Optimization modeling with spreadsheets 3rd edition

CONTENTS COVER TITLE PAGE PREFACE WHY MODEL BUILDING? WHY SPREADSHEETS? WHAT’S SPECIAL? WHAT’S NEW? THE AUDIENCE ACKNOWLEDGMENTS INTRODUCTION TO SPREADSHEET MODELS FOR OPTIMIZATION 1.1 ELEMENTS OF A MODEL 1.2 SPREADSHEET MODELS 1.3 A HIERARCHY FOR ANALYSIS 1.4 OPTIMIZATION SOFTWARE 1.5 USING SOLVER SUMMARY EXERCISES REFERENCES LINEAR PROGRAMMING: ALLOCATION, COVERING, AND BLENDING MODELS 2.1 LINEAR MODELS 2.2 ALLOCATION MODELS 2.3 COVERING MODELS 2.4 BLENDING MODELS 2.5 MODELING ERRORS IN LINEAR PROGRAMMING SUMMARY EXERCISES LINEAR PROGRAMMING: NETWORK MODELS 3.1 THE TRANSPORTATION MODEL 3.2 THE ASSIGNMENT MODEL 3.3 THE TRANSSHIPMENT MODEL 3.4 FEATURES OF SPECIAL NETWORK MODELS 3.5 BUILDING NETWORK MODELS WITH BALANCE EQUATIONS 3.6 GENERAL NETWORK MODELS WITH YIELDS 3.7 GENERAL NETWORK MODELS WITH TRANSFORMED FLOWS SUMMARY EXERCISES SENSITIVITY ANALYSIS IN LINEAR PROGRAMS 4.1 PARAMETER ANALYSIS IN THE TRANSPORTATION EXAMPLE 4.2 PARAMETER ANALYSIS IN THE ALLOCATION EXAMPLE 4.3 THE SENSITIVITY REPORT AND THE TRANSPORTATION EXAMPLE 4.4 THE SENSITIVITY REPORT AND THE ALLOCATION EXAMPLE 4.5 DEGENERACY AND ALTERNATIVE OPTIMA 4.6 PATTERNS IN LINEAR PROGRAMMING SOLUTIONS SUMMARY EXERCISES LINEAR PROGRAMMING: DATA ENVELOPMENT ANALYSIS 5.1 A GRAPHICAL PERSPECTIVE ON DEA 5.2 AN ALGEBRAIC PERSPECTIVE ON DEA 5.3 A SPREADSHEET MODEL FOR DEA 5.4 INDEXING 5.5 REFERENCE SETS AND HCUs 5.6 ASSUMPTIONS AND LIMITATIONS OF DEA SUMMARY EXERCISES INTEGER PROGRAMMING: BINARY-CHOICE MODELS 6.1 USING SOLVER WITH INTEGER REQUIREMENTS 6.2 THE CAPITAL BUDGETING PROBLEM 6.3 SET COVERING 6.4 SET PACKING 6.5 SET PARTITIONING 6.6 PLAYOFF SCHEDULING 6.7 THE ALGORITHM FOR SOLVING INTEGER PROGRAMS SUMMARY EXERCISES INTEGER PROGRAMMING: LOGICAL CONSTRAINTS 7.1 SIMPLE LOGICAL CONSTRAINTS: EXCLUSIVITY 7.2 LINKING CONSTRAINTS: THE FIXED COST PROBLEM 7.3 LINKING CONSTRAINTS: THE THRESHOLD LEVEL PROBLEM 7.4 LINKING CONSTRAINTS: THE FACILITY LOCATION MODEL 7.5 DISJUNCTIVE CONSTRAINTS: THE MACHINE-SEQUENCING PROBLEM 7.6 TOUR CONSTRAINTS: THE TRAVELING SALESPERSON PROBLEM SUMMARY EXERCISES NONLINEAR PROGRAMMING 8.1 ONE-VARIABLE MODELS 8.2 LOCAL OPTIMA AND THE SEARCH FOR AN OPTIMUM 8.3 TWO-VARIABLE MODELS 8.4 NONLINEAR MODELS WITH CONSTRAINTS 8.5 LINEARIZATIONS SUMMARY EXERCISES HEURISTIC SOLUTIONS WITH THE EVOLUTIONARY SOLVER 9.1 FEATURES OF THE EVOLUTIONARY SOLVER 9.2 AN ILLUSTRATIVE EXAMPLE: NONLINEAR REGRESSION 9.3 THE MACHINE-SEQUENCING PROBLEM REVISITED 9.4 THE TRAVELING SALESPERSON PROBLEM REVISITED 9.5 BUDGET ALLOCATION 9.6 TWO-DIMENSIONAL LOCATION 9.7 LINE BALANCING 9.8 GROUP ASSIGNMENT SUMMARY EXERCISES Appendix 1: SUPPLEMENTAL FILES AND SOFTWARE A1.1 SUPPLEMENTAL Microsoft® Office Excel® FILES A1.2 ANALYTIC SOLVER PLATFORM FOR EDUCATION SOFTWARE A1.3 OPENSOLVER SOFTWARE Appendix 2: GRAPHICAL METHODS FOR LINEAR PROGRAMMING A2.1 AN EXAMPLE A2.2 GENERALITIES Appendix 3: THE SIMPLEX METHOD A3.1 AN EXAMPLE A3.2 VARIATIONS OF THE ALGORITHM REFERENCES INDEX END USER LICENSE AGREEMENT List of Tables Chapter 01 Table 1.1 Advantages of Spreadsheet and Algebraic Solution Approaches Chapter 02 Exhibit 2.1 Price for Each Passenger Route Exhibit 2.2 Regular Demand during One Bank Exhibit 2.3 Senior Demand during One Bank Chapter 03 Exhibit 3.1 Last Year’s Sales By Geographic Region Exhibit 3.2 Plant Capacities and Production Exhibit 3.3 Total Costs (per Ton) Exhibit 3.5 Plant Fixed Costs Exhibit 3.6 Last Year’s Transportation Rates Per Ton Exhibit 3.7 Last Year’s Profits Per Ton Exhibit 3.8 Anticipated Costs For New Facilities Chapter 04 Table 4.1 Comparison of Solver Sensitivity and the Sensitivity Report Table 4.2 GD’s Products, Arranged by Priority Table 4.3 Computational Scheme for the Investment