671

Appendix A: Standard Distributions

A.1. Cumulative Normal Distribution

Figure A.1 and Table A.1 show the cumulative standard normal distribution in func-tion of z, i.e., P [x ≤ z] in function of z , where x = N (0,1). The values can also be computed with the NORMSDIST function in the Excel spreadsheet.

Fig. A.1 Cumulative standard normal distribution

M. Goetschalckx, Supply Chain Engineering, International Series in Operations Research & Management Science 161, DOI 10.1007/978-1-4419-6512-7 , © Springer Science+Business Media, LLC 2011

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Table A.1 Cumulative standard normal distribution

Fig. A.2 Standard normal distribution

Appendix A: Standard Distributions

673673

The standard normal density function with mean equal to zero and standard de-viation equal to one is shown in Fig. A.2 .

A.2. Unit Loss Function

Figure A.3 and Table A.2 show the unit loss distribution in function of z . The unit loss function is defined as L(z) =

∫ ∞z (t − z)φ(t)dt, where ϕ(t) is the standard

normal density function. The unit loss function can be computed with the Excel formula NORMDIST(z,0,1,0)-z*(1-NORMDIST(z)).

Fig. A.3 Unit loss function

Table A.2 Unit loss function

A.2. Unit Loss Function

675

AA Math Programming Language, 174,

176–179, 204–207, 547, 568, 571, 574, 576, 603, 605, 607, 610, 641

ABC, 498, 506Activity based costing, see ABCAdaptive models, 65, 76Adaptive smoothing, 72Additive decomposition, 99Advanced planning systems, 10AGV, 145, 146Algorithms, 49, 160–163, 167, 188–190, 193,

226–228, 230, 233, 238, 253, 254, 273, 274, 280, 297, 316, 342, 354, 380, 526, 553, 601, 636, 653, 666

2-opt, 3073-opt, 307alternative-generating, 53, 273alternative-selecting, 53, 273approximate, 51chain-opt, 307cheapest insertion, 239, 240, 241, 243,

258, 305, 348–351, 353, 422construction, 53, 227, 228, 280, 295, 427cyclic exchange, 308deterministic, 53dual, 52, 228, 230exact, 51, 251extreme crossovers, 346, 348farthest insertion, 243, 244first descent, 53, 246GAP, 294giant tour, 280, 292heuristic, 11, 51, 53, 214–216, 251, 259,

274, 300, 482, 639improvement, 53, 245–247, 253, 279, 280,

306–310, 331, 351, 354, 355, 366, 403, 429

move, 308, 351, 353nearest addition, 244, 245nearest insertion, 242–244Nearest Neighbor, 224, 225, 226, 237, 248,

251, 253, 263, 266, 280, 281, 307, 334, 336, 338, 374, 378, 385, 427, 429

non-deterministic, 53optimal, 51, 165, 274priciest insertion, 240–243, 263, 264, 266,

267, 349, 350, 380, 385primal, 52quad, 228, 230, 231savings, 231, 232, 233, 261–263, 266, 267,

280–283, 285, 309, 318, 327, 331, 341, 342, 344, 346, 363, 390, 403, 405, 414, 425

simulated annealing, 53, 246–248, 308–310

simulation, 55SPP, 161–163, 166, 354, 355steepest descent, 53, 246, 308swap, 310, 352sweep, 226, 228, 251, 263, 266, 280,

287–290, 296, 298, 338–341, 375, 379, 388, 390

AMPL, see A Math Programming LanguageAP, 219, 252, 277, 347APS, see Advanced planning systemsArc-based model, 572, 574, 575, 576, 607ARIMA, 66ATSP, 218–220, 252Average, 79Average weighted age, 83Average-case error bound, 52

BBackorder, 437Balanced network, 204

Index

M. Goetschalckx, Supply Chain Engineering, International Series in Operations Research & Management Science 161, DOI 10.1007/978-1-4419-6512-7, © Springer Science+Business Media, LLC 2011

676

Benchmarking, 28Bias, 68, 71Bill of lading, 151Bill of materials, 30, 63, 481, 525, 540, 541,

543, 573BOL, see Bill of ladingBOM, see Bill of materialsBox-Jenkins methods, 66

CCarrier, 129Carrying cost, 436Casual models, 66Center, 525, 531, 532, 536, 539, 547, 548,

