Index

A Analytic hierarchy process, 16-24, role of ORIMS, 29-30 17-18 Availability,31 A * algorithm, 1 absolute, relative measurement Averch-lohnson hypothesis, 31 Acceptance sampling, 1 structural information, 17 Accounting prices. 1 absolute measurement, 23t, 23-24, Accreditation, 1 24 B Active constraint, 1 applications in industry, Active set methods, 1 government, 24 Backward chaining, 33 Activity, 1 comments on costlbenefit analysis, Backward Kolmogorov equations, 33 Activity-analysis problem, 1 17-19 Backward-recurrence time, 33 Activity level, 1 decomposition of problem into Balance equations, 33 Acyclic network, 1 hierarchy, 21 Balking, 33 Adjacency requirements formulation, eigenvector solution for weights, Banking, 33-36 facilities layout, 210 consistency, 19-20, 20t banking, 33-36 Adjacent, 1 employee evaluation hierarchy, 24 portfolio diversification, 35-36 Adjacent extreme points, 1 examples, 21-24 portfolio immunization, 34-35 Advertising, 1-2, 1-3 fundamental scale, 17, 18, 18t pricing contingent cash flows, competition, 3 hierarchic synthesis, rank, 20-21 33-34 optimal advertising policy, 2-3 pairwise comparison matrix for BarChart, 37 sales-advertising relationship, 2 levell, 21t, 22 Barrier, distance functions, 37-39 Affiliated values bidding model, 4 random consistency index, 20t modified barrier functions, 37-38 Affine-scaling algorithm, 4 ranking alternatives, 23t modified interior distance Affine transformation, 4 ranking intensities, 23t functions, 38-39 Agency theory, 4 relative measurement, 21, 21-22t, Basic feasible solution, 40 Agriculture 21-24 Basic solution, 40 crop production problems at farm structural difference between Basic vector, 40, 41 level,429 linear, nonlinear network, 18 Basis,40 food industry and, 4-6 structuring hierarchy, 20 Basis inverse, 40 natural resources, 428-429 synthesis, 23t Batch shops, 41 regional planning problems, 429 three level hierarchy, 17 Battle modeling, 41-44 AHP, 7 Animation, 24 attrition laws, 42-43 AI, 7. See Artificial intelligence Anticycling rules, 24 classification, 41-42 Air Force operations analysis, 7-10 Antithetic random variates, 25 Bayes rule, 45 1970s,9 Application areas for ORIMS in Bayesian decision theory, 44-45 1980s,9 industry,297 subjective probability, 44-45 issues, 9-10 Applied probability, 25 Beale tableau, 47 postwar Air Force OA under AFR Apportionment, 496 Bender's decomposition method, 47 20-7,8-9 Apprenticeship, 507 Bidding models, 47-49 World War II Air Force OA, 8 Arc, 25 Big-M method, 50 Air pollution, control of, 194-195 Archimedean axiom, 25 Bilevellinear programming, 50 Airline industry, 10-12 Arima, 25 Bin-packing crew , 11-12 Arrival-point distribution, 25 one-demensional,51-52 fleet assignment, 11 Arrival process, 25 two-dimensional, 52-53 flight schedule planning, 10-11 Arrow diagram, 25 Binary variable, 50 yield management, 12 Artificial intelligence, 25-27, 319 Bipartite graph, 53 Algebraic modeling language for artificial neural networks, Birth-death process, 53 optimization, 12-15, 13-14 319-320,320 Bland's anticycling rules, 53 Algorithm,16 computational logic, 26-27 Blending problem, 54 Algorithmic complexity, 16 expertlknowledge-based systems, Block-angular system, 54 Allocation, health care systems, 274 319 Block pivoting, 54 Alternate optima, 16 Heuristicsearch,25-26 Block-triangular matrix, 54 Alternate paths, 16 logic programming, expert Bootstrapping, 54 Alternatives, ranking, analytic systems, 27 Bounded rationality, 54 hierarchy process, 23t Artificial variables, 28 Bounded variable, 54 Analyst's manual, documentation Assignment, of fleet, airline industry, Brachistochrone problem, 57-58 and,170 11 Branch,54 Analytic combat model, 16 Assignment problem, 28 Brownian motion, 54 Automation, 28-30 Brown's algorithm, search theory, 619

Italic entries indicatefigures. 742 Index

BTRAN,55 Computer-based group decision Crime, 126--131 Buffer, 55 process, 270 ambiguity, 129-130 Bulk queues, 55 Computer models, fire models, homicide, 126 Burke's theorem, 55, 446 224-225 Criterion Busy period, 55 Computer science, OR, 103-105 cone, 131 Concave function, 106 space, 132 Condition number, 106 vector, 132 c Cone, 106 Critical activity, 132 Congestion stock, inventory Critical path, 132 Calculus of variations, 57-59 modeling, 312 Critical path method (CPM), 132 Call priorities, 59 Congestion system, 106 Crossover, 132 Candidate rules, 59 Conjugate gradient method, 106 CSC. See Cumulative sum chart Capacitated transportation problem, 59 Connected graph, 106 Cumulative sum chart, quality Capital budgeting, 59-62 Conservation of flow, 106 control, 544-546 CDF,62 Consistency, eigenvector solution for, Curse of dimensionality, 132 Center for Naval Analysis, 62-66 analytic hierarchy process, Customer distribution, 132 military buildup, 65 19-20,20t Cut, 132 World WarIl, 63 Constrained optimization problem, Cut set, 132 Certainty equivalent, 66 107 Cutting stock problem, 132-137 Certainty factor, 66 Constraint, 107 CV,137 Chain, 66 Constraint qualification, 107 Cybernetics, 137-142 Chance-constrained programming, 66 Construction applications, 107-108 ergonomics, 138-139 Chaos theory, 66 Continuing role for field analysis, system design, 141-142 Chapman-Kolmogorovequations, 66 222-223 Cycle, 142 Chinese postman problem, 67-69 Continuous-time Markov chain, 199 Cyclic queueing network, 142 cycles, 67-69 Control Cyclic service discipline, 142 tours, 67-69 charts, 109 Cycling, 143 Choice strategies, 69 theroy, 109-113 Choice thoery, 72-72 Controllable variables, 109 Chromatic number, 72 Convex combination, 113 D Chromosome, 72 Convex cone, 113 CIM,72 Convex function, 113 Danzig-Wolfe decomposition Circling, 72 Convex hull, 113 algorithm, 145 Classical optimization, 72 Convex polyhedron, 113 Data envelopment analysis, 145-149 Closed network, 72 Convex-programming problem, 113 Farrell measure, 146 Cluster analysis, 72-74 Convex set, 113 ratio form model, 147-148 Cobb-Douglas production function, 75 Convexity rows, 113 Database design, 145 COEA,75 Cooperative games, 244, 244-245 DEA,150 Coefficent variation, 