Model Table 4.4 Computational Scheme for the Delta Oil Model Exhibit 4.1 Contract Delivery Schedule and Prices Exhibit 4.2 Production Capabilities, in Hours per Reel Exhibit 4.3 Unscheduled Production Hours Exhibit 4.4 Accounting Data for Production Chapter 05 Table 5.1 Scaled Values from Example 5.2 Table 5.2 Inputs and Outputs for Seven Hospitals Table 5.3 Inputs and Outputs for Five Restaurants Table 5.4 Inputs and Outputs for 17 Branch Banks Exhibit 5.1 Branch Manager Salaries Exhibit 5.2 Sample Branch Profitability Statement ($000) Exhibit 5.3 Raw Data for the Analysis Exhibit 5.4 Branch Efficiencies and Output Factor Weightings Chapter 06 Table 6.1 Playoff Schedule for LASA Exhibit 6.1 Proximity Data and Economic Estimates Chapter 07 Exhibit 7.3 Warehouse Cost Data Exhibit 7.4 Forecast for Annual Demands Exhibit 7.5 Unit Costs for Distribution Chapter 08 Table 8.1 Comparison of the Linear and Nonlinear Algorithms Exhibit 8.1 Summary of Product Costs and Revenues Chapter 09 Table 9.1 Initial Population Table 9.2 First Generation of Offspring Table 9.3 Population Updated for Fitness Table 9.4 Second Generation of Offspring Table 9.5 Second Updated Population List of Illustrations Chapter 01 Figure 1.1 Spreadsheet model for determining price Figure 1.2 Alternative spreadsheet model for determining price Figure 1.3 Solver Parameters window Figure 1.4 Add Constraint window Figure 1.5 Optimal solution produced by Solver Figure 1.6 Solver Results window Figure 1.7 Solver Parameters window for the model with range names Chapter 02 Figure 2.1 Model for the Brown Furniture example Figure 2.2 Formulas in the Brown Furniture model Figure 2.3 Specifying the model in Solver Figure 2.4 Adding constraints in Solver Figure 2.5 Solver Results window Figure 2.6 Optimal solution to the Brown Furniture model Figure 2.7 Product mix model Figure 2.8 Optimal solution to the product mix model Figure 2.9 Model for Herrick Foods example Figure 2.10 Optimal solution for the Herrick Foods model Figure 2.11 Herrick Foods model with additional constraints Figure 2.12 Optimal solution to the modified Herrick Foods model Figure 2.13 Staffing model Figure 2.14 Hourly staffing model Figure 2.15 Modified product mix model Figure 2.16 Keogh Coffee Roasters model Figure 2.17 Formula Auditing with the trace precedence command Chapter 03 Figure 3.1 Flow diagram for Example 3.1 Figure 3.2 Spreadsheet model for Example 3.1 Figure 3.3 Formulas in the spreadsheet for Example 3.1 Figure 3.4 Optimal flows for Example 3.1 Figure 3.5 Flow diagram for Example 3.2 Figure 3.6 Spreadsheet model for Example 3.2 Figure 3.7 Flow diagram for Example 3.3 Figure 3.8 Spreadsheet model for Example 3.3 Figure 3.9 Standard linear programming format for Example 3.2 Figure 3.10 Flow diagram for the augmented version of Example 3.1 Figure 3.11 Spreadsheet model for the augmented version of Example 3.1 Figure 3.12 Spreadsheet model for Example 3.4 Figure 3.13 Flow diagrams for Example 3.5 Figure 3.14 Unified flow diagram for Example 3.5 Figure 3.15 Spreadsheet model for Example 3.5 Figure 3.16 Flow diagram with optimal flows for Example 3.5 Figure 3.17 Flow diagram for Example 3.6 Figure 3.18 Spreadsheet model for Example 3.6 Chapter 04 Figure 4.1 Solution for transportation model of Example 3.1 Figure 4.2 First input window for Solver Sensitivity Figure 4.3 Second input window for Solver Sensitivity Figure 4.4 Solver Sensitivity report for PA unit cost Figure 4.5 Solver Sensitivity results on a refined grid Figure 4.6 Solver Sensitivity report for Pittsburgh capacity Figure 4.7 Solution for allocation model of Example 2.1 Figure 4.8 Solver Sensitivity input window for allocation model Figure 4.9 One-Way Inputs window for allocation model Figure 4.10 Solver Sensitivity