   McGraw­ Hill/Irwin  6–30 Table Table6–8 6–8 Numerical NumericalExample Examplefor forthe theAssignment AssignmentProblem Problem Copyright © 2007 The McGraw­Hill  Companies. All rights reserved.   McGraw­ Hill/Irwin  6–31 Exhibit Exhibit6–10 6–10 Excel ExcelInput Inputand andOutput OutputWorksheet Worksheetfor forthe theAssignment AssignmentProblem Problem Copyright © 2007 The McGraw­Hill  Companies. All rights reserved.   McGraw­ Hill/Irwin  6–32 Exhibit Exhibit6–11 6–11 Parameter ParameterSpecifications SpecificationsScreen Screenfor forthe theAssignment AssignmentProblem Problem Copyright © 2007 The McGraw­Hill  Companies. All rights reserved.   McGraw­ Hill/Irwin  6–33 Exhibit Exhibit6–12 6–12 Excel ExcelWorksheet Worksheetfor forthe theTransportation TransportationProblem ProblemininSolved SolvedProblem Problem11 Copyright © 2007 The McGraw­Hill  Companies. All rights reserved.   McGraw­ Hill/Irwin  6–34 Exhibit Exhibit6–13 6–13 Parameter ParameterSpecification SpecificationScreen Screenfor forSolved SolvedProblem Problem11 Copyright © 2007 The McGraw­Hill  Companies. All rights reserved.   McGraw­ Hill/Irwin  6–35 Exhibit Exhibit6–14 6–14 Excel ExcelWorksheet Worksheetfor forthe theAssignment AssignmentProblem ProblemininSolved SolvedProblem Problem22 Copyright © 2007 The McGraw­Hill  Companies. All rights reserved.   McGraw­ Hill/Irwin  6–36 Exhibit Exhibit6–15 6–15 Parameter ParameterSpecification SpecificationScreen Screenfor forSolved SolvedProblem Problem22 Copyright © 2007 The McGraw­Hill  Companies. All rights reserved.   McGraw­ Hill/Irwin  6–37 Exhibit Exhibit6–16 6–16 Excel ExcelWorksheet Worksheetfor forthe theTransportation TransportationProblem ProblemininSolved SolvedProblem Problem33 Copyright © 2007 The McGraw­Hill  Companies. All rights reserved.   McGraw­ Hill/Irwin  6–38 Exhibit Exhibit6–17 6–17 Parameter ParameterSpecification SpecificationScreen Screenfor forSolved SolvedProblem Problem33 Copyright © 2007 The McGraw­Hill  Companies. All rights reserved.   McGraw­ Hill/Irwin  6–39 ... Companies. All rights reserved.   McGraw­ Hill/Irwin ? ?6? ??28 Table Table6? ?6 6? ?6 System Systemwith withChicago ChicagoWarehouse Warehouse Table Table6–7 6? ??7 System Systemwith withDetroit DetroitWarehouse Warehouse... problem is given in Figure 6- 3 Table Table6–2 6? ??2 Cost CostofofShipping ShippingOne OneUnit Unitfrom fromthe theFarms Farmsto toWarehouses Warehouses Table Table6–2 6? ??2 Cost CostofofShipping ShippingOne... Companies. All rights reserved.   McGraw­ Hill/Irwin ? ?6? ??25 Example Example 6-3 6- 3 Copyright © 2007 The McGraw­Hill  Companies. All rights reserved.   McGraw­ Hill/Irwin ? ?6? ?? 26 Table Table6–5 6? ??5 Transportation TransportationTable