75 Corner point, 113 Decision analysis, 150-154 Cognitive mapping, 75 Corporate strategy, 114-118 Decision maker (DM), 155 Coherent system, 75 Cost Decision making, 155 Column generation, 76 allocation game, 244 Decision problem, 156 Column vector, 76 analysis, 119-121 Decision support system, 156--158 Combat analytic hierarchy process, 17-19 Decision trees, 159-160 model,76 coefficient, 122 Decision variables, 161 simulation, 76 effectiveness analysis, 122-125 Decomposition Combinatorial, integer optimization, evolution, 119-120 algorithm, 161 76-83 game, solutions to, 244 analytic hierarchy process, 21 Combinatorial explosion, 83 methods, 120-121 Degeneracy, 161 Combinatorics, 83 range, 125 Degenerate solution, 161 Common random variates, 85 row, 125 Degree, 161 Common value bidding model, 85 slope, 125 Delaunay triangulation, 161 Communications networks, 86-91 vector, 125 Delay, 161 design, 88-91 COV,125 Delphi method, 161-163 modeling, 87-88 Covering problem, 125 Density, 163 Community OR, 91 facility location, 214 function, 163 Competition, advertising and, 3 Coxian distribution, 125 Departure process, 163 Complementarity condition, 91 CPM,I25 Descriptive model, 163 Complementary pivot algorithm, 92 CPP, 125 Design, control, 164 Complementary problems, 92-94 Cramer's rule, 125 Detailed balance equations, 164 Complementary slackness theorem, 95 Cranes, material handling, 378 Determinant, 164 Computational complexity, 95-98 Crash Deterministic model, 164 Computational geometry, 98-101 cost, 125 Developing countries, 164-165 Computational logic, artificial time, 125 Development tool, 166 intelligence, 26-27 Crew scheduling, 125 Devex pricing, 166 Computational probability, 103 airline industry, 11-12 Deviation variables, 166 logistics, 355-356 DFR,166 Index 743

Diameter, 166 common history, 178-179 ETA file, 196 Diet problem, 166 electric power systems, 185-187 ETA matrix, 196 Diffusion approximation, 166 emergency services, 188-190 ETA vector, 196 Diffusion process, 166 fuel inventory planning, 186 Ethics, 197-199 Digraph, 166 generation system expansion Euler tour, 199 Dijkstra's algorithm, 166 planning, 186 Eulerian, Hamiltonian cycles, 262 Directed graph, 167 optimal dispatch of generating Evaluation, 199 Direction of set, 167 units, 185-186 EVOP, 199 Directional derivative, 167 optimal generation system EWMA chart. See Exponentially Discrete-event stochastic systems, reliability, 185 weighted moving average chart 62(H)32 optimal maintenance scheduling, Ex ante forecasts, 199 elements of simulation model, generating units, 186 Exclusive-or node, 199 62(H)28, 627t OR, common interests, 180-182 Expected utility theory, 199 input data, 627t perspectives, OR, 179-180 Expert systems, 199-202 input distribution selection, 628 utility resource planning, 186-187 artificial intelligence, 27 model validation, 632 Edge, 184 expert system development, 202 output analysis, 629~31 Efficiency, 184 general nature of expert system, simulation programming Efficiency frontier, 184 200-201 languages,62~29 Efficient algorithm, 184 inference-engine, 201-202 variance reduction techniques, Efficient point, 184 Exploratory modeling, 203-204 631-632 Efficient solution, 184 Exponential arrivals, 205 Discrete-programming problem, 167 Eigenvalue, 184 Exponential-bounded algorithm, 205 Discrete-time Markov chain, 167 Eigenvector, 185 Exponential smoothing, 205-206 Dispatching, logistics, 356 Eigenvector solution, analytic Exponentially weighted moving Distribution selection for stochastic hierarchy process, 19-20, 20t average chart, 544-546 modeling, 167-169 Electrical networks, quadratic Extremal, 207 data, 169 programming, 533 Extremal column, 207 hazard rate, 167-169 Elementary elimination matrix, 187 Extremal problem, 207 range of random variable, 169 Elimination method, 187 Extreme direction, 207 DMU, 169 Ellipsoid algorithm, 187 Extreme point, 207 Documentation, 169-172 ELSP, 188 Extreme point solution, 207 analyst's manual, 170 Embedding, 188 Extreme ray, 207 common characteristics, 173 graph theory, 263 dynamic programming, 171-173 Emergency management services, 191 examples, 172-173 Emergency medical services, 189 F manager's manual, 170 Emergency service, 188, 188-189 programmer's manual, 170 emergency medical services, 189 Face validity, 209 roots, key references, 172 emergency response system, 188 Facilities layout, 209-212, 210-211 user's manual, 170 fire services, 189 adjacency requirements Domain knowledge, 170 police services, 189-190 formulation, 210 DSS, 171 policy questions, 190 heuristic solution methods for DTMC. See Discrete-time Markov Employee QAP, 211-212 chain evaluating for raises, analytic implicit enumeration, 210-211 Dual linear-programming problem, hierarchy process, 23t, linearization, 210 171 23-24,24 optimal algorithms for QAP, Dual-simplex method, 171 evaluation hierarchy, analytic 210-211 Duality theorem, 171 hierarchy process, 24 quadratic assignment formulation, Dualplex method, 171 EMS. See Emergency management 209-210 Dummy arrow, 171 services Facility location, 213-215 Dynamic programming, 171-173 Entering variable, 191 field analysis, 220 Environmental systems analysis, Factorable programming, 216-218 191-195 Failure-rate function, 219 E air pollution, control of, 194-195 Familiarity with successful cases, 508 solid wastes management, 194 Family disaggregation model, Earliest finish time, 175 urban water management, 191-194 hierarchical production Earliest start time, 175 EOQ,196 planning, 278 Econometrics, 175-177 Equilibrium models, quadratic Farkas' lemma, 219 definition, 175 programming,532-533 Farrell measure, 219 other modeling techniques, Ergodic theorems, 196 Fathom, 219 176-177 , 196 FCFS, 219 simultaneous equation models, 176 B formula, 196 Feasible basis, 219 single equation regression models, C formula, 196 Feasible region, 220 175-176 delay model, 196 Feasible solution, 220 Economic applications, fractional distribution, 196 FEBA,220 programming,234-235 loss model, 196 Feedback queue, 220 Economic order quantity, 177 Error analysis, 196 Field analysis, 220 Economics, 178-183 numerical analysis, 463-465 FIFO, 223 744 Index

Finite source, 223 allocation game, 244 optimaation,263-264 Fire models, 223-225, 224-225 cooperative games, 244, 244-245 theory, 261-264,262 Fire services, 189 game, solutions to, 244 trees, 263 Firing rule, 226 matrix games, 242-243 undirected graph, 262 First feasible solution, 226 noncooperative games, 243, 243t Graphical evaluation, review First-fit decreasing algorithm, 226 stretegies,241-242 technique, 261 First-order conditions, 226 Gaming, 245-247 Graphics, 261 Fishing, natural resources, 429-430 analysis relationships, 247 Greedy algorithm, 264 Fixed-charge problem, 226 learning from, 246 GRG method, 264 Fleet assignment, airline industry, 11 prospects for, 247, 247 Group Flexible manufacturing systems GAMMA distribution, 248 analytic hierarchy process, (FMS),226--229 Gantt charts, 248 268-269 Flight schedule planning, airline definition, 248 block method decision making, industry, 10-11 example, 248, 248 266 Float, 229 extensions, 249,249 computer-based group decision Flow, 229 four-activity Gantt chart, 248 process, 270 Flow shop, 229 history, 249 consensus, 266-268 Flow time, 229 implementation issues, 249 decision computer technology, FMS,229 milestone Gantt chart, 249 264-265 Forecasting, 229-233 Gauss-Jordan elimination method, 250 decision making, 265-270 accuracy of methods, by situation, Gaussian elimination, 250 game theory, 269-270 231 Gene, 250 group analytic hierarchy process, demand, health care systems, 274 Generalized upper-bounded problem, 268-269 framework for, 229 250 social choice theory, 269 implementation of forecasts, 232 Generator, of Markov process, 250 utility analysis, 265-266 in management, 232 Genetic algorithm, 250-252, 251 methodology tree, 230 applications, 252 methods, 230, 230-231 theoretical foundations, 251-252 H needs for forecasts, 232 Geographic information systems, selection of methods, 231-232 253-255 Half space, 273 Forestry, natural resources, 427-428 capabilities, 253 Hamiltonian tour, 273 Forward chaining, 233 GIS in urban planning, 254 Hazard rate, 273 Forward Kolmogorov equations, 233 modeling communications distribution selection, stochastic Forward-recurrence time, 233 networks, 254-255 modeling, 167-169 Fourier-Motzkin elimination method, NeGIA initiative 6, 253-254 Health care systems, 273-275 233 SDSS for decision making, 254 allocation, 274 Fractional programming, 234-237 Geometric programming, 255-257 forecasting demand, 274 economic applications, 234-235 computational methods, 257 medical-decision making, 274-275 indirect applications, 235 convex programs, 256 scheduling, 273-274 maximizing, smallest of several polynomial, 256--257 supplies/materials planning, 274 ratios, 236 GERT,257 Heavy-traffic approximation, 275 multi-objective fractional GIS, 257. See Geographic Hessenberg matrix, 275 programs, 236 information systems Hessian matrix, 276 multi-ratio fractional programs, Global balance equations, 257 Heterogeneous Lanchester equations, 236 Global maximum (minimum), 258 276 non-economic applications, 235 Global models, 258 Heuristic procedure, 276 notation, definitions, 234 Global solution, 259 Heuristic search, artificial problem, 237 Goal intelligence, 25-26 properties, 235-236 constraints, 259 Heuristic solution methods, facilities single-ratio fractional programs, GP modeling, 259-260 layout, 211-212 234-235 GP research, applications, 260 construction methods, 211-212 Framing, 237 GP solution methods, 260 improvement methods, 212 Frank-Wolfe method, 237 programming, 259-261 limited enumeration, 211 quadratic programming, 533 Gomory cut, 261 Hierarchical production planning, Free float, 237 Goods-oriented siting, location 276--279, 277 Free variable, 237 analysis, 350-351 aggregate production planning for Freight routing, 237 Gordan's theorem, 261 product types, 277-278 FTRAN,237 Government, analytic hierarchy conceptual overview of Fuel inventory planning, economics, process, 24 hierarchical planning 186 GP,261 system, 277 Fuzzy sets, 237-239 Gradient vector, 261 family disaggregation model, 278 Graeco-Latin square, 261 hierarchical production planning, Graph, 261 276-277,277 G coloring, 263 item disaggregation model, directed graph, 262 278-279 GA. See genetic algorithms embedding, 263 Higher education, 279-283 Game theory, 241-245 Eulerian, Hamiltonian cycles, 262 historical background, 280 Index 745

literature, 280-282 mnemonic notation, 303, 303 J ORIMS on campus, 282-283 models, databases, 302, 302 Hirsch conjecture, 283 object-oriented database structure, , 317, 441-443 Homogeneous Lanchester equations, 304 arrivals, departures, 442 283 object oriented modeling, 303, 304 possible open network Homogeneous linear equations, 284 rational database structure for, 303 configuration, 442 Homogeneous solution, 284 relational databases, 302 routing, 442, 442 Horn clause, 284 Informs, 304 states of process, 442 Hospitals, 284-286 Initial feasible solution, 304 steady-state ~tribution of access, 284 Input-output analysis, 304 process, 442-443 cost, 284-285 Input-output coefficients, 304-305 JIT manufacturing. See Just-in-time need for OR, 285-286 Input process, 304 manufacturing quality of care, 285 Insensitivity,305 Job shop scheduling, 317-323 Hundred percent rule, 286 Institute for Operations Research, artificial intelligence techniques, Hungarian method, 286 Management Sciences 319 Hypercube queueing model, 286-290 (INFORMS), 305 artificial neural networks, approximations, 289-290 Institute of Management Sciences, 679 319-320,320 early work, 286-287 Integer goal programming, 305 dispatching rules, 318-319 implementations, 290 Integer-programming problem, 305 expertlknowledge-based systems, physical assumptions, original Intellectual bas~, 507 319 model, 288-289 Intensity genetic algorithms, 320-321 state, transition, probabilities, 288 function, 305 learning, 321-322 Hyperexponentiald~tribution,291 ranking, analytic hierarchy mathematical programming, Hypergame analys~, 291 process,23t 317-318 Hyperplane, 291 Interactive optimization, 305 newtrends,322-323 