report for profit contribution Figure 4.11 Solver Sensitivity report for machining hours Figure 4.12 Solver Sensitivity report for machining hours on a refined grid Figure 4.13 Graph showing optimal profit as a function of machining hours available Figure 4.14 Inputs for a two-way sensitivity analysis Figure 4.15 Two-way Solver Sensitivity report Figure 4.16 Selecting the Sensitivity Report after a Solver run Figure 4.17 Sensitivity Report for the transportation example Figure 4.18 Sensitivity Report for the allocation example Figure 4.19 Sensitivity Report for the near-degenerate case Figure 4.20 Solution with multiple optima Figure 4.21 Precedence logic for the computational scheme in the transportation model Figure 4.22 Optimal solution for GD Figure 4.23 Precedence logic for the computational scheme in the GD model Figure 4.24 Optimal solution to the investment model of Example 3.5 Figure 4.25 Network model corresponding to Figure 4.22 Figure 4.26 Precedence logic for the computational scheme in the investment model Figure 4.27 Precedence logic for the computational scheme in the allocation model Figure 4.28 Spreadsheet model for the refinery of Example 3.6 Figure 4.29 Precedence logic for the computational scheme in the refinery model Figure 4.30 Sensitivity Report (Constraints section) for the refinery model Chapter 05 Figure 5.1 Outputs for each of the branches in Example 5.2 Figure 5.2 Outputs for the HCUs in Example 5.2 Figure 5.3 Model for Branch in Example 5.2 Figure 5.4 Model for Branch in Example 5.2 Figure 5.5 Model for any branch in Example 5.2 Figure 5.6 Summary of the analysis for Example 5.2 Figure 5.7 Analysis of Branch in Example 5.2, with indexing Figure 5.8 Analysis for Facility in Example 5.3 Figure 5.9 Sensitivity Report for Facility in Example 5.3 Figure 5.10 Analysis of Branch with lower bounds Chapter 06 Figure 6.1 Spreadsheet model for Example 6.1 Figure 6.2 Declaring integer variables in Example 6.1 Figure 6.3 Model specification for Example 6.1 Figure 6.4 Options window in Solver Figure 6.5 Optimal integer solution to Example 6.1 Figure 6.6 Linear program for Example 6.2 Figure 6.7 Optimal solution to the linear program for Example 6.2 Figure 6.8 Optimal solution to the linear program for Example 6.2 with ceilings of Figure 6.9 Optimal integer solution for Example 6.2 Figure 6.10 Sector map for Example 6.3 Figure 6.11 Adjacency array for Example 6.3 Figure 6.12 Optimal solution for Example 6.3 Figure 6.13 Map of the target area for NSH Figure 6.14 Optimal solution for Example 6.4 Figure 6.15 Spreadsheet model for Example 6.5 Figure 6.16 Portion of the spreadsheet model for Example 6.6 Figure 6.17 Spreadsheet model for Example 6.6 Figure 6.18 First level of branching Figure 6.19 Second level of branching Figure 6.20 Final status of tree search Chapter 07 Figure 7.1 Solution to Example 7.1 with international constraint Figure 7.2 Solution to Example 7.1 with mutually exclusive constraint added Figure 7.3 Solution to Example 7.1 with contingency constraint added Figure 7.4 Total cost with fixed and variable components Figure 7.5 Solution to Example 7.2 with variable profits optimized Figure 7.6 Spreadsheet layout for Example 7.2 in traditional format Figure 7.7 Alternative layout for Example 7.2 Figure 7.8 Cost trade-off in facility location Figure 7.9 Spreadsheet model for Example 7.3 Figure 7.10 Optimal solution for Example 7.3 Figure 7.11 Alternative model for Example 7.3 Figure 7.12 Optimal solution for the unconstrained model Figure 7.13 Optimal solution for the alternative unconstrained model Figure 7.14 Spreadsheet model for Example 7.4 Figure 7.15 Distance array and decision array for Example 7.5 Figure 7.16 Solution to the assignment model for Example 7.5 Figure 7.17 