Contents. 3. Multicriteria optimisation theory MCDA and MCDM: the context MultiCriteria Decision Making 54

Transcription

1 Contents 1. Introduction to scheduling Definition Some areas of application Problems related to production Other problems Shop environments Scheduling problems without assignment Scheduling and assignment problems with stages General scheduling and assignment problems Constraints Optimality criteria Minimisation of a maximum function: "minimax" criteria Minimisation of a sum function: "minisum" criteria Typologies and notation of problems Typologies of problems Notation of problems Project scheduling problems Some fundamental notions Basic scheduling algorithms Scheduling rules Some classical scheduling algorithms Complexity of problems and algorithms Complexity of algorithms Complexity of problems The complexity of decision problems The complexity of optimisation problems The complexity of counting and enumeration problems Application to scheduling Multicriteria optimisation theory MCDA and MCDM: the context MultiCriteria Decision Making 54

2 X Contents MultiCriteria Decision Aid Presentation of multicriteria optimisation theory Definition of optimality Geometric interpretation using dominance cones Classes of resolution methods Determination of Pareto optima Determination by convex combination of criteria Determination by parametric analysis Determination by means of the e-constraint approach Use of the Tchebycheff metric Use of the weighted Tchebycheff metric Use of the augmented weighted Tchebycheff metric Determination by the goal-attainment approach Other methods for determining Pareto optima Multicriteria Linear Programming (MLP) Initial results AppHcation of the previous results Multicriteria Mixed Integer Programming (MMIP) Initial results Application of the previous results Some classical algorithms The complexity of multicriteria problems Complexity results related to the solutions Complexity results related to objective functions Summary Interactive methods Goal programming Archimedian goal programming Ill Lexicographical goal programming Ill Interactive goal programming Ill Reference goal programming Multicriteria goal programming An approach to multicriteria scheduling problems Justification of the study Motivations Some examples Presentation of the approach Definitions Notation of multicriteria scheduling problems Classes of resolution methods Application of the process - an example Some complexity results for multicriteria scheduling problems 124

3 Contents XI 5. Just-in-Time scheduling problems Presentation of Just-in-Time (JiT) scheduling problems Typology of JiT scheduling problems Definition of the due dates Definition of the JiT criteria A new approach for JiT scheduling Modelling of production costs in JiT scheduling for shop problems Links with objective functions of classic JiT scheduling Optimal timing problems The l\di,seq\fe{f'',e^) problem The Poo\prec, fi convex\ ^^ fi problem The l\fi piecewise linear\fi{y^^ fi^ ^. 7^) problem Polynomially solvable problems The l\di = d> Y.Vi\F(>{E,f) problem The l\di = d unknown^nmit\f {E^T^d) problem The l\pi C [pijpj HN, di = d non restrictive\fe(e,t, CC"^) problem ^._^ The P\di = d non restrictive^nmit\f {E^T) problem The P\di = d unknown^ nmit\fe{e^t) problem The P\di = d unknown,pi = p,nmit\f(>{e, T^d) problem The R\pi^j [Pi,j;Pij],cfi = d unknown\fi{t,e, CC"^) problem Other problems TVP-hard problems The l\di, nmit\fe(e'',t^)_pioblem The F\prmu,di,nmit\Fe{E'^,T^) problem The P\di = d non restrictive, nmit\fmax{e, T ) problem Other problems Open problems The Q\di = d unknown, nmit\fi{e,t) problem Other problems Robustness considerations Introduction to flexibility and robustness in scheduling Approaches that introduce sequential flexibility Groups of permutable operations Partial order between operations Interval structures Single machine problems Stability vs makespan Robust evaluation vs distance to a baseline solution

4 XII Contents 6.4 Flowshop and jobshop problems Average makespan of a neighbourhood Sensitivity of operations vs makespan Resource Constrained Project ScheduUng Problems (RCPSP) Quality in project scheduling vs makespan Stability vs makespan Single machine problems Polynomially solvable problems Some l\di\c, /max problems The l\si,pmtn,nmit\fe{c^pmax) problem The l\pi [pi;piidi\fe{tmax.'cc^) problem The l\pi e [pi',piidi\fe(c,cc'^) problem Other problems J\fV-hdiid problems_ The l\di\t, C problem The l\rupi [pi;pj H N\Fe{Cmax,CC^) problem The l n,pi G [pi'.pi] n N\Fe(Ü'^.CC'") problem Other problems Open problems.^ The l\di\ü,tmax problem Other problems Shop problems Two-machine flowshop problems The F2\prmu\Lex{CmaxjC) problem The F2\prmu\Fi{Cmax^ C)problem The F2\prmu,ri\Fe{Cmax,C) problem The F2\prmu\e{C/Cmax) problem The F2\prmu,di\#{Cmax,Trnax) problem The F2\prmu, di\#{cmax,u) problem The F2\prmu,di\#{Cmax^T) problem m-machine flowshop problems The F\prmu\Lex{Cmax2_C) problem The F\prmu\#{Cmax,C) problem The F\prmu,di\e{Cmax/Tmax) problem The F\pij [pij;pi^j],prmu\fe{cmax, CC"^) problem The F\pi^j =Pie [2uPi],prmu\#{Cmax,'CC^) problem Jobshop and Openshop problems Jobshop problems The 02\\Lex{Cmax,C) problem The 03\\Lex{Cmax,C) problem 286