Interchange heuristic, 305 three-layer feed-forward neural Interfering float, 305 network, 320 I Interior point, 305 Johnson's theorem, 324 Interior-point, 305-308 Just-in-time manufacturing, 317, 324 Identity matrix, 293 brief history, 306-307 Justice, 126-131 IFR,293 status, extensions, 307-308 IIASA. See International institute for International Federation of applied systems analysis Operational Research K Imbedded Markov chain, 293 Societies, 293, 308 Implementation, 293-294 International Institute for Applied Karmarkar's algorithm, 325 Implicit enumeration, 294 Systems Analys~, 293, Karush-Kuhn-Tucker,325 facilities layout, 210-211 308-309 Kendall's notation, 325 Implicit price, 294 Intervention model, 309 Kilter conditions, 325 Importance sampling, 294 Inventory KKT. See Karush-Kuhn-Tucker Impossibility theorem, 294 categories of inventory-related Klee-Minty problem, 325 Inactive constraint, 294 costs, 310-311 Knapsack problem, 325-326 Incidence matrix, 295 changing givens in, 314 Knowledge acquisition, 326 Incident, 295 congestion stock, 312 Knowledge base, 326 Independent float, 295 economic order quantity (Wilson Knowledge engineer, 326 Independent private values bidding Lot-size),311-312 Kolmogorov equations model,295 inventory level versus time, 311 backward, 33 Indirect costs, 295 log~tics, 356 forward, 233 Industrial applications, 295-299 modeling,309-314 Konig's theorem, 326 Industrial dynamics, 299 newsvendor problem, 312-313 Konigsberg Bridge problem, 326 Industrial engineering, OR and, reasons for carrying inventories, Kruskal's algorithm, 326 299-301, 301 309-310 KT conditions. See Kuhn-Tucker IE from manufacturing to service, uncertain dem, in on-going conditions 300 situation, 313--314 Kuhn-Tucker conditions, 326 industrial engineering curricula, Inverse matrix, 315 300-301 IP,315 The World of Industrial IS, 315 L Engineering, 299 IsomOJphic graph, 315 Industry, analytic hierarchy process, ISOP 9000 Standard, 315 Lack of memory, 327 24 Isoquant, 315 Lagrangian decomposition, 327 Infeasible solution, 301 Item disaggregation model, Lagrangian function, 327 Inference engine, 201-202,301 hierarchical production Lagrangian relaxation, 327 Influence diagrams, 301 planning, 278-279 Lanchester attrition, 327 Information systems, database design Iteration, 315 Lanchester's equations, 327-330 in ORlMS, 301-304 NHS,315 ancient warfare, 328 advantage of integration, 303--304 extensions, 329-330 architecture of comprehensive historical background, 327-328 information systems, 302 modern warfare, 328-329 746 Index

validation of equations, 330 solving linear programming limiting behavior, 366-367 Languages, algebraic modeling, for models, 345-346 properties of chain, 366 optimization, 13 Linearization, facilities layout, 210 , 559 Laplace-Stieltjes transform, 330 Lipschitz, 347 reflecting random walk example, Laplace transform. 330 Little's law, 347-348 366 Large-scale systems, 330-332 Little's theorem, queueing theory, 556 theorem, 367 algorithms, macro-structure, 332 Livestock production, natural Markov processes, 368-374 block-angular structure, 331 resources, 429 classification, 371-373 block-triangular structure, 332 Local balance equations, 348 dynamic programming macro-structure, 331-332, Local improvement heuristic, 348 formulation, 369 331-333 Local maximum, 348 infinite horizon discounted reward micro-structure, 331 Local minimum, 349 case, 369 staircase structure, 332 Local optimum, 349 linear programming, 369 state-of-the-art. 332 Local solution, 349 policy iteration, 369-370 Latest finish time, 333 Location analysis problem formulation, 368-369 Latest start time, 333 goods-oriented siting, 350-351 solution procedures, 369-370 Latin square, 333 network location problems, 350 successive approximations, 369 LCFS, 333 planar location problems, 349-350 without discounting, 370 LCP, 333 public service oriented siting, Markov property, 374 LDU matrix decomposition, 333 351-353 Markov random field, 374 Learning, 333-335 Log-linear model, 357 Markov routing, 375 curve,335-338,336,337 Logic programming, 354 Markovian processes, 370 experience units, 334 artificial intelligence, 27 Marriage problem, 375 log-log plot, learning curve Logical variables, 354 Master problem, 375 geometries, 337 Logistics, 354-357 Matching, 375-376 metrics, 334-335 crew scheduling, 355-356 arc routing, 376 other factors affecting, 337 dispatching, 356 on bipartite graphs, 375-376 performance criteria, 334 integrated logistics systems, 357 job scheduling, 376 power model, 336-337 inventory, 356 Material handling, 377-379 Least-squares analysis, 338 networking, 354-355 capacity of system, 379 Leontiefmatrix, 338 routing, 354-355 container size, standardization, 379 Level crossing methods, 338-340 Longest-route problem, 357-358 cranes, 378 applicability, 339-340 Loss function, 358 hoists, 378 conservation law, 339 Lottery, 358 material handling equipment, 378 estimation, 340 Lower-bounded variables, 358 number of pieces of equipment, sample paths, 338-339, 339 Lowest index anticycling rules, 358 379 stationary distribution, 338, 339 LP,358 OR models in material handling, Level curve, 340 379 Lexico-positive (negative) vector, 340 system design, 379 Lexicographic ordering, 340 M unit load concept, 379 LGP, 340 Material requirements planning, 380 Libraries, 340-342 MAD,359 Mathematical model, 380 model,402 Maintenance, 359 Mathematical programming, 380 LIFO,343 Makespan, 359 problem, 380 Likelihood ratio, 343 Malcolm Baldrige award, 359, society, 381 Limiting distribution, 343 688-689 system, 381 Lindley's equation, 343 Manager's manual, documentation Matrix,381-384 Line, 343 and,170 algebra, 381-384 Line segment, 347 Manhattan metric, 359 basic operations, 381-382 Linear, nonlinear network, structural Manpower planning, 359 eigenvalues, 383 difference, analytic hierarchy forecasting, control, 360 eigenvectors, 383 process, 18 stochastic models, 359-360 game, 242-243,388 Linear combination, 343 Marginal value (cost), 361 geometric, 388 Linear equation, 343 Marketing, 361-364 historical sketch, 384 numerical analysis, 463 marketing science, 362-363 inverse, 383 Linear-fractional programming measurement models, 362 laws of matrix algebra, 381-382 problem, 343 ORIMS marketing model types, linear equations, 382-383 Linear functional, 343 362 norms, 383-384 Linear inequality, 343 stylized theoretical models, 362 Matrix-analytic stochastic models, Linear least squares, quadratic trends, 363-364 384-387 programming, 531 Markov chain, 365-367 Markovian arrival processes, Linear programming, 343-347, 347 coin toss sequence problem, 367 386-387 applications, 345 Erlang distributions, 558 matrix-analytic M/G/l-type duality theory, post-optimality examples, 365-366 queues, 384-385 analysis, 346-347 extended Erlang family of matrix-geometric solutions, linear programming models, distributions, 558-559 385-386 344-345 Ganbler's run problem, 367 MAUT,388 Index 747

Max-flow min-cut theorem, 388 model libraries, 402 Multiple pricing, 425 Maximum, 388 model management n, 402-403 Multiplier vector, 425 Maximum feasible solution, 388 model representation, 402 Maximum-flow network problem, 388 model selection, 402 Maximum matching problem, 388 operations, 401 N MCDM. See Multi-criteria decision MODl,404 making MOE. See Measure of effectiveness Nash saddle-point, 427 Measure of effectiveness, 388 MOIP,404 Natural resources, 427-430 computer simulation, 389 MOLP,404 agriculture, 428-429 directions of development, 390 Monorails, cranes, material handling, crop production problems at farm mathematical programming, 389 378 level,429 medical decision making, 389-390 Monte Carlo sampling, variance fishing, 429-430 Monte Carlo methods, stochastic reduction, 405-407 forestry,427-428 models, 389 antithetics,405-406 livestock production, 429 stochastic models, 389 control random variables, 406 mining, 429 Measurement, analytic hierarchy importance sampling, 406-407 regional planning problems, 429 process, 17 MOR,407 wildlife management, 428 Medical-decision making, health care MORS,401 Near-optimal solution, 431 systems, 274-275 MRP,407 Neighboring extreme point, 431 Memoryless property, 391 MS,401 Network, 431. See also Neural Menu planning, 391-392 MSE,407 network Metagame analysis, 392 Multi-attribute utility theory, 407-409 activity on node, 438 Metamodeling, 392-393 Multi-criteria decision making, 388, Burke's theorem, 446 Desert ShieldlDesert Storm, 412 design, 431,434,434-435 396-397 Multi-echelon inventory systems, 412 flow models, 434, 434 emergence of systems analysis, 396 Multi-echelon logistics systems, 413 Jackson networks, 441-444 general linear metamodel, 393 Multi-objective linear-programming location problems, location institutionalization, impact of problem, 413 analysis, 350 systems analysis, 396 Multi-ratio fractional programs, 236 logistics, 354-355 metamodel in system simulation, Multicommodity network flow, models,435 392, 392-393 410-411 operational planning, 431 military OR, 394-397 Multidimensional transportation optintization, 431-437,433 MOR,397 problem, 412 planning, 437-440 postwar MOR developments, Multiobjective programming, production/distribution system, 433 395-396 413-418,418 project control, 438 wartime combat OR in Korea, average number of MOLP quasi-reversibility, partial balance, Vietnam, 396 efficient extreme points, 445-446 World Warn MOR 416t queue with feedback, 446-447, 447 accomplishments, 395 background concepts, 414-416, of queues, 441-449 Method of stages, 394 414-416 reversibility, detailed balance Military OR, 394-397 criterion space, 415 equations, 444-445 MIMD,398 decision space, 414 reversing of, 444 Minimum, 398 general algorithmic outline, 417 schematic of simple feedback Minimum-cost network-flow interactive procedures, 416-417, queue,447 problem, 398 417 simplex algorithm, 441 Minimum feasible solution, 398 projection of q onto nondominated single-server networks, 448 Minimum spanning tree problem, 398 set, 418 sojourn times, 447-448, 448 Mining, natural resources, 429 selected interactive procedures, solution methods, 435-437 Minor, 398 417-418,418 steady-state probabilities, 444 MIP, 398. See Mixed-integer terminology, 413-414 sub-networks,447 programming problem vector-maximum algorithms, 416, symmetric networks, insensitivity, Mixed-integer programming problem, 416t 446 398 Multiple criteria decision making, system design, 432 Mixed network, 398-399 419-424 traffic processes, 446-447 Model,399 basic concepts, 420 transition intensities, 444 accreditation, 399 deterministic decision analysis, 421 types of models, 434-435, builder's risk, 399 explicit decision space methods, 434-435t building, 298 422-424 uncertain durations, 438-439 evaluation, 399-400 illustration of convex cones, 423 Neural network, 449-451 optimization, 13 methodological approaches, artificial neural structure, 450 user's risk, 404 421-424 four node, single PE network, 451 validation, 404 multiobjective mathematical structure of, 450-451, 451 verification, 404 programming,421-424,423 why use neural networks, 449-450 Model management, 400-404 stochastic decision analysis, 421 New York City-RAND Institute, 569 model configuration, 402-403 taxonomy, of MCDM approach, Newsboy problem, 452 model formulation, 401 420, 421, 42lt Newsvendor problem, 452 model interpretations, 402 Multiple optimal solutions, 425 inventory modeling, 312-313 748 Index

Newton's method, 452 end of ORO, 474 Parametric analysis, parametric NLP,452 ORO activities, projects, 472-474 programming, 487 Node, 452 ORO director, 472 Parametric bound, 485 Node-arc incidence matrix, 452 pot-World Warn activities, 471 Parametric linear programming, 485 Non-archimedean number, 452 RAC's project portfolio, 474-475 Parametric programming, 486-488 Non-compensatory choice strategies, transition to RAC, 474 applications, 487-488 452 Operations Research Society of degeneracy, 488 Non-preemptive, 461 America, 475-476 historical sketch, 486 Nonactive (nonbidding) constraint, Opportunity cost, 476 parametric analysis, 487 452 Optimal feasible solution, 476 postoptimal analysis, 486-487 Nonbasic variable, 452 Optimal solution, 476 SA, PP in other fields, 488 Noncooperative games, 243, 243t Optimal value, 476 sensitivity analysis, 487 Nondegenerate basic feasible Optimal value function, 476 Parametric solution, 489 solution, 453 Optimality criteria, 476 Pareto-optimal solution, 489 Nondominated solution, 453 Optimization, of queues, 476 Partial balance equations, 489 Nonlinear programming, 453-461 Optimization of network, 432-434, Partial pricing, 489 Nonnegative solution, 461 433 Path,489 Nonnegativity conditions, 461 design models, 435 Payoff function, 489 Nonsingular matrix, 461 design problems, 434, 434-435 Payoff matrix, 489 Nontrivial solution, 461 flow models, 434, 434 PDA,489 Nonzero-sum game, 462 operational planning, 431 PDF. See Probability density function Normative model, 462 production/distribution system, 433 PDSA,489 Northwest-corner solution, 462 solution methods, 435-437 Periodic review, 489 NP, NP-complete, NP-hard, 462 system design, 432 PERT. See Program evaluation, Null matrix, 462 types of models, 434-435, review technique Null space, 462 434-435t Perturbation,490 Numerical analysis, 462-465 Organuation, 476-480 Petro-chemical industry, 490 error analysis, 463-465 future of, 480 PFI, 492. See Product form, of inverse impact of computers, 462-463 information processor, 477-479 Phase I procedure, 492 linear equations, 463 management science Phase n procedure, 492 contributions, 479-480 Phase-type distribution, 492 Origin node, 481 Phase-type probability distributions, o ORO, 481 492-494 ORSA, 481. See Operations Research Piecewise linear function, 494 0, 0 notation, 467 Society of America Pivot Object-oriented database, 467 Out-of-kilter algorithm, 481 column, 494 Objective function, 467 Output process, 481 element, 494 OEG, 467. See Operations evaluation Outside observer distribution, 481 row, 494 group Overachievement variable, 482 selection rules, 494 Offered load, 467 Overflow process, 482 Planar location problems, location Open network, 467 Overtaking, 482 analysis, 349-350 Operations evaluation group, 467 Plant location problem, facility Operations management, 467-470 location, 214-215 designing system, 468-469 p PO, 495 managing system, 470 Point stochastic processes, 495 OR office, research analysis P-center problem, facility location, Point-to-set map, 496 corporation, 470 214 Poisson arrivals, 496 planning system, 469-470 Packing problem, 483 Poisson process, 496 Operations research, management Pairwise comparison matrix Police services, 189-190 science, 504-508 for levell, analytic hierarchy Policy, advertising, optimal, 2-3 communication, 506 process, 22 Politics, 496-497 context of ORlMS, 504-505 levell, analytic hierarchy process, apportionment, 496 elements in, 505 2It promotion of candidates, 497 evaluation, presentation, 506 Palm measure, 483 redistricting, 496-497 following through, 506-507 Parallel computing, 483-485 voting methods, logistics, 497 formulation, 505 applications in OR, 484-485 Pollaczek-Khintchine formula, 498 implementation, 506 efficiency, scalability, 484 Polling models, single-server ORIMS as science, 504 kinds of parallel computers, networks, 448 processes of practice, 505, 505 483-484 , 498 relation between analyst, client, parametric programming, 486-488 Polyhedron, 498 507 programming models, 484 Polynomial hierarchy, 498 research, 505-506 scalability, 484 Polynomial programming, 503 situations of practice, 505 speedup, efficiency, scalability, Polynomial time, 498 skills of practice, 507-508 484 Polynomially bounded (-time) variations, 506 Parameter, 485 algorithm (polynomial Operations research office Parameter-homogeneous stochastic algorithm), 498 early military, 471 process, 485 Portfolio Index 749

analysis, 498 professional opportunities, unconstrained quadratic diversification, banking and, 35-36 organizations, 524 minimization in classical estimation problems, 500-502 program components, scope of mathematics, 530-531 immunization, banking and, 34-35 evaluation, 523-524 Quality control, 536-547 selection problem, 499 review technique, 489, 525 ARLs of Shewhart, 546t short selling, 500 Programmer's manual, documentation comparison of Shewhart, solution of portfolio selection and, 170 CUSUM,EWMA model, 499-500 Project procedures, 545-546, 546t theory, 498-502 management, 525 conformity; nonconforming units, use of mean, variance, 499 scoop, 526 538-539 POS,503 Projection matrix, 525 cumulative sum charts, 544-545 Postoptimal analysis, 503 Promotion of candidates, 497 CUSUM, EWMA charts, 544-546 Postwar Air Force, operations Proper coloring, 526 determination of control limits, 540 analysis, under APR 20-7, 8-9 Prospect theory, 526 exponentially weighted moving Power model, 503 Protocols, 526 average charts, 545 Power system scheduling, quadratic Pseudo-polynomial-time algorithm, interpreting control chart patterns, programming, 533 526 544 PP,503 Pseudoconcave function, 526 judging control chart performance, PPB(S),503 Pseudoconvex function, 526 540 Precedence diagramming, 508 Pseudoinverse, 526 multivariate control charts, 546 Predictive model, 508 Pseudorandom numbers, 526 process, 539 Preemption, 509 Public policy analysis, 526-528 setting up statistical process Preemptive priorities, 509 ORIMS, public policy, 527-528 control scheme, 541 Preference theory, 509-511 policy analysis steps, 527, 527 Shewhart charts, 541-544 Prescriptive model, 512 steps in policy analysis study, 527 sources of variation, 539 Prices, 512 Public service oriented siting, location specification limits, process Pricing multipliers, 512 analysis, 351-353 capability, 538-539 Pricing out, 512 Pull system, 528 terminology, 537-538; Pricing vector, 512 Pure-integer programming problem, specification limits, 538 Primal-dual algorithm, 512 528 TQM, ISO, other developments, Primal-dual linear programming Push system, 528 546-547 problems, 512 types of control charts, 540-541 Primal problem, 512 typical univariate Shewhart chart Prim's algorithm, 512 Q for means, 539 Prisoner's dilemma game, 512-513 uses of SQC procedures, 536-537 Probabilistic algorithm, 513 Q-GERT,529 Quality control chart, 539, 539-543 