Solution for Example 7.5 with one elimination constraint Figure 7.18 Solution for Example 7.5 with two elimination constraints Figure 7.19 Solution for Example 7.5 with three elimination constraints Figure 7.20 Solution for Example 7.5 with integer requirements Figure 7.21 Optimal solution for Example 7.5 Exhibit 7.1 Potential Warehouse Locations for the New Region Exhibit 7.2 Cost Structure at a Typical Warehouse Chapter 08 Figure 8.1 Examples of nonsmooth functions Figure 8.2 Hypothetical nonlinear objective function Figure 8.3 Spreadsheet model for Example 8.1 Figure 8.4 Spreadsheet model for Example 8.2 Figure 8.5 A concave function Figure 8.6 A convex function Figure 8.7 A convex region Figure 8.8 A nonconvex region Figure 8.9 Spreadsheet for Example 8.3 Figure 8.10 Spreadsheet for Example 8.4 Figure 8.11 Linear and nonlinear objective functions Figure 8.12 Spreadsheet for Example 8.5 Figure 8.13 Sensitivity Report for Example 8.5 Figure 8.14 Spreadsheet model for Example 8.6 Figure 8.15 The efficient frontier in Example 8.6 Figure 8.16 Spreadsheet model for Example 8.7 Figure 8.17 Optimal solution for Example 8.7 Figure 8.18 Spreadsheet for Example 8.7 with absolute value objective Figure 8.19 Spreadsheet for Example 8.7 with absolute value objective Chapter 09 Figure 9.1 Spreadsheet model for Example 8.3 Figure 9.2 Evolutionary tab in the Options window Figure 9.3 Best solution found for Example 8.3 Figure 9.4 Spreadsheet for Example 7.4 Figure 9.5 Specifying the alldifferent constraint Figure 9.6 Final solution for Example 7.4 Figure 9.7 Spreadsheet model for Example 7.5 Figure 9.8 Final solution for Example 7.5 Figure 9.9 Initial model for Example 9.1 Figure 9.10 Modified model for Example 9.1 Figure 9.11 Spreadsheet model for Example 9.2 Figure 9.12 Spreadsheet model for Example 9.2 Figure 9.13 Final solution for Example 9.3 Figure 9.14 Spreadsheet model for Example 9.4 Figure 9.15 Final solution for Example 9.3 Exhibit 9.1 Wave Concept Statement Appendix Figure A2.1 Sketch of first constraint Figure A2.2 Sketch of second constraint Figure A2.3 Sketch of third constraint Figure A2.4 Sketch of objective function lines Figure A2.5 Sketch of optimal point Appendix Figure A3.1 Simplex tableau OPTIMIZATION MODELING WITH SPREADSHEETS Third Edition KENNETH R BAKER 10 playoff scheduling problem portfolio optimization problem price, demand and profit problem pricing problem purchase discount problem refinery scheduling problem set-covering problem set-packing problem set-partitioning problem staff-scheduling problem transportation problem transshipment problem traveling salesperson problem two-dimensional location problem yield gain problem yield loss problem CEILING function Cell Edit function Cell Reference box Cell references Change Constraint option Changing Variable Cells window Chemical compounds, blending models CHOOSE function Client Coffee blending, blending model College planning, funds flow model Composite product Computational scheme Concave functions Conservation law Constraint box Constraint constants Constraints alldifferent constraint allocation constraints counting constraints disjunctive constraints graphical analysis inconsistency in inequality constraints infeasible constraints 342 linear constraints linearizing the maximum linking constraints logical constraints lower-bound constraints modeling errors in nonlinear models with qualitative constraints see Logical constraints subtour elimination constraints tight constraints see Binding constraints tour constraints upper and lower limits upper-bound constraints Contingency relationship Convergence message Convex feasible region Convex functions COUNTIF function COVAR function Covering models Covering problem diet problem staff-scheduling