4/3 conjecture, 450-451

λ-interchange, 490-491, 493

1-tree, 442-447, 459, 460, 470

2-flexibility design, 248, 250, 252

2-matching, 470

inequality, 413-415, 458

relaxation, 410, 449-451

1. opt heuristic, see Traveling salesman problem (TSP): 2-opt heuristic

2. opt heuristic, see Traveling salesman problem (TSP): 3-opt heuristic

Activation function, 23

Agere Systems, 30

Algorithm, see Individual algorithms

All-or-nothing policy, 208, 211, 212, 223

Almost sure convergence, 452, 485-487, 498

Amazon, 2

Ant colony optimization, 430, 489

Apple, 222

Applications of supply chain theory, 615-641 disaster relief, 347-348, 632-635

electricity system, 351, 615-624

energy, 639-641

health care, 625-631

homeland security, 635-637

public sector planning, 269, 637-638

Approximation algorithm, 138, 416, 451, 514 Arc design, see Supply chain network design: arc

design

Assembly system, 188, 202, 204

Assignment problem, 484, 501

Assortment problem, 37

Asymptotic efficiency, 602

Asymptotic optimality, 138, 184, 484, 486-487,

500

Auction, 591-608, 616, see also Combinatorial auction problem (CAP)

business-to-business (B2B), 591

case study, 608-610

combinatorial, 595-610

double, 601, 612, 613

Dutch, 592

English, 591, 593-595, 610-611

reverse, 591, 608-610

sealed-bid, 592, 599

Vickrey, 592

Vickrey-Clarke-Groves (VCG), 599-608

Autoregressive process, 543

Average-cost criterion, 105-106, 108, 118, 137

b-matching, 470-471

Backhaul, see Vehicle routing problem (VRP): with backhauls

Backorder, 48, 50, 88, 110, 136-138, 155, 158,

170, 190-192, 194, 205, 217, 231,

238, 361, 533

planned, 67-70

terminal, 102, 127

712 Fundamentals of Supply Chain Theory, Second Edition. Lawrence V. Snyder and Zuo-Jun Max Shen.

© 2019 John Wiley & Sons, Inc. Published 2019 by John Wiley & Sons, Inc. Companion website: www.wiley.com/go/Snyder/SupplyChainTheory

Backorder matching, 202

Backpropagation, 23

Bagging, 20

Balanced system, 249, 250

Base-stock level, 90, 103, 104, 106, 126-128,

189, 190, 203, 206, 217, 219, 231,

238, 362-364, see also Base-stock policy

echelon, 192-194, 196, 200

local, 192, 201

Base-stock policy, 89-114, 124-129, 202, 203,

231, 238, 384, see also Newsvendor problem

continuous review, 178

echelon, 192-193

finite horizon, 102-104, 153

DP algorithm, 102-104, 127, 136, 149

infinite horizon, 105-114, 139-140, 145

lost sales, 137, 153 minimum order quantity, 153

nonzero lead time, 107-109, 137-138

optimality of, 104, 124-129, 136-139, 153,

243, 360, 362, 542, 648

ordering capacity, 150 relationship to (r, Q) policy, 178 relationship to (s, S) policy, 115 service level, 109-114, 146

single period, see Newsvendor model Basis function, 20

Bass diffusion model, 24-30, 38-39, 138

discrete-time version, 28

extensions, 29-30

multiple markets, 43

parameter estimation, 26, 29

seasonality, 28

Batch size, 47, 71, 155, see also Order quantity

Bayes' rule, 26, 28

Bayesian update, 38

Beer game, 540, 560-562

Benders decomposition, 272, 297, 331, 624

Benetton, 236

Best-improving strategy, 303, 478

Bethlehem, PA, 508

Bidder-dominant payoff vector, 606 Bidder-submodular, 607-608

Big bang, 410

Big-M , 499

Bilevel optimization, 315

Bill-of-materials, 188

Bin-packing problem, 466-467, 471, 485, 509

constant, 485

Binomial distribution, 549, 587

Bipartite graph, 245, 246

Bisection search, 172, 312, 313, 359

Blood platelets, 513, 628-631

Blossom inequalities, see 2-matching inequalities BMW, 244

Boolean function, 306

Boosting, 20

Branch-and-bound, 272, 278, 280, 283, 290, 297,

300, 307, 309, 317, 393, 408-410,

447, 469-471, 474, 475, 523, 526,

531, 533, 675, 680

Branch-and-cut, 331, 410-416, 452, 471-472,

474, 475, 499

Branch-and-price, 474, 680

Budget design problem, 331, see also Supply chain network design: arc design

Bullwhip effect, 531, 539-559

case study, 556-559

causes for, 540-541

centralizing demand information, 555-556 demand signal processing, 540, 542-546,

552-553

order batching, 541, 548-551, 554

price speculation, 541, 551-552, 554-555 proving existence of, 541-552

rationing game, 540, 546-548, 554

reducing, 552

Bundle method, 673

Buyback contract, see Contract: buyback

Capacitated concentrator location problem (CCLP), 298, 481-484, 486, 488

Capacitated fixed-charge location problem (CFLP), 296-298, 324, 338, 349, 482

Lagrangian relaxation, 296-297

Variable splitting, 349-350

Capacitated vehicle routing problem (CVRP), see

Vehicle routing problem (VRP) Capacity constraint, see Capacity-cut constraint Capacity uncertainty, 355, 356, 373

Capacity-cut constraint, 466-468, 470, 471, 499,

507, 531

generalized, 509

Car 54 TSP instance, 404, 405, 418-423, 425,

426, 431, 432, 434-438, 440, 442-

444, 447

Case study, 76-77, 138-140, 180-182, 222-223,

257-258, 332-335, 395-396, 453-

455, 501-502, 534-535, 556-559,

584-586, 608-610, 639-641

Chain inequality, 416

Chain-barring constraint, 531

Chaining structure, 243, 246-248, 253, 256 Cheapest insertion heuristic, see Traveling sales-

man problem (TSP): cheapest inser-

tion heuristic Chicken egg, 626

China National Petroleum Corporation (CNPC), 639-641

Choice probability, 34

Choice set, 34

Christofides' heuristic, see Traveling salesman problem (TSP): Christofides' heuris- tic