Probabilistic programming, 513 Quadratic assignment formulation, for attributes, 543 Probability density function, 489,513 facilities layout, 209-210 for average number of Probability distribution, 513 Quadratic assignment problem, 529 conformities per unit, Probability distribution selection, 513 Quadratic form, 529 543-544 Probability generating function, 513 Quadratic-integer programming, 529 for measures of variability, 542 Probability integral transformation Quadratic programming, 529-536 for nonconformities (constant method, 513-514 active set methods, 534 sample size), 543 Problem solving, 514 applications, 531-533 for number of nonconforming Problem structuring methods, 514-516 classification of quadratic units, 543 , 516 programs, 530 for proportion nonconforming Product form, 516 conjugate gradient method, units, 543 of inverse, 516 530-531 for sample means (X chart), 542 Product-form solution, 516-517 electrical networks, 533 for variables, 541-542 Product-mix problem, 522 equilibrium models, 532-533 for X, 542 Production function, 517 finance, 531-532 Quality of care, hospitals, 285 Production management, 517 Frank-Wolfe method, 533 Quasi-concave function, 549 batch shops, 519-520 interior point methods, 534 Quasi-convex function, 549 flows lines, continuous operations, linear least squares, 531 Quasi-reversibility, 549 521 methods based on LCP, 533-534 consequences of job shops, 517-519 methods for nonconvex QP, 534 quasi-reversibility, 445-446 operational problems, 517-520 power system scheduling, 533 partial balance, 445-446 strategic, tactical problems, recent algorithmic developments, quasi-reversibility, 445 518-521,519 533-534 transitions in network, 445 tradeoff curves, 519 reduced gradient methods, 533 Queue inference engine, 549-553 Production planning for product software, 534 background, motivation, 549 types, hierarchical production solutions, computed efficiently, cumulative distribution of queue planning and, 277-278 531 delay, 553 Production rule, 522 to solving general nonlinear density function of arrival time of Program evaluation, 522-524 programs, 533 queued customer, 552 methodologies, 524 taxation, 532 distribution of queue length, 553 types of solutions, 531 750 Index

illustrative queue inferencing third ten years (1968-1977), development, 588-592 problems, 549-550 569-570 project planning, 591-592 invisible queues in Random consistency index, analytic R&D project selection, 588-591 telecommunication systems, hierarchy process, 20t Resource 550 Random field, 571 aggregation, 593 maximum experienced queue Random number generators, 571-578 leveling, 593 delay, 553 combined generators, 575-576 smoothing, 593 maximum queue length, 553 discrepancy,low-discrepancy Response time, 593 order statistics, 550-553, 552-553 sequences, 575 Restricted-basis entry rule, 593 pedestrian queueing example, lattice structure, 575 Retailing, 594-595 550-551 linear recurring sequences, analysis of movement of queue inference in more general 573-575 customers, 595 queues,551-552,552t non-inversion methods, 577 classification of goods by sales research literature, 553 non-uniform random numbers, volume, 594-595 Queueing discipline, 554 576--578 inventory control, 595 Queueing networks, 554 nonlinear generators, 576 prediction of number of customers Queueing theory, 554-561 random number generators, visiting store, 594 balking, reneging, 558 571-578 Revenue basic notions, 554-555 regression analysis, 581-583 equivalence theorem, 595 birth-and-death queues, 556--558 Random variable, range of, neutrality theorem, 595 bulk queues, 559 distribution selection, Reversibility, detailed balance Erlang distributions, 558 stochastic modeling, 169 equations,444-445 extended Erlang family of Random variates, 578 Reversible Markov process, 595 distributions, 558--559 Random walk, 578-579 Revised simplex method, 596 feedback queues, 560 Ranging, 579 RHS, 596 flow of probability argument, 557 Rank,579 Right-hand-side, 596 general theorems, 555-556 Rate matrix, 579 ranging, 596 GIlMlc, GIIG!1 queues, 560 Ray, 579 Risk,596 history, 554 R&D, 579 Risk assessment, 596--598 Jackson networks, 560-561 Reasoning, 579 Risk management, 598-605 Little's theorem, 556 Reasoning knowledge, 579 hierarchical holographic modeling MlG!lIpriority queue, 560 Recognition problem, 579 for,602-604,602-605 MlG!1 queue, 559-560 Recourse linear program, 579 role of software in larger system, MIMIlnN queue, 557 Redistricting, 496--497 601-602 MIMII queue, 557 Reduced costs, 579 software, engineering, 602-604 MIMIc!c queue, 557-558 Reduced gradient methods, 579 technical VS. non-technical risk, machine-repair (finite-source) quadratic programming, 533 600-601 queue, 558 Redundancy, 579-580 Robustness analysis, 606 Markov chain models, 558--559 Redundant constraint, 580 Rosen's partitioning method, 606 non-Markovian queues, 559-560 Regeneration points, 580 Roundoff error, 606 output theorem, 558 Regression analysis, 581-583 Route construction heuristic, 606 queueing networks, 560-561 alternatives to classical least Route improvement heuristic, 606 tandem networks, 560 squares, 582-583 Row vector, 606 taxonomy, 555 classical least-squares analysis, Rule, 606--607 581-582 Rule set, 607 departures from classical Running time of algorithm, 607 R assumptions, 582 Relational database, 583 R-chart, 579 Relative costs, 583 s RAC. See Research analysis Relaxed problem, 583 corporation Reliability, 583 S-model, 633 Rail freight operations, 563-565 Reliability function, 583 SA,609 blocking, 564-565 Reliability of systems, 583-587 Saddle-point freight car utilization, 563-564 lifetime probabilities, 584, of function, 609 line dispatching, 565 585-586 of game, 609 Rand Corporation, 566-571 maintained systems, 584-586 problem, 609 background, 566 N-out-of-K systems, 584 Safety,609 current situation, 570-571 redundant & standby parallel Sales-advertising relationship, 2 first ten years (1948-1957), systems, 585-586 Sample path realization of number in 566--568 structure function, 586--587 system over time, 348 fourth ten years (1978-1988), 570 Reneging discipline, 587 SAST. See Strategic assumption The New York City-RAND Renewal equation, 587 surfacing, testing Institute, 569 Renewal processes, 587-588 Satisficing, 610 policy analysis studies for Dutch Representation theorem for Scale, fundamental, analytic hierarchy Government, 569-570 polyhedral set, 588 process, 17,18, 18t second ten years (1958--1967), Research Scaling, 610 568--569 analysis corporation, 588 Scenario analysis, 614 Index 751