problem Crossover method Curve fitting Cycle time Data envelopment analysis (DEA) algebraic perspective on assumptions and limitations of criticisms of graphical perspective on hypothetical comparison units (HCUs) indexing reference sets spreadsheet model for Data Table tool Debugging, Linear programming formulations Decision model Decision variables alldifferent constraint bounds for in branch and bound 343 in the computational scheme in DEA funds-flow models general-network models initial values in integer programs in sensitivity analysis set to zero special-network models Decision-making units (DMUs) Degenerate solution Diet problem Diminishing marginal returns Disjunctive constraints Displaying formulas Divisibility Efficiency Efficient frontier Elementary row operations Entering variables Equal-to (EQ) constraints Euclidean distance Evolutionary solver Facility location model capacitated version uncapacitated version Fathomed Feasibility Feasible region Feasible solution Fitness criterion Fixed-cost problem FLOOR function Flow see Flow diagrams Flow diagrams assignment models conservation law funds flow model general-network models with transformed flows general-network models with yield gains network models transportation models 344 transshipment model Formula Auditing tools Formulas tab From/To structure network models with balance equations special-network models transportation models Funds flow model Gap Gasoline blends, blending models General-network models with transformed flows with yield gains with yield losses Global optima Graphical methods generalities linear programming Greater-than (GT) constraints GRG algorithm Group assignment GT constraints see Greater-than (GT) constraints Heuristic procedure Hypothetical comparison units (HCUs) IF function INDEX function Indexing, data envelopment analysis (DEA) Inequality constraints Infeasible constraints Inner product Input parameters INT function Integer Optimality option Integer programming algorithm for binary choice disjunctive constraints facility location model fixed-cost problem integer variables linking constraints 345 machine-sequencing problem matching problem models with logical constraints qualitative constraints set-covering problem set-packing problem set-partitioning problem Solver with threshold-level problem traveling salesperson problem Integer variables Investment allocation model see also Portfolio optimization model Investment portfolios funds flow problems optimization model portfolio variance sensitivity analysis Isovalue line Kink Lagrange multiplier Left-hand-side (LHS) Less-than (LT) constraints Line balancing Linear constraints function models Linear programming graphical methods modeling errors in patterns in sensitivity analysis Linear programming formulations allocation models alternative optima blending models covering models data envelopment analysis (DEA) debugging degeneracy design and setup layout 346 linear constraints modeling errors in network models optimization results patterns in product mix problem staff-scheduling problem Linear solver see also Simplex algorithm Linearity Linearizations linearizing the absolute value linearizing the maximum Linking constraints facility location problem fixed-cost problem threshold-level problem Local optima Logical constraint models fixed-cost problem machine-sequencing problem threshold-level problem traveling salesperson problem Logical constraints LOOKUP function Lower bounds Lower-bound constraints LT constraints see Less-than (LT) constraints Machine-sequencing problem Marginal value Matching problem Mathematical models Mathematical programming problems MAX function Max Time parameter Max Time without Improvement option Maximization problems Microsoft® Office