Chrysler, 244

Clarke-Wright savings heuristic, see Vehicle rout- ing problem (VRP): Clarke-Wright savings heuristic

Classification tree, 20

Clique-tree inequality, 416

Clustering, 18, 23, 30, 475

Coalition, 605-608

Coalitional value function, 605 Collaborative planning, 557

Column generation, 472-474, 499, 501, 514,

524-527, 531, 675-680

restricted master problem, 526 Column reduction, 300, 307

Comb inequality, 413, 415-416, 458, 471-472,

507

Combinatorial auction, 595-610

Combinatorial auction problem (CAP), 595-598, 609

Lagrangian relaxation, 597-598

truthful bidding, 598

VCG auction, 599-608

Committed service time (CST), 190, 203, 204,

207, 209, 211, 219, 222, 225

Competitive location, 315-316

Complementary slackness condition, 282, 284,

289, 594

Complete pooling, 238, 239, 243

Complex number, 623

Compliance regime, 583

Concave function, 207, 211, 219, 222, 232, 375,

377, 381, 382, 513, 519, 521, 568,

569, 571, 582, 673

Concorde TSP solver, 416, 453

mobile app, 406, 450

Conic optimization, 527-529

Conic quadratic mixed-integer program (CQMIP), 527

Conservation of flow, 106-109, 137, 157, 177,

194, 206

Constraint generation, 531, 533

Construction heuristic, 291, 416-436, 442, 460,

475-487, 500, 650, see also Individ- ual problems

Consumer packaged goods (CPG), 233 Consumer utility, 34

Continuous approximation, 501, 514 Continuous location problem, 315

Continuous review, see Inventory model: contin- uous review

Contract, 563-586, 648-649

buyback, 574-578, 580, 581, 649

case study, 584-586

cost-sharing, 628

efficiency of, 571

notation, 565-566

quantity flexibility, 581-584, 588

revenue sharing, 578-581 supplier's profit share, 572 wholesale price, 568-573, 628

Contradiction, proof by, 73, 132-134, 286, 413,

417, 519, 655-656

Contrapositive, 656 Control band policy, 152

Control zone, 449-450, 461

Convex function, 53, 57, 93, 96, 196, 202, 219,

367

Convex hull, 303, 345, 411, 416, 425, 427, 459

Convex hull heuristic, see Traveling salesman problem (TSP): convex hull heuris- tic

Convex optimization, 382

Convexity, 101, 118, 124-127, 129-131, 136,

158-160, 177, 202, 258, 359

Convolution, 202

Cook County, Illinois, 638 Cooperative game, 605-608

Coordination, 557, 563, 610, see also Contract

Core, 605-608

Council of Supply Chain Management Profes- sionals (CSCMP), 2

Coverage, 267, 305, 317

radius, 305

Covering model, 305-313

CPLEX, 77, 272, 276, 312, 313, 332, 335, 527,

534, 638

Critical fractile, see Critical ratio

Critical ratio, 94, 102, 181, 364, 370, 374, 377

Cross-decomposition, 297

Crossover, 491-493

Curse of dimensionality, 137, 631

Cutting plane, 307, 331, 410, 412, 453

Cycle (in graph), 189, 204

Cycle length, 51, 110, 118, 119, 357, 358

Cycle service level, see Service level: type-1 Cycle stock, 88, 91, 97, 108, 165, 181, 364, 513

Dalhousie University, 76

Dantzig-Wolfe decomposition, 272, 680

Data science, 18

Davenport, Tom, 502

Day-ahead market, 619-621, 641

Days-of-supply policy, 260, 556 DC power flow, 623

Decomposition-aggregation heuristic, 202 Dedicated system, see Process flexibility: dedi-

cated system Deep neural network, 23

Degree, 406, 414, 427, 431, 433, 446, 447, 470

constraint, 406, 470, 530, 533 Delayed differentiation, see Postponement Dell, 1, 180-182

Delphi method, 6

Demand, 47, 89, 204-205, 217, 322, 468, 476,

485

correlated, 231, 234, 529, 546

deterministic, 51-76, 356, 361, 366, 369

distribution, 88-89, 91, 155, 156, 158, 161,

177, 181, 486

discretizing, 104, 258

dynamic, 72

forecasting, 74, 99-100, 217, 223

lead-time, 56, 106, 108, 110, 139, 156-158,

165, 167, 173, 185, 193, 194, 200,

543, 555, 558

net-lead-time, 140, 206

rate, 27, 46, 357

seasonal, 6, 10-13, 47, 625

serially correlated, 542

stochastic, 46, 87-140, 155-182, 191, 193,

230, 232, 373

trend, 5, 6, 9-13 Demand lead time, 205

Demand modeling, see Forecasting

Demand signal processing, 540, 542-546, 552-

553

Demand-weighted distance, 299

Depot, 463, 465-468, 470, 472, 475, 483, 485,

492, 500, 501

Deterministic annealing, 489

Deterministic equivalent, 318

Dial-a-ride problem, 500 Differentiation of integrals, 665 Diffusion, see Bass diffusion model Directed arc, 210, 329

Disaster relief, 347-348, 632-635

Discounted-cost criterion, 105-106, 118, 137 Discrete choice model, 33-38

Disruption, 247, 355-364, 373, 384-394, 647,

648, see also Individual problems and stochastic demand, 386

case study, 395-396

probability, 356, 361, 384, 390

rate, 357

stochastic-demand equivalent, 399

Distance, 270-271, 406, 408, 416, 437, 483, see

also Triangle inequality asymmetric, 460

constraint, 465, 499

demand-weighted, 299

Euclidean, 41, 270, 298, 437, 449, 451

great circle, 270, 298, 350, 505

highway/network, 271 Manhattan or rectilinear, 270 matrix, 271

shortest-path, 299

symmetric, 406, 465

Distribution center (DC), 230, 269, 322

Distribution system, 189, 202-204, see also One-warehouse, multiple-retailer (OWMR) system