550, 553–557, 564, 572, 578, 579, 581, 597, 598, 601, 602

Centralization, 511Chain-opt, 306Change-constrained optimization, 643Cheapest insertion, 239, 348CLM, 1Coefficient of determination, 506COFC, 138Co-location, 514Column generation, 320Common carrier, 129Complete graph, 162Cone of uncertainty, 102Confidence interval, 69Consecutive ones property, 187Consolidation, 512, 514Constant data pattern, 77, 79, 82, 92, 107Container-on-flat-car, 138Continuous review policies, 465Contract carrier, 129Cost, insurance, and freight, 150CPM, 167CPP, 213Critical path method, see CPMCritical ratio, 455CSCMP, 1, 3, 432Curve fitting, 89Customer focus, 514Customer service, 501Cwt, 131, 132Cycle inventory, 433, 444Cycle length, 97Cyclic exchange, 310

DDamping factor, 80, 87, 92Days of stock, 440Deadweight ton, 132, 150

Decision support systems, 516Delivered with Duty Paid, 151Delphi method, 64DEP, 643, 646, 651–661, 666, 667Derived shortage cost, 475Deterministic equivalent problem, see DEPDirect service, 516Diseconomies of scope, 32Dispersion, 512, 514Disposal cost, 437Distance, 528, 548, 552, 554, 557, 558, 583,

586, 588–591, 593, 594, 599Euclidean, 37, 43, 423, 554, 588, 591, 593

Distance norms, 15, 42, 43, 46, 47, 49, 217, 222, 223, 266, 295, 333, 390, 528, 548, 552, 558, 589, 594, 599

chebyshev, 42, 43, 45Euclidean, 46, 223, 248, 251, 261, 263,

274, 302, 321, 334, 381, 385, 390, 548, 587, 588, 591, 593

great circle, 42, 46, 47, 558rectilinear, 42–44ring-radial, 42, 45, 46

Distribution requirements planning, 10, 441, 480

Distribution resource planning, 10, 441, 480DOS, see Days of stockDouble exponential smoothing, 91–93, 95, 96Double-stack, 137, 138Draft, 142–144DRP, see Distribution resource planningDwt, see Deadweight

EECO, 20Economic order quantity, 446, 450, 451, 468,

470, 472, 473, 482, 491Economic production quantity, 448, 450Economies of scale, 32, 33, 128, 130–132,

136, 433, 511–514, 516, 526, 617, 618Efficiency frontier, 500, 651, 658Emergency inventory, 435Engineering change order, see ECOEnterprise resource planning, 2, 10–13, 23,

517, 616EOQ, see Economic order quantityEPQ, see Economic production quantity ERP, see Enterprise resource planningEU, 3, 8, 14, 131European Union, see EUEx Works, 150Excess cost, 453, 454Expected lost sales, 437, 464, 488, 498

Index

677

Exponential smoothing, 80Extreme crossovers, 346

FFarthest insertion, 225, 243, 244, 385FEU, 146, 150Fill rate, 31, 34, 437, 439, 442, 463, 464, 472,

480, 484, 486, 490First descent, 53, 246–248, 308–310Fishyback, 142Fixed costs, 33, 129, 449, 498, 553, 538, 562,

565, 574, 577, 582, 638, 648, 654Flexibility penalty, 32Forecast error, 67–73, 78, 80, 82, 87, 88, 93,

102, 120, 122, 124, 125, 446Foreign trade zone, 151, 152Fragility, 501, 511, 627Free On Board, 150Free trade zone, 151Freight bill, 23, 151Freight ton, 132, 150FTL, 27, 33, 133FTZ, see Foreign trade zoneFull truck load, see FTL

GGAP, 274, 277, 278, 293–295, 297, 298, 300,

303, 366, 414, 415, 420, 423, 424, 429GDP, 4, 8Generalized network, 184, 185, 199Geocoding, 23, 24, 519Geoffrion and Graves distribution model, 569,

570Giant tour, 280, 291, 292Gross domestic product, see GDPGross tonnage, 132GT, see Gross tonnage

HHolding cost, 432, 436, 446, 447, 451, 468,

480, 532, 578, 579, 581Holding cost rate, 436, 442, 443, 446, 486,

532, 535, 537, 581Holt’s method, 91Hub and spoke, 4, 132, 133, 496, 516Hundredweight, 131, 132Hyperboloid approximation, 594

IICC, 150, 151Incoterms, 127, 150, 151

CIF, 150, 151

DDP, 151EXW, 150, 151FOB, 150, 151, 639

In-stock probability, 437, 455Integrality property, 185, 187, 199, 325International Chamber of Commerce, see ICCIn-transit inventory, 434, 536Inventory age, 440Inventory velocity, 436, 440