Excel® ABS function CEILING function Cell Edit function CHOOSE function COUNTIF function 347 COVAR function Data Table tool FLOOR function Formula Auditing tools IF function INDEX function INT function LOOKUP function MAX function MIN function range names ROUND function Solver see Solver SUMIF function SUMPRODUCT function SUMSQ function MIN function Minimization problems Modeling errors in linear programming debugging infeasible constraints logic unbounded objective function Models Modularity Multiple optima MultiStart option Mutations Network flow diagrams see Flow diagrams Network models assignment models with balance equations general-network models special-network models transportation model transshipment models Nodes Nonbasic variables Nonconvex regions Nondegenerate solution Nonlinear models with constraints Nonlinear programming 348 with constraints linearizations local optima one-variable models portfolio optimization model sensitivity analysis for two-variable models Nonlinear regression, evolutionary solver Nonlinear solver Nonnegative variables Nonprofit industries Nonsmooth functions Normalizing conditions Normalizing constraints Objective see Objective functions Objective function coefficients sensitivity analysis Objective functions concave functions convex functions fixed costs in linear programming model nonlinear programming model optimal values of penalty in unbounded Offspring solution Oil refining One-dimensional problem One-input, one-output case One-variable nonlinear models order-quantity example quantity-discount example Optimality message Optimization Optimization models Options button Options window Order-quantity example Parameters constraint in the Evolutionary Solver 349 objective function sensitivity analysis of Parent solutions Part-time shifts Patterns allocation model investment model in linear programming formulations product portfolio model refinery model transportation model Pivot equation Pivot value Playoff scheduling problem Population Report Population Size parameter Portfolio model optimization model variance Price, demand and profit problem Pricing example, two-variable model Product mix problem Proportionality Prototype Qualitative constraints see Logical constraints Quantity-discount example Range names Reduced Cost column Reduced gradient Reference sets Refinery model Relaxed problem Reliable algorithm Require Bounds on Variables option Return Right-hand-side (RHS) Risk ROUND function Scalar product Selection 350 Sensitivity analysis allocation example investment model for nonlinear programming product portfolio model refinery model transportation example Sensitivity Report allocation example for nonlinear programming transportation example Sequencing problems Set Cell Set Objective window Set-covering problem Set-packing problem Set-partitioning problem Shadow price Simplex algorithm Simplex tableau Simplex/LP Engine Slack variables Smooth functions Software Solver Add Constraint window Automatic Scaling option branch-and-bound procedure Cell Reference box Change Constraint window Constraint box convergence message debugging error message evolutionary solver see Evolutionary solver infeasibility message Integer Optimality option integer solver linear solver see Linear solver Max Time parameter Max Time without Improvement option MultiStart option 351 Mutation Rate parameter nonlinear models nonlinear solver see Nonlinear solver Nonnegative option optimality message Population Report range names with Require Bounds on Variables option unbounded objective function using Solver Parameters window Solver Results window Solver Sensitivity Solver specification allocation problem assignment problem blending problem capacitated facility location problem capital budgeting