Dogus University, 332

Double auction, 601, 612

Double marginalization, 570

Downstream, 3, 189, 213 Dual

condensed, 283

Lagrangian, 256, 597

linear programming (LP), 282, 449, 473,

597, 641, 675, 677

variable, 473

Dual-adjustment procedure, 284, 289-291

Dual-ascent procedure, 282-289, 331

DUALOC, 282-291, 300, 317, 331, 339-340

Dynamic economic lot-sizing (DEL) model, see

Wagner-Whitin model Dynamic location, 317

Dynamic programming (DP), 73-76, 102-104,

116, 136, 137, 204, 209-210, 214,

222, 317, 408, 468-469, 552, 619-

621, 624, 637

truncation, 104

EAX operator, 493, 494

eBay, 591, 592

Echelon, 3, 191, 321, 322, 348

base-stock level, see Base-stock level: ech- elon

base-stock policy, see Base-stock policy: echelon

inventory, see Inventory: echelon

inventory position, see Inventory: position: echelon

Economic lot size problem, 51

Economic order quantity (EOQ) problem, 51-70, 155, 157, 166-167, 174, 554, 625

cost function, 52-53, 165

optimal solution, 53-55, 122, 163, 165,

513, 516

reorder point, 56

sensitivity analysis, 55-56, 176

with disruptions, 357-360, 398 with fixed batch sizes, 80

with market selection, 645

with nonlinear holding costs, 81 with nonzero lead time, 56, 79

with planned backorders, 67-70, 166, 170,

173-177

as special case of (r, Q), 174, 185 optimal solution, 69, 176

sensitivity analysis, 80 with planned lost sales, 81

with quantity discounts, 60-67

with yield uncertainty, 366-370, 399 Economic production lot (EPL) problem, see

Economic production quantity (EPQ) problem

Economic production quantity (EPQ) problem, 70-72

Economies of scale, 46, 237, 316, 513, 554, 609 Economies of scope, 609

Edelman Award, 464, 501, 616, 639 Efficient frontier, see Trade-off curve

eil51 VRP instance, 463, 464, 478, 479, 481,

482

Electricity system, 142, 316, 615-624

energy storage, 616-621

network design, 623-624

transmission capacity planning, 621-623

Electronic data interchange (EDI), 554

Energy, 322, 615-624, see also Electricity system market, 619

renewable, 616

Enumeration, 118, 298, 316, 408, 526, 675

EOQ problem, see Economic order quantity (EOQ) problem

EOQB problem, see Economic order quantity (EOQ) problem: with backorders

EOQD problem, see Economic order quantity (EOQ) problem: with disruptions

Epidemiological model, 626

Euclidean distance, see Distance: Euclidean Euclidean TSP, see Traveling salesman problem

(TSP): Euclidean Eulerian

network, 431, 433

tour, 431, 433, 434

Everyday low pricing (EDLP), 554 Evolutionary algorithm, 493

Excel, 98, 666

Exchange heuristic, see Swap heuristic Exchangeable demand, 249-251

Exponential distribution, 117, 356-358, 571

Exponential smoothing, 7-13, 100

double, 9-10

forecast error, 17

Holt's method, 9-10

single, 8-9

triple, 10-13

Facet-defining inequality, 415

Facility location, 267-321, 464, 637-638, 650,

see also Individual problems robust, 317-318, 320-321

stochastic, 317-320

uncertainty in, 317-321, 387-394

Farthest insertion heuristic, see Traveling sales- man problem (TSP): farthest insertion heuristic

Federal Communications Commission (FCC), 595 FedEx, 464

Feed-in tariff, 621 Fermat's last theorem, 654

Fill rate, 70, 77, see also Service level: type-2, 165

Finite difference, 101, 363

Finite horizon, see Inventory model: finite horizon Fire station, 332-335

First-improving strategy, 301, 478 Fisher-Jaikumar heuristic, see Vehicle rout-

ing problem (VRP): Fisher-Jaikumar heuristic

fitcsvm function (MATLAB), 22 fitrsvm function (MATLAB), 22 Fixed cost

for facility location, 235, 269, 298, 306,

329, 390

for inventory, 46, 48, 49, 87, 88, 114, 116,

124, 129, 145, 156, 157, 162, 173,

191, 357, 358

Fixed-charge design problem, 331, see also Sup- ply chain network design: arc design

Flexibility, see Process flexibility

Flow balance constraint, 330, 639-641 fmincon function (MATLAB), 382 Ford Motor Company, 244, 395-396

Forecasting, 5-39, see also Individual forecasting methods

Bass diffusion model, 24 classical methods, 6-14

Delphi method, 6

discrete choice, 33-38

exponential smoothing, 7, 17

forecast accuracy, 15-17

forecast error, 15-17, 99, 100, 543, 555

mean of, 100

standard deviation of, 99, 100, 181 in (r, Q) policy, 181

in newsvendor model, 99 leading indicator, 30, 38-39

linear regression, 13-14

moving average, 6, 16-17

Frito Lay, 534-535

Full flexibility, see Process flexibility

Game theory, 315-316, 564-565, 592

cooperative game, 605-608

prisoner's dilemma, 565

Stackelberg game, 315, 565, 626

static game, 565

Gamma distribution, 571

GAMS, 335

Gaussian distribution, see Normal distribution General system, 189, 203, 204, 210, 222 Generalized logistic distribution, 571 Generalized traveling salesman problem (GTSP),

see Traveling salesman problem (TSP): generalized

Genetic algorithm, 295, 304, 309, 331, 407, 489,

491-493, 501

GENI heuristic, see Traveling salesman problem (TSP): generalized insertion (GENI) heuristic

GENIUS heuristic, see Traveling salesman prob- lem (TSP): GENIUS heuristic

GEODUAL software, 450

Geographic information system (GIS), 271, 334

Geometric distribution, 356, 361

Geometric series, 666

Georgia Tech, 453

Gradient descent, 23

Great circle distance, 270, 298, 350, 505 Greatest angle insertion heuristic, see Traveling

salesman problem (TSP): greatest an- gle insertion heuristic

Greedy heuristic, 252, 291, 317, 461, 637

greedy-add, 291-295, 300, 308, 331, 335,

536

greedy-add with substitution, 309 greedy-drop, 295, 300, 331

Gross domestic product (GDP), 2, 625

Guaranteed-service model, 189-191, 203-222

Gumbel distribution, 35, 571

Gurobi, 272, 312

Hakimi property, 298, 311, 315, 350

Hamiltonian cycle problem, 404, 417

Handshaking lemma, 433, 458

Health care, 625-631

Held-Karp bound, 442-447, 452, 458-459 Heuristic, see Individual heuristics Heuristic concentration, 309