JJIT, 433, 434, 441Just-in-time, 434, 441

LLabel correcting algorithms, 166Label setting algorithms, 166LAP, 53, 547, 552, 553, 555, 556Leading indicators, 67Least squares method, 89Less than truck load, 23, 33, 132Linear programming, 21, 50, 51, 170, 173,

177, 189, 207, 210, 278, 303, 319, 324, 347, 354, 356, 360, 365, 420, 429, 527, 528, 540, 543, 558, 635, 639–642, 646

Linear regression, 89, 91–94, 101, 115Local content requirements, 616, 634, 663Location problem, 42, 548, 550, 552, 559,

588, 600Location-allocation problem, see LAPLong hundredweight, 131Long ton, 132Lost sales, 436–438, 464, 478, 488LP, see Linear programmingLP format, 177, 178LTL, see Less than truck load

MMAD, 67, 68Make to order, 31, 62, 448, 632Make to stock, 31, 62MAPE, 68, 69, 86, 95–97, 105, 114, 119, 122Marginal loss, 453, 458Marginal profit, 452, 453, 458Master planning, 10, 540Material requirements planning, 10, 441, 480,

481MCMFP, 182–184MCNFP, 159, 160, 168, 170, 173, 174, 177,

183, 184, 201, 204, 206ME, 68Mean absolute percentage error, see MAPE

Index

678

Mean error, see MEMean squared error, 68Mean value problem, 501, 642Min–max inventory policy, 477Median, 556Metric ton, 132Milk run, 133Min-cut, max-flow problem, see MCNFPMinimum cost network flow problem, see

MCNFPMinimum spanning tree, 252–256MIP, 11, 21, 38, 50, 354, 547, 558, 565, 566,

571, 577, 616Mixed-integer programming, see MIPModels

analog, 36deductive, 39descriptive, 38, 56, 527deterministic, 39, 616, 642, 649iconic, 36inferential, 39mathematical, 21, 36, 38, 51, 63, 483, 524,

525, 547, 616normative, 10, 38, 41, 49, 56physical, 36stochastic, 39symbolic, see Mathematical

Monetary equivalent flow, 635Move, 3, 44, 45, 136, 139, 182, 214, 215, 217,

230, 265, 280, 308, 310, 351–353, 355, 515

Moving averages, 66, 71, 75, 77, 79, 80, 82–87, 94, 95

MRP, see Material requirements planningMSE, see Mean squared errorMST, see Minimum spanning treeMTO, see Make to orderMTS, see make to stockMulticommodity network flow problem, 184Multi-echelon, 521, 525, 571–573, 575, 607,

610Multiplicative decomposition, 99MVP, see Mean value problem

NNAFTA, 3Naïve forecast, 79Nearest addition, 244Nearest insertion, 242Nearest Neighbor, see AlgorithmNet tonnage, 132Node potential, 189, 190, 192–198, 200North American Free Trade Association, see

NAFTA

NT, see Net tonnage

OOpportunistic service, 516Optimality gap, 52, 633, 639–641, 643, 653,

657, 667Order of running time, 49, 50, 327Order-up-to quantity, 476, 477Overage cost, 453

PPareto curve, 27, 504–506, 508, 509Pareto’s principle, 504Path-based model, 572, 576, 610P-Center problem, 528, 556, 559Peddling, 133Periodic review policies, 465, 476Periodicity, 97–100PERT, 167Piggyback, 138, 578Pipeline, 129, 135, 136, 150, 535Pipeline inventory, 434, 443, 480, 625P-median problem, 556–559, 623Point estimate, 69Point-to-point, 132, 133Polynomial fitting, 89Priciest insertion, see AlgorithmsPricing problem, 54, 193, 315, 316, 320–327,

330, 331, 354, 362, 363, 365, 368, 425, 426, 428, 429

Private carrier, 129Private fleet, 129, 332Process focus, 513Product focus, 513Product life cycle, 503, 504, 632Profiling, 23, 511Program evaluation and review technique, see

PERT

QQuad, 228, 230, 231Qualitative methods, 64Quantity discounts, 31, 32, 130, 512, 617–619

RReady rate, 438, 439Regionalization, 511, 513Regression analysis, 39, 89Reorder cost, 436Request for proposal, 19Residual, 67, 69, 70, 102, 104, 189, 190, 192,