SCERT,614 equilibrium, 624-625 Stationary distribution, 646 Scheduling mathematical exposition, 624 Stationary , 646 families or groups, 613-614 performance, 625 Stationary transition probabilities, 646 generalized resources, 613 Simulator, 633 Statistical eqUilibrium, 646-647 health care system and, 273-274 Single-ratio fractional programs, Statistical process control, 647 preliminaries, 611 fractional programming, Steady state, 647 results, 611-613 234-235 Steady-state distribution, 647 sequencing, 613-614 Single-server network, 448, 633 Steepest descent method, 647 single-machine models, 611-613 Singular matrix, 633 Steiner tree problem, 647 solution techniques, 611 Sink node, 633 Stepping-stone method, 647 stochastic machine scheduling, 613 SIRORO, 633 Stigler's diet problem, 647 Score functions, 614 SKEW-Symmetric matrix, 633 Stochastic decision analysis, 421 discrete event dynamic systems, Slack variable, 633 Stochastic duel, 648 616 Slack vector, 633 Stochastic model, 648 discrete-event static systems, SLP, 633 distribution selection for, 167-169 615-616 Smooth patterns for production, 633 Stochastic programming, 648-650 optimization, 617 Social choice theory, 269 Strategic assumption surfacing, queueing delays, 616-617 SODA. See Strategic options testing, 651 system reliability, 616 development, analysis Strategic choice, 651 Scoring model, 617 Soft systems methodology, 634 Strategic options development, Scripted battle model, 617 Sojourn time, 447-448,634 analysis, 651 Search, Heuristic, artificial feedback queue again, 447-448 Strictly quasi-concave function, 651 intelligence, 25-26 overtaking, 448 Strictly quasi-convex function, 651 Search theory, 617-620 three-node network, 448 Strong duality theorem, 651 applications, 620 Solid wastes management, 194 Strongly NP-complete (NP-hard), 652 Brown's algorithm, 619 Solution, 634 Strongly polynomial-time algorithm, history, 618 analysis, 349-353 652 optimal searcher path problem, 619 space, 634 Structural information, analytic search for moving target, 619 SOS, 634. See Special-ordered sets hierarchy process, 17 search for stationary target, Source node, 634 Structural variables, 652 618-619 Space, 634-635 Structured modeling, 652-655 two sided search problems, 620 Spanning tree, 636 Structuring process, analytic uniform, incremental optimality, Sparse matrix, 636 hierarchy process, 20 619 Sparsity, 636 SUB. See Simple upper-bounded Second-order conditions, 620 Special-ordered sets, 636 problem Self-dual parametric algorithm, 620 Splines, 636-638, 637 Sub problem, 655 Semi-Markov process, 620 application, 637 Subjective probability, 655 Semi-strictly quasi-concave function, as approximating functions Suboptimization, 655 620 ORlMS, 637, 637 Super-sparsity, 655 Semi-strictly quasi-convex function, B-spline representation, 638 Supplemental variables, 656 620 dynamic mechanical analysis of Supplies/materials planning, health Sensitivity analysis, 621 nylon fiber, 637 care systems, 274 Separable function, 621 multivariate approximation, 638 Surplus variable, 656 Separable-programming problem, 621 Sports, 639-640 Surplus vector, 656 Separating hyperplane theorem, 621 baseball, 639 Symmetric matrix, 656 Series queues, 621 football, 639 Symmetric network, 656 Service systems, 621 general league issues, 639 Symmetric primal-dual problems, 656 Set-covering problem, 621 golf,640 Symmetric zero-sum two-person Set-partitioning problem, 621 hockey,639 game, 656 SEU, 621 individual sports, 640 Synthesis Shadow prices, 621 soccer, 639 analytic hierarchy process, 23t Shapely value, 622 team sports, 639 hierarchic, analytic hierarchy Shell,622 tennis, 640 process, 20-21 Shewhart chart, 541-544, 622 track, field, 640 System, 656 Shortest-route problem, 622 Spreadsheets, 643-645 reliability, 660 Signomia1 programming, 622 basic operations, 644-645 System dynamics, 656-659 SIMD,622 budgetspreadsheet,644t behavior, system structure, 659 Simple upper-bounded problem, 622 capabilities,645 endogenous point of view, 658 Simplex, 622 example, 643-644, 644t feedback loops, 658 Simplex method (algorithm), 622 SQC,646 feedback thinking, 657-658,658 Simplex multipliers, 622 Square root law, 646 levels, 659 Simplex tableau, 623 SSM. See Soft systems methodology loop dominance, nonlinearity, 658 Simulated annealing, 623-625 St, 646 rates, 659 applications, 625 St. Petersburg paradox, 609 system structure, 658-659 convergence, 624-625 Stages, 646 Systems analysis, 660-670 cooling schedule, equilibrium, Staircase structure, 646 CASE tool intelligence, 669 624-625 Stanford-B model, 646 752 Index

computer aided software Malcolm Baldrige award, 688-689 uncertainty, 712 engineering,66~ 669-670 principle based management, 688 computer systems, 661,661-666 tools,687t data administration, 667-668 TQM,690 v encapsulated objects, object Traffic communication,665 analysis, 690-694 Vacation model, 713 history, 66

planning water resource WIMP, 734 y development, 731-732, 732 Wolfe's quadratic-programming resources, 732 problem algorithm, 734 Yield management, 737 water quality, 733 Work schedule, 734 airline industry, 12 Weak duality thereon, 734 World War II Weakly-coupled systems, 734 Air Force, operations analysis, 8 Weber problem, 734 MOR accomplishments, z Weights, eigenvector solution for, metamodeling, 395 analytic hierarchy process, Worst-case analysis, 734 Zero one goal programming, 739 19-20,20t Zero one variables, 739 Wildlife management, natural Zero-sum, 739 resources, 428 x Zero-sum game, 739 Wilkinson equivalent random two person, 739 technique, 734 X-bar chart, 735 Wilson Lot-size, inventory modeling, 311-312