Hewlett-Packard, 236, 539 Hidden Markov model, 18 Highway distance, 271

Hitachi, 138-140

Hockey stick phenomenon, 541

Holding cost, 48, 52, 81, 88, 95, 156, 157, 161,

181, 191, 230, 231, 235, 260, 357,

358, 367

echelon, 192, 197, 204, 223

local, 192, 204

terminal, 102

Holt's method, 10

Holt-Winters method, 12

Homeland security, 635-637

Honda, 244

Hub location problems, 316 Hypohamiltonian inequality, 416

IBM, 236, 609

Ice cream, 76-77

Implicit penalty function, 197

Improvement heuristic, 276, 291, 436-442, 475,

488, 490, 491, 499, 500, 521, 650

exchange, 295, 521

neighborhood search, 303-304

retailer reassignment, 521

swap, 295, 300-304

In-transit inventory, see Inventory: in-transit Inapproximability bound, 451

Increasing generalized failure rate (IGFR), 571 Induction, proof by, 469, 630, 656-657

Infinite horizon, see Inventory model: infinite horizon

Infinitesimal perturbation analysis (IPA), 243 Influenza vaccine, 370, 625-628

Information pooling, 237, 257

INFORMS, 39, 464, 501, 616, 639

INFORMS Journal on Applied Analytics, xxxv Insertion heuristic, 417

Institute of Medicine, 625

Integer programming (IP), 76, 208, 210, 675 Integrality

constraint, 410

gap, 288, 450-451

property, 275, 298, 447, 671

Intel Corporation, 38-39 Interfaces journal, xxxv Inventory

echelon, 191

in-transit, 181, 191, 192, 194

inventory-transit position, 194

level, 50, 106-108, 155, 157-158, 161,

191, 193

echelon, 191, 192

local, 191

negative, 91, 161

on-hand, 50, 158, 173, 191, 206, 361

echelon, 191

on-order, 50, 192, 205, 206

position, 50, 90, 106-108, 115, 155, 157-

160, 177-178, 194

echelon, 192

reasons for, 45-47

terminal, 102, 127

types of, 47 Inventory model

classifying, 47-48

continuous review, 47, 51-72, 107, 110,

122, 155-182, 191, 357-360, 365-

369

deterministic, 45-76

finite horizon, 47, 89, 102-104, 116, 126-

136, 192

infinite horizon, 47, 89, 105-114, 117-123,

129, 136, 145, 191, 192, 203, 238,

360

multiechelon, 187-222

guaranteed-service, 189-191, 203-222

network topologies, 188-189

stochastic-service, 189-203, 217, 219-

222

periodic review, 47, 72-76, 87-140, 156,

191, 201, 203, 231, 238, 360-364,

369-372, 384

stochastic, 87-140, 155-182, 187-222,

230-387

with disruptions, 356-364

with multiple suppliers, 372-383 with supply uncertainty, 355-387 with yield uncertainty, 365-372

Inventory policy, 87-88, 202, see also Individual policies

optimality of, 88, 123-137, 192

parameters, 88

Inventory-routing problem (IRP), 531-535, 633 Istanbul Technical University, 332

Istanbul, Turkey, 332-335

JUNAEB, 595

K-convexity, 130-136, 150, 152

0-convexity, 131

k-opt, 436-438, 499, 502

K-tree, 470-471

Kernel function, 22

Kernel method, 18

Kirchhoff's laws, 623

KKT condition, 376 Knapsack problem

0-1, 297, 483

continuous, 256, 297, 325

integer, 680

Kodak, 203, 217-219

Kruskal's algorithm, 430, 431

Lq-convexity, 138

R1 norm, see Manhattan metric R2 norm, see Distance: Euclidean Ladder inequality, 416

Lagrangian decomposition, see Variable splitting Lagrangian relaxation, 254-256, 272-282, 296-

297, 299-300, 309, 324-326, 331,

342, 345-346, 349, 392-393, 447,

483, 499-502, 669-675, see also In-

dividual problems bound, 276, 298, 670-672

dual, 597

maximization problem, 674

multiplier, 273, 277-278, 300, 597, 670,

674

stopping criteria, 278, 674

subgradient optimization, 277-278, 300,

672-674

subproblem, 501, 670

Last-mile distribution, 632

Law of total expectation, 112, 157, 377

Lead time, 46, 47, 56, 106-109, 118, 122, 136-

138, 145, 155, 157, 191, 205

demand, see Demand: lead-time net lead time, 140, 206

safety, 556, 558

stochastic, 157, 167, 181, 185, 189, 202,

356

Leader-follower game, see Stackelberg game Leading indicator, 30-33, 38-39

Least absolute shrinkage and selection operator (LASSO), 20

Least squares, 13, 19

Least unit cost heuristic, 74 Lehigh University, 38

Leibniz's rule, 242, 371, 666

Less-than-truckload (LTL) delivery, 464, 632 Lin-Kernighan heuristic, see Traveling sales-

man problem (TSP): Lin-Kernighan heuristic

Linear programming (LP), 616, 675

relaxation, 272, 275-276, 282, 288, 297,

299, 300, 307, 309, 312, 331, 337-

338, 410-411, 413, 416, 447, 449-

451, 467, 473-475, 499, 678-680

Linear regression, 13-14, 18-20, 29, 31

simple, 18 Linearized power flow, 623

Local search, 489, 493, 501

Location model with risk pooling (LMRP), 54, 165, 235, 276, 512-529

capacitated, 528-529

column generation, 472, 524-527

conic optimization, 527-529

formulation, 516-517

Lagrangian relaxation, 517-523 algorithm (for subproblem), 519 improvement heuristic, 521

notation, 514

objective function, 515-516

problem statement, 514 set covering model, 525

Location-allocation problem, see Facility location Location-inventory model, 512-529, see also Location model with risk pooling

(LMRP)

Location-routing problem (LRP), 529-531, 649 with distance constraints, 536

Location-based heuristic, see Vehicle rout- ing problem (VRP): location-based heuristic

Logistics, 3, 501

Logit model, 33, 34

multinomial, 34-38

Lognormal distribution, 89, 144, 146

loss function, 146

Loss function, 92, 97-98, 162, 167-169, 382,

662-665

complementary, 92, 375, 662-665

derivative of, 93, 147

discrete distribution, 101

lognormal distribution, 146

nonstandard normal distribution, 97, 147,

664

Poisson distribution, 665

second-order, 167

standard normal distribution, 97, 164, 663

uniform distribution, 147

Loss of goodwill, 50, 91, 95, 374, 566

Lost sales, 48, 81, 88, 136-138, 153, 257, 357,

533, 629, 633

Machine learning, 17-23

Make-to-order system, 217

Make-to-stock system, 217

Manhattan distance, 270 Markov chain

continuous time (CTMC), 356, 357

discrete time (DTMC), 356, 361, 384, 390

Markov decision process (MDP), 619, 637 Markov random field, 18

Mars, Incorporated, 608-610

Massachusetts Institute of Technology (MIT), 257, 395

Master problem, 331, 526, 675, 677

Matching, 433, 480

perfect, 410, 433, 434, 436

Material requirements planning (MRP), 541, 550

MATLAB, 22, 98, 278, 300, 382, 666

Maximal covering location problem (MCLP), 307-309

as special case of p-median, 350 case study, 332-335

Lagrangian relaxation, 309 relationship to p-center problem, 350

with mandatory closeness constraints, 350 Maximum capture (MAXCAP) problem, 315 Maximum flow problem, 415

Maximum margin classifier, 21 Maxisum location problem, 314, 346 McGriff Treading Company, 584-586 Meals on Wheels, 453-455

Mean absolute deviation (MAD), 15

Mean absolute percentage error (MAPE), 16, 39 Mean squared error (MSE), 15

Mean-variance objective, 387

Memetic algorithm, 491, 493

Memoryless property, 358

Mercator projection, 305

Metaheuristic, 295, 304, 309, 331, 407, 430,

488-493, 500-502, 624, see also In-

dividual metaheuristic types METRIC model, 202

Metric TSP, see Traveling salesman problem (TSP): metric

Miller-Tucker-Zemlin constraints, 459

Minimax, 312, 320

-cost model, 321

-regret model, 321

Minimax fixed-charge location problem (MFLP), 320-321

formulation, 320

Minimum order quantity, 153, 185

Minimum spanning tree (MST), 417, 430, 433,

434, 436, 442, 443

bound for TSP, 442

heuristic for TSP, 430-434, 458

Kruskal's algorithm, 430, 431

Prim's algorithm, 430, 431

Minimum-cut problem, 413 Minisum location problem, 295-296

Mixed-integer programming (MIP), 72-73, 324,

501, 616, 635

Mixture models, 18

Mona Lisa, 453

Mosek, 527

Moving average, 6-7, 99, 100, 140, 543

forecast error, 16-17

weighted, 7

Moving standard deviation, 99

Multi-objective optimization, 219, 393 Multicommodity network flow problem, 331 Multiobjective optimization, 637-638

Mutation, 491, 493

Myopic policy, 127

Nash equilibrium, 315, 547, 564-565, 592, 605

Nash, John, 564

National Academy of Engineering, 625 National Academy of Medicine, 625 Natural gas supply chain, 639-641

Nearest insertion heuristic, see Traveling sales- man problem (TSP): nearest insertion heuristic

Nearest neighbor heuristic, see Traveling sales- man problem (TSP): nearest neighbor heuristic

Negative part (of number), 661

Neighborhood search heuristic, 276, 303-304,

336, 350, 489

Net lead time (NLT), 140, 206, 219

Network design, see Supply chain network design Network distance, 271

Neural network, 22-23, 489

Newsboy problem, see Newsvendor problem Newsvendor problem, 90-102, 106, 174, 257,

376, 514, 564, 621-623, 625, 629

cooperative, 146

cost function, 92-93, 158, 196, 231, 567,

620

critical ratio, 94

discrete demand distribution, 95, 101-102,

146, 178

explicit formulation, 95-96, 146, 374, 566

forecasting, 99

implicit formulation, 91-95, 146

infinite horizon, 105, 629

nonzero starting inventory level, 99 normally distributed demand, 97-99 optimal solution, 93, 158, 165, 547 Poisson distributed demand, 147 profit maximization, 95

type-1 service level, 94, 377

with disruptions, 360-364

with multiple suppliers, 372-383

with yield uncertainty, 369-372, 376, 626 Node design, see Supply chain network design:

node design

Node expansion, see also Process flexibility guideline, 248

ratio, 248

Nonlinear integer program (NLIP), 516 Nonlinear optimization (NLP), 616

Normal distribution, 89, 97-99, 106, 108, 139,

165, 181, 204, 206, 231, 370, 571

in Excel and MATLAB, 666 loss function, 97, 147, 663-664

standard, 231, 662

NP-complete, 331, 404, 417, 499

NP-hard, 76, 210, 269, 272, 297, 299, 306, 308,

312, 315, 319, 324, 331, 404, 408,

410, 416, 451, 467, 471, 474, 499,

529, 531, 535, 638

Obnoxious facility location, see Undesirable fa- cility location

Offered load, 183

On-hand inventory, see Inventory: on-hand

On-order inventory, see Inventory: on-order

One-warehouse, multiple-retailer (OWMR) sys- tem, 202-203, 559

algorithms for, 202

deterministic, 57

Open chain, 249, 251-252

Operational decision, 4, 511

Operations research (OR), 2, 269, 322, 404, 464,

501, 615, 678

Optimal power flow (OPF) problem, 616, 624 Optimization-by-simulation, 243

Or-opt heuristic, see Traveling salesman problem (TSP): Or-opt heuristic

Order batching, 140, 541, 548-551, 554

Order cycle, 48, 109, 110, 159, 357, 360, see also Cycle length

Order quantity, 52, 53, 63, 65, 71, 155, 355, see also Individual inventory problems

Order-up-to level, 103, 115, see also Base-stock level

Order-up-to policy, see Base-stock policy Ordering capacity, 150

ORION (UPS route-optimization system), 464, 501-502

Outdate cost, 629

Overage cost, see Holding cost

P vs. NP, 406, 416, 458

1. nter problem (pCP), 309-313, 348

   absolute, 311, 313, 348

   relationship to maximal covering location problem, 350

   relationship to set covering location prob- lem, 312

   vertex, 311, 348

2. spersion problem, 314

p-hub median problem, 316

1. dian problem (pMP), 272, 283, 290, 298-

   304, 316, 350

   exact algorithms, 299-300

   formulation, 298-299

   heuristics, 300-304

   Lagrangian relaxation, 299-300, 349

   LP relaxation, 338

2. ighborhood, 429, 430, 440

Parallel computing, 453, 490, 501 Pareto

curve, see Trade-off curve optimal, 564-565

Part period balancing, 74 Partial expectation, 667

Passenger screening, 635-637

Path inequality, 416

Penalty cost, see Stockout cost

Perfect matching, see Matching: perfect

Periodic review, see Inventory model: periodic review

Perishability, 47, 48, 90, 91, 115, 628-631

Philips Electronics, 556-559

Piecewise-linear function, 101, 363, 626, 673

Planning horizon, 47, 89

Plug-in hybrid electric vehicle (PHEV), 617 PMX operator, 492

Point-of-sale (POS), 553

Poisson distribution, 89, 147, 177, 518

loss function, 665

normal approximation, 89

Poisson process, 89, 117, 155, 517

compound, 89, 156

Polynomial-time algorithm, 38, 210, 299, 313,

411, 471

Polynomial-time approximation scheme (PTAS), 451

Population search, 489 Positive part (of number), 661

Postponement, 223, 236-237, 258, see also Risk- pooling effect

relationship to risk pooling, 236-237 Power approximation, 122-123, 559

Power distribution, 572

Power-of-two policy, 57-60, 514

error bound, 58, 80

Predecessor, 188, 189, 210, 211

Price speculation, 47, 541, 551-552, 554-555

Pricing problem, 501, 527, 675, 677

Prim's algorithm, 430, 431

Primal algorithm, 594

Primal-dual algorithm, 282, 291, 594

Printed circuit board, 453, 557

Prisoner's dilemma, 565

Probit model, 34

Process flexibility, 243-256

dedicated system, 245

design guidelines, 245-248

full-flexibility, 245

optimization model, 253-256

Procter & Gamble (P&G), 222-223, 404, 539,

554

Procurement auction, see Auction: reverse Product proliferation, 223, 244

Production capacity, 47

Projection algorithm, 202 Proof

kinds of statements, 653-654 techniques, 655-657

Pseudopolynomial-time algorithm, 210 Public housing location, 637-638 Public sector planning, 269, 637-638

Pull system, 217, 219

Purchase cost, 49, 88, 91, 95, 96, 105, 156, 357

Push system, 217, 219

Push-pull boundary, 219

Python, 98

Quantity discount, 46, 60-67, 541, 609

all-units, 60, 62-64

carload, 66

incremental, 60, 64-66

modified all-units, 66-67

Quantity flexibility contract, see Contract: quan- tity flexibility

Quasiconcave function, see Unimodal function Quasiconvex function, 82, 127, 131, 359

Queuing model, 183

(r, Q) policy, 115, 122, 155-180

approximate models with continuous distri- bution, 161-169

performance of, 169

EOQ+SS approximation, 123, 166-167,

169, 185

EOQB approximation, 166-167, 169, 173,

176-177

exact model with continuous distribution, 123, 156-161, 170-177

algorithm, 172

controllable cost, 172-173

expected cost, 157-159

noncontrollable cost, 172-173

optimality conditions, 159-161 properties of optimal solutions, 170-172 relationship to EOQB, 173-177 sensitivity analysis, 176

exact model with discrete distribution, 177- 180

expected-inventory-level (EIL) approxima- tion, 161-166, 168, 169, 184, 186,

515

loss function approximation, 167-169 relationship to (s, S) policy, 115, 156 relationship to base-stock policy, 178 service level, 164-166

Radial basis function (RBF), 22 Random forest, 20

Randomization, 303, 478

Rationing game, 540, 546-548, 554

Real-time market, 619-621, 641

Recourse cost, 253

Recovery probability, 361

Recovery rate, 357

Rectilinear metric, 270

Recursive optimization heuristic, 203 Recursive partitioning, 20

Reduced cost, 474, 527, 677, 679

Regression tree, 20-21

Regret, 321, 352

Reinforcement learning (RL), 23

Reliable fixed-charge location problem, 389-394 facility-dependent disruption probabilities,

400

formulation, 391-392

Lagrangian relaxation, 392-393

notation, 390-391

trade-off curves, 393-394

ReLU function, 23

Renewal process, 117 Renewal-reward

process, 117

theorem, 117, 118, 358, 366, 367

Reorder interval, 57, 106, 108-109, 222, 549

Reorder point, 56, 115, 119-120, 156, 165, 181

Reproduction, 491

Reservation payment, 554

Residual, 13, 19, 20

Restriction-decomposition heuristic, 202

Revenue management, 147-148

Revenue sharing contract, see Contract: revenue sharing

Review period, see Reorder interval Review type, 47

Ridge regression, 20, 41

Risk-diversification effect, 384-387

Risk-pooling effect, 230-237, 257-258, 356, 384,

385, 513

negative safety stock, 260 Robust optimization, 317, 320

Rolling horizon, 76, 633

Row reduction, 300, 307

(r|p) centroid, 315

(r|Xp) medianoid, 315

(s, S) policy, 114-123, 129-136

continuous demand distribution, 122-123 discrete demand distribution, 118-122 finite horizon, 116, 129-136

DP algorithm, 116, 150

infinite horizon, 117-123, 136

DP algorithm, 149

exact algorithm, 117-122, 149

heuristic, 122-123

power approximation, 122-123, 559

(r, Q) approximation, 122-123 lost sales, 137, 138

nonzero lead time, 118 optimality of, 129-138

ordering capacity, 150

relationship to (r, Q) policy, 115, 156 relationship to base-stock policy, 115 single period, 115-116, 129

S-policy, see Base-stock policy Safety lead time, 556, 558

Safety stock, 88, 91, 97, 100, 108, 161, 165,

167, 181, 203-208, 211, 217, 219,

222, 223, 230, 232, 260, 364, 369,

513

negative, 91, 260

Salvage value, 91, 95, 257, 374

Sampling distribution, 38

Scenario, 253, 256, 258, 317, 633

Scotsburn Dairy Group, 76-77

Second-order loss function, see Loss function: second-order

Semiconductor, 30, 38-39, 244, 557

Separation problem, 411, 415, 416, 471

Sequence of events, 72, 90, 205, 207, 238, 562,

566, 617

Serial system, 3, 188, 202, 204, 211

guaranteed-service, 207-210

stochastic-service, 191-201

exact approach, 193-197, 223

heuristic approach, 223

optimal policy, 192

Shang-Song heuristic, 197-201 Series system, see Serial system

Service level, 4, 109-114, 180, 190, 223, 237,

241-243, 400, 514

for (r, Q) policy, 164-166, 184

type-1, 164-165, 181, 514

type-2, 165

for base-stock policy, 110-114 constraint, 114, 140

type-1, 110

type-2, 110-113, 138, 140

for newsvendor problem type-1, 94, 377

type-1, 109, 230, 364, 379

type-2, 109, 146

Set covering location problem (SCLP), 306-307, 350, 596, 610

case study, 332-335

relationship to p-center problem, 312

Set covering problem, 472-474, 499, 524, 526,

678

Set packing problem (SPP), 596 Lagrangian relaxation, 597-598

Set partitioning problem, 500, 531, 536, 596 Setup cost, see Fixed cost

Shang-Song heuristic, 197-201, 223

Shortcutting, 431, 433, 434

Shortest path problem, 74, 271

Shortfall, 232, 237, 246, 249

optimization problem, 246

Sigmoid function, 23

Silver-Meal heuristic, 74

Simple linear regression, 13, 18 Simple logistic diffusion model, 38 Simplex method, 276, 283, 594, 677

Simulated annealing, 295, 304, 407, 489, 502

Simulation, 34, 145-146, 225, 243, 245, 247,

384, 546, 552

Simultaneous game, 315

Single-sourcing constraint, 297, 482

Single-stage system, 138, 200, 204-207 Skiadas diffusion model, 38

Sobel, Matthew, 91

Space-filling curve, 500, see Traveling salesman problem (TSP): space-filling curve heuristic

Spanning path, 430

Spherical law of cosines, 271, 350

Spline, 20

Spreadsheet, 103, 140, 181

Stackelberg game, 315, 565, 626, see also Con- tract

Stage, 3, 187-189, 203, 212, 217

demand stage, 210, 211, 214, 223

supply stage, 210

Standard normal distribution, 97, 185, 662-663

fractile, 97

loss function, 97, 164, 663

Stanford University, 138

Star inequality, 416

State of charge, 617-619

State-space relaxation, 468-469

Statistical learning, 18 Steiner tree problem, 290

Stochastic dynamic programming, see Dynamic programming (DP)

Stochastic fixed-charge location problem (SFLP), 318-320

formulation, 318

Lagrangian relaxation, 319

Stochastic optimization, 257, 317, 318

deterministic equivalent, 318

multistage, 619

two-stage, 253, 257

Stochastic-service model, 189-203, 217, 219-222

Stock-keeping unit (SKU), 76, 223

Stockout, 48, 109, 110, 161, 162, 165, 173, 189,

190, 356, 366, 385

Stockout cost, 50, 88, 95, 156, 157, 161-162,

164, 181, 191, 197, 200, 217, 235,

257, 260, 357, 374

terminal, 102

Storage capacity, 47, 533

Strategic decision, 4, 267, 396, 511

Strategic safety stock placement problem (SSSPP), 190, 203-222

demand, 204

serial system, 207-210

single stage network, 204-207 tree system, 210-217

dynamic programming, 214, 225

solution method, 211-214

Subgradient optimization, 277-278, 300, 326,

393, 446, 447, 597, 672-674

stochastic, 258

Subtour, 406, 407, 427, 437, 449, 466, 493, 531

Subtour-elimination constraint, 406-407, 410-

413, 415, 451, 459, 460, 466, 468,

533

Successor, 188, 189, 210, 211

Superadditive, 596

Supervised learning, 18

Supply chain management definition, 2 Supply chain network design, 290, 321-332

arc design, 73, 329-332

node design, 322-326

software, 322

Supply uncertainty, 355-387, 616

Supply-curve auction, 609

Support graph, 413

Support vector machine (SVM), 21-22 Support vector regression (SVR), 22 Susceptance, 624

Susceptible, infectious, and recovered (SIR) model, 626

Swap heuristic, 276, 295, 300-304, 316, 335,

336, 350, 521

Sweep heuristic, see Vehicle routing problem (VRP): sweep heuristic

Tabu search, 295, 331, 407, 430, 489-491, 493,

501

TABUROUTE heuristic, 490-491, 501

Tactical decision, 4, 396, 511 Tauber Manufacturing Institute, 181

Technion-Israel Institute of Technology, 257 Technische Universiteit Eindhoven, 557 Telecommunications, 269, 316, 322, 331, 595

Terminal cost function, 102-103, 124, 126-127,

129, 136, 153, 619, 620

Texas A&M University, 534 Third-party logistics (3PL), 554

Time window, 465, 499-500, see also Vehicle routing problem (VRP): with time windows

Tire retreading, 584-586

Toyota, 395 Toys “R” Us, 5

Trade-off curve, 219, 393-394, 638

weighting method, 394, 638

Transfer payment, 563, 567, 568, 578, 581

Transportation cost, 235, 267, 270 Transportation Security Administration (TSA), 635, 636