193, 209, 211Residual sum of squares, 69

Index

679

RFID, 8, 633RFP, 19Risk analysis, 499Risk analysis graph, 500, 524, 650, 651, 653,

660, 662Robustness, 501, 514, 615, 616, 643, 656, 660Roll-on, roll-off, 142, 143Root mean squared error, 67, 68, 78, 118Roro, 142Row price heuristic, 315, 316, 423RPP, 213RSS, see Residual sum of squares

SSAA, 643, 652, 653, 656, 657, 660Safety inventory, 434, 465Salvage value, 437, 452Sample efficiency envelop, 500, 501, 510Sampling-average approximation, see SAASavings, 231, 281, 283, 287, 341–343, 376,

390, 405Scenario-based optimization, 643SCM, 3, 11Seasonal data pattern, 77, 97, 101Seasonal inventory, 434, 445Seasonal linear regression, 101Seasonality factors, 105SEE, see Sample efficiency envelopSet partitioning problem, 156, 159–163, 165,

166, 168, 170, 177, 190, 201, 274, 311–316, 318–320, 326, 327, 355, 356, 365, 373, 424, 425, 429

column generation, 274, 320, 368, 380formulation, 312, 313, 315, 316pricing problem, see Pricing problemrow price heuristic, 316, 423

Ship class, 143capesize, 144Malacamax, 144Panamax, 144Suezmax, 144ULCC, 143, 144, 150

Shipper, 129, 131, 136, 139, 151, 156, 432Short hundredweight, 132Short ton, 132Shortage cost, 437, 452Shortest path problem, 156Shortest path problem with resource

constraints, 325Simple exponential smoothing, 80Simulated Annealing, 246Single sourcing, 31Site relative cost, 567

Smoothing constant, 80SOP, 16SOS1, 619Special ordered set constraints, 619Speculative inventory, 434SPP, 156, 312, 353SPPRC, see Shortest path problem with

resource constraintsSSE, 69Standard deviation, 69Standard operating procedure, 16Standard type library, 163, 288Static models, 65, 67, 76, 78Steepest descent, 53, 246, 248, 290, 308–310STL, see Standard type libraryStock out, 437Stock turnover, 440STSP, 222, 251, 252, 259Successive shortest path algorithm, 188, 190,

193, 200, 210, 211Sum of squared errors, see SSESupply chain, 3, 10, 29, 57, 497, 521, 523

channels, 32customers, 571facilities, 528locations, 29periods, 29products, 30scenarios, 34, 644suppliers, 31transformers, 32

Supply chain components, 13, 29, 498, 528Supply chain management, see SCMSupply chain planning meta-model, 34Swap, 308, 352Sweep, 226–228, 263, 266, 287, 289, 291,

338, 339, 375, 379, 388, 390

TTCO, 18TEU, 144, 146, 150Time series, 76Time series models, 65, 76TOFC, 138Ton, 132Total cost of ownership, see TCOTP, 184Tracking signal, 71Trailer-on-flat-car, see TOFCTransfer pricing, 515Transit time, 131Transportation problem, see TPTrend data pattern, 87–89

Index

680

Triple exponential smoothing, 105–107, 113–115

TSP, 213, 214, 216–219, 222, 224–226, 228, 230, 232, 233, 237, 238, 245, 246, 248, 251–253, 255, 260, 272, 280, 289, 291, 292, 298, 305, 307, 317, 323, 366, 368, 415, 422

Two-bin inventory policy, 476

UULCC, 143, 144, 150Underage cost, 452Unimodularity property, 199Unit cost, 436Unit loss function, 461, 462, 473, 493, 537,

673Unit value, 436, 443

VValidation, 28, 29, 54, 55, 57, 475, 499

benchmarking, 28component validation, 28face validation, 28

scientific method, 28sensitivity analysis, 28

Variable costs, 130Vehicle routing with backhauling, 272, 324,

332, 333, 335, 354, 356, 365, 375, 379Vehicle routing with time windows, 273, 324,

364–366VRP, 217, 272–274VRPB, see Vehicle routing with backhauling VRPTW, see Vehicle routing with time

windows

WWarehouse location problem, 521, 528, 559,

560, 562–569, 572, 573, 603Weighted moving averages, 79, 80Winter’s method, 105, 112WIP, 434, 480WLP, see Warehouse location problemWork-in-process inventory, see WIPWorst-case error bound, 51WTO, 14, 128WWW, 8, 24, 48, 165

Index