problem covering problem curve-fitting problem data envelopment analysis (DEA) fixed cost problem funds flow problem general-network models group assignment problem line balancing problem linearizing the absolute value linearizing the maximum machine-sequencing problem order quantity problem playoff scheduling problem portfolio optimization problem product mix problem product portfolio problem quantity-discount problem set-covering problem set-packing problem set-partitioning problem special network models staff-scheduling problem transportation problem 352 transshipment problem traveling salesperson problem two-dimensional location problem two-variable problems uncapacitated facility location problem Spreadsheet models allocation model assignment model blending model capacitated facility location model capital budgeting model covering model curve fitting model data envelopment analysis (DEA) model fixed-cost model funds flow model group assignment model linearizing the absolute value linearizing the maximum line-balancing model machine-sequencing model order quantity model playoff scheduling model portfolio optimization model product mix model product portfolio model quantity-discount model set-covering model set-packing model set-partitioning model staff-scheduling model transportation model transshipment model traveling salesperson model two-dimensional location model two-variable models uncapacitated facility location model Spreadsheet-based optimization Spreadsheets advantages and disadvantages of conciseness flexibility 353 form and content input parameters Staff-scheduling problem Standard Evolutionary Engine Steepest ascent method Strategic information Structural scheme Subtour elimination constraints Subtours SUM formula SUMIF function SUMPRODUCT function allocation model assignment model blending model covering model data envelopment analysis (DEA) fixed cost model funds flow model linear programming models network models with balance equations portfolio optimization model pricing model refinery model set-covering model set-packing model set-partitioning model transportation model transshipment model traveling salesperson model SUMSQ function Tactical information Tardiness Threshold-level problem Tight constraints Tour Tour constraints Trace Precedents icon Transformed flows Transportation models Transportation problem sensitivity analysis 354 Transshipment models Transshipment problem Traveling salesperson problem Tree diagram Two-dimensional location Two-variable nonlinear models curve fitting pricing example two-dimensional location Two-way tables Unbounded objective function Uncapacitated facility location problem Unique optimum Upper bounds Upper-bound constraints Variables artificial variables auxiliary variables basic variables binary variables entering variables integer variables leaving variables in linear functions nonbasic variables nonnegative variables slack variables see also Decision variables Virtual input Virtual output Weighted-average blending What-if questions Yield gains Yield losses 355 WILEY END USER LICENSE AGREEMENT Go to www.wiley.com/go/eula to access Wiley’s ebook EULA 356 ... R., 1943– Optimization modeling with spreadsheets / Kenneth R Baker – Third Edition pages cm Includes bibliographical references and index ISBN 978-1-118-93769-3 (hardback) Mathematical optimization. .. topics as well WHY SPREADSHEETS? Now that optimization tools have been made available with spreadsheets (i.e., with Excel), every spreadsheet user is potentially a practitioner of optimization techniques... SPREADSHEET MODELS FOR OPTIMIZATION This is a book about optimization with an emphasis on building models and using spreadsheets Each facet of this theme—models, spreadsheets, and optimization has