Transshipment, 237-243, 262

Traveling salesman problem (TSP), 403-455, 463,

465, 472, 480, 482-484, 490, 492,

493, 495, 498-500, 633, 649

4/3 conjecture, 450-451

1. matching relaxation, 410, 449-451

   2-opt heuristic, 437-438, 440, 442, 456,

   488, 493

2. opt heuristic, 437-438, 456

applications, 404, 452

approximation bounds, 451

asymmetric, 460

bounds, 442-451

branch-and-bound algorithm, 408-410, 447

branch-and-cut algorithm, 410-416, 452,

471

case study, 453-455

cheapest insertion heuristic, 422, 423, 456,

460, 534

Christofides' heuristic, 422, 433-436, 450,

456, 458

constant, 451, 460, 498

construction heuristics, 416-437, 455, 456

control zones, 449-450, 461 convex hull heuristic, 425

dynamic programming algorithm, 408, 468

Euclidean, 425, 437, 449, 451, 452, 458-

460

exact algorithms, 408-416, 438

farthest insertion heuristic, 423-425, 456,

481

for VRP bounds, 495-497 formulation, 406-407, 466

generalized (GTSP), 650

generalized insertion (GENI) heuristic, 427-430, 440, 442, 458, 460, 490,

501

GENIUS heuristic, 442

greatest angle insertion heuristic, 427 greedy heuristic, 461

history, 405

improvement heuristics, 436-442, 456, 458,

475

integrality gap, 450-451

Lin-Kernighan heuristic, 438, 440, 442,

452, 500

metaheuristics, 407, 430

metric, 406, 451

minimum spanning tree heuristic, 430-434, 456

nearest insertion heuristic, 419-423, 456

nearest neighbor heuristic, 417-419, 456,

460

NP-hard, 404, 408, 451

Or-opt heuristic, 438-440, 456, 488, 499

periodic, 501

polynomial-time approximation scheme (PTAS), 451

prize-collecting, 460, 501

problem statement, 404

relationship to Hamiltonian cycle problem, 404, 417

space-filling curve heuristic, 453-455 square-root approximation, 442, 451-452,

460, 497, 498, 649

symmetric, 406, 408

unstringing and stringing (US) heuristic, 430, 440-442, 488, 490

with time windows, 501 world records, 452-453

Tree system, 189, 203, 222, 299, 313, 321, 348

guaranteed-service, 210-217

Tree-based model, 20-21

Triangle inequality, 238, 406, 416-418, 420, 431,

434, 450, 458, 460, 465

Trucking industry, 397, 584-586

Truckload (TL) delivery, 464, 554

Tsinghua University, 639

TSPLIB, 463

Two-moment approximation, 202

Uncapacitated fixed-charge location problem (UFLP), 269-295, 297, 324, 474,

529, 636, 638

DUALOC algorithm, 282-291

formulation, 270-272

genetic algorithm, 491-492

heuristics, 291-295

Lagrangian relaxation, 272-282, 345-346

alternate relaxation, 281-282

lower bound, 274-276

subproblem, 273

updating the multipliers, 277-278 upper bound, 276

variable fixing, 280-281

LP relaxation, 337-338 neighborhood search heuristic, 489 partial assignment, 338

problem statement, 269-270

Uncapacitated lot-sizing (ULS) model, see

Wagner-Whitin model Underage cost, see Stockout cost Undesirable facility location, 314-315 UNESCO World Heritage List, 334 Uniform distribution, 158

discrete, 177

loss function, 147

Unimodal function, 81, 127, 571, 573

Unit commitment (UC) problem, 616, 619 University of Alabama, 584

University of California, Berkeley, 639 University of Michigan, 181 Unsupervised learning, 18

UPS, 464, 501-502, 554

Upstream, 3, 189, 213

US heuristic, see Traveling salesman problem (TSP): unstringing and stringing (US) heuristic

Utility, see Consumer utility

Vaccine, 368-370, 625-628

Valid inequality, 413-415, 459, 468, 471, 472,

507

Variable neighborhood search (VNS), 304, 430

Variable splitting, 297, 349-350, 499

Vehicle routing problem (VRP), 403, 463-502,

529, 531, 633, 650

branch-and-bound algorithm, 469-471, 475

branch-and-cut algorithm, 471-472, 475

capacitated, 465

case study, 501-502

Clarke-Wright savings heuristic, 475-480, 499, 500, 502, 505, 508, 534

construction heuristics, 475-487, 502, 505

distance-constrained, 465, 499

dynamic programming algorithm, 468-469, 509

exact algorithms, 468-474

extensions, 465, 498-501

Fisher-Jaikumar heuristic, 484

formulation, 465-468

genetic algorithm, 491-493, 501

heuristics, 475-493

improvement heuristics, 475, 480, 488 iterated optimal tour partition (IOTP)

heuristic, 496, 507

periodic, 465, 500-501 reformulation as TSP, 472

set covering algorithm, 472-474 state-space relaxation, 468-469

sweep heuristic, 480-481, 502, 505

tabu search, 489-491, 493, 501

TABUROUTE heuristic, 490-491

three-index formulation, 467-468, 499, 508

TSP-based bounds, 495-497

two-index formulation, 465-468, 470, 499

two-phase method, 480, 501

with backhauls, 465, 500

with conflicting product types, 508 with pickups and deliveries, 465, 500

with precedence constraints, 467, 508

with time windows, 465, 467, 474, 499-

500, 508

Vendor-managed inventory (VMI), 531, 534, 553 Very-large-scale integration (VLSI), 453

Vickrey-Clarke-Groves (VCG) auction, see Auc- tion: Vickrey-Clarke-Groves (VCG)

Voltage, 623

Volume algorithm, 673

Wagner Prize, 39

Wagner-Whitin model, 72-76, 87

algorithm, 73-76, 214

case study, 76-77

extensions, 76

MIP formulation, 72-73 randomly perishable goods, 85 statement, 72

Walmart, 1

Warranty, 138-140

Water distribution system, 322 Weeks of supply, 140

Weibull diffusion model, 38 Weibull distribution, 622

Wholesale price contract, see Contract: wholesale price

Wind power, 619-623

Winner-determination problem, 609

Winters's method, 12

Working inventory, see Cycle stock World Health Organization (WHO), 625 World TSP data set, 453

Worst-case error bound, 138, 507

for (r, Q) policy, 166, 167, 170, 176-177,

185

for traveling salesman problem, 416-420, 422-425, 431, 434, 451

tight, 422, 423, 433, 436

Worst-case error error bound

for newsvendor problem, 643

location-based heuristic, 480-487,

502, 508

500,

Yedioth Group, 257-258

Yield uncertainty, 355, 356, 365-372, 557

metaheuristics, 488-493, 500, 501

multi-depot, 465

additive, 366-367, 369-371, 374, 376

multiplicative, 366, 368-369, 371-373

multidepot, 501

notation, 465

Zero-inventory ordering (ZIO), 51, 72-73