5 Contents XIII 9. Parallel machines problems Problems with identical parallel machines The P2\pmtn,di\e{Lmax/Cmax) problem The P3\pmtn,di\e{Lma^/Cmax) problem The P2\di\Lex{Trriax, U) problem The P di #(C,[/)^roblem The P\pmtn\Lex{C, Cmax) problem Problems with uniform parallel machines The Q\pi = p\e{fmaxl9max) problem The Q\pi = v\ei^/fmax) problem The Q\vmtn\e{C/Cmax) problem Problems with unrelated parallel machines The R\pi^j [^i^j,pißft(c,'cc^) problem The R\pmtn\e{Fi{Imax,'M)/Cmax) problem Shop problems with assignment A hybrid flowshop problem with three stages Hybrid flowshop problems with k stages The HFk, (PM(^))f^i F^_(C^ax,C) problem The HFk, lpm^^"^)\^^\\e{c/crnax) problem The HFk, {PM^^^(t))t^i rf ^, df ^ \e{cmax/tmax) problem 318 A. Notations 323 A.l Notation of data and variables 323 A.2 Usual notation of single criterion scheduling problems 323 B. Synthesis on multicriteria scheduling problems 329 B.l Single machine Just-in-Time scheduhng problems 329 B.2 Single machine problems 330 B.3 Shop problems 333 B.4 Parallel machines scheduling problems 333 B.5 Shop scheduling problems with assignment 334 References 335 Index 357

6 List of algorithms and mathematical formulations The algorithm EELl of [Lawler, 1973] 23 The algorithm EJMl of [Moore, 1968] 24 The algorithm ESJl of [Johnson, 1954] 24 The algorithm HCDSl of [Campbell et al., 1970] 25 The algorithm HNEHl of [Nawaz et al, 1983] 26 The algorithm ESSl of [Sahni, 1979] 27 The algorithm EGTWl of [Garey et al., 1988] 148 The algorithm ECSl of [Chretienne and Sourd, 2003] 152 The algorithm EJKl of [Kanet, 1981a] 154 The algorithm EPSSl of [Panwalker et al, 1982] 156 The mathematical formulation ECLTl of [Chen et al, 1997] 158 The algorithm ESAl of [Sundararaghavan and Ahmed, 1984] 160 The algorithm EEMl of [Emmons, 1987] 162 The algorithm EEM2 of [Emmons, 1987] 164 The algorithm ECCl of [Cheng and Chen, 1994] 169 The algorithm HOMl of [Ow and Morton, 1988] 175 The algorithm HZIEl of [Zegordi et al., 1995] 178 The algorithm HLCl of [Li and Cheng, 1994] 180 The algorithm HLC2 of [Li and Cheng, 1994] 181 The mathematical formulation EFLRl of [Pry et al., 1987b] 188 The algorithm HEM3 of [Emmons, 1987] 190 The algorithm EWGl of [VanWassenhove and Gelders, 1980] 208 The algorithm EHVl of [Hoogeveen and van de Velde, 2001] 216 The algorithm ERVl of [Vickson, 1980b] 218 The mathematical formulation ECLT2 of [Chen et al., 1997] 220 The algorithm HGHPl of [Gupta et al., 1999a] 232 The algorithm HGHP2 of [Gupta et al., 1999a] 233 The algorithm HCRl of [Rajendran, 1992] 236 The algorithm ECRl of [Rajendran, 1992] 238 The algorithm EGNWl of [Gupta et al., 2001] 242 The algorithm HGNWl of [Gupta et al., 2001] 243 The algorithm HTGBl of [T'kindt et al., 2003] 246 The algorithm HTMTLl of [T'kindt et al., 2002] 249 The algorithm HNHHl of [Nagar et al, 1995b] 252

7 XVI List of algorithms and mathematical formulations The algorithm HSUl of [Sivrikaya-Serifoglu and Ulusoy, 1998] 253 The algorithm ESUl of [Sivrikaya-Serifoglu and Ulusoy, 1998] 255 The algorithm HCLl of [Chou and Lee, 1999] 257 The algorithm ESKl of [Sayin and Karabati, 1999] 258 The algorithm ESK2 of [Sayin and Karabati, 1999] 260 The algorithm EDCl of [Daniels and Chambers, 1990] 264 The algorithm HDC3 of [Daniels and Chambers, 1990] 265 The algorithm ELYJl of [Liao et al., 1997] 268 The algorithm HLYJl of [Liao et al., 1997] 269 The algorithm ELYJ2 of [Liao et al, 1997] 270 The mathematical formulation ESHl of [Selen and Hott, 1986] 272 The mathematical formulation EJWl of [Wilson, 1989] 273 The algorithm HGRl of [Gangadharan and Rajendran, 1994] 274 The algorithm HGR2 of [Gangadharan and Rajendran, 1994] 274 The algorithm HCR3 of [Rajendran, 1995] 276 The algorithm HCR5 of [Rajendran, 1994] 278 The algorithm HDC4 of [Daniels and Chambers, 1990] 279 The algorithm ECSl of [Cheng and Shakhlevich, 1999] 283 The algorithm HSHl of [Sarin and Hariharan, 2000] 294 The algorithm ELYl of [Leung and Young, 1989] 298 The algorithm ETMMl of [Tuzikov et al., 1998] 300 The algorithm ETMM2 of [Tuzikov et al., 1998] 301 The algorithm ETMM3 of [Tuzikov et al., 1998] 303 The algorithm EMPl of [Mc Cormick and Pinedo, 1995] 308 The algorithm EMP2 of [Mc Cormick and Pinedo, 1995] 309 The mathematical formulation ETBPl of [T'kindt et al., 2001] 312 The algorithm ETBP2 of [T'kindt et al, 2001] 313 The mathematical formulation ERMAl of [Riane et al., 1997] 317 The mathematical formulation ERMA2 of [Riane et al, 1997] 319 The algorithm EVBPl of [Vignier et al., 1996] 321