Minimizing the weighted number of tardy jobs on multiple machines: a review. (English) Zbl 1364.90002
Summary: We provide an overview of the history, the methods and the people who researched on minimizing the (weighted) number of tardy jobs as a performance measure. The review presents cases on multiple machines: parallel machines (including the identical, uniform and unrelated machines, flow shop, job shop and the open shop). The literature is divided into various sections for proper categorization. This includes setup time, preemption, batching, on-line and off-line scheduling, and other classifications. The complexity status of the various classifications is enumerated with its results and methods. Possible extension for future work is also highlighted.
MSC:
| 90-02 | Research exposition (monographs, survey articles) pertaining to operations research and mathematical programming |
| 90B35 | Deterministic scheduling theory in operations research |
| 90B36 | Stochastic scheduling theory in operations research |
| 90C59 | Approximation methods and heuristics in mathematical programming |
References:
| [1] | M. O. Adamu, Parallel machine scheduling to maximize the weighted number of just-in-time jobs,, Journal of Applied Science and Technology, 15, 27 (2010) |
| [2] | M. O. Adamu, Metaheuristics for scheduling on parallel machines to minimize the weighted number of early and tardy jobs,, International Journal of Physical Sciences, 7, 1641 (2012) |
| [3] | M. O. Adamu, Single machine review to minimize weighted number of tardy jobs,, Journal of Industrial and Management Optimization, 10, 219 (2014) · Zbl 1276.90001 · doi:10.3934/jimo.2014.10.219 |
| [4] | M. O. Adamu, A Note on just-in-time scheduling on flow shop machines,, Journal of the Nigerian Mathematical Society, 33, 321 (2014) · Zbl 1335.90030 |
| [5] | R. H. Ahmadi, <em>Coordinated Scheduling of Customer Orders</em>,, Updated Paper (1997) |
| [6] | S. Albers, The complexity of one machine batching problem,, Discrete Applied Mathematics, 47, 87 (1993) · Zbl 0792.90035 · doi:10.1016/0166-218X(93)90085-3 |
| [7] | A. Allahverdi, A review of scheduling research involving setup considerations,, OMEGA The International Journal of Management Science, 27, 219 (1999) |
| [8] | A. Allahverdi, A survey of scheduling problems with setup times or costs,, European Journal of Operational Research, 187, 985 (2008) · Zbl 1137.90474 · doi:10.1016/j.ejor.2006.06.060 |
| [9] | H. Allaoui, Integrating simulation and optimization to schedule a hybrid flow shop with maintenance constraints,, Computer and Industrial Engineering, 47, 431 (2004) |
| [10] | K. R. Baker, Scheduling with earliness and tardiness penalties: A review,, Operations Research, 38, 22 (1990) · Zbl 0699.90052 · doi:10.1287/opre.38.1.22 |
| [11] | M. F. Baki, One operator, two machine open shop and flow shop problems with setup times for machines and weighted number of tardy jobs objective,, Optimization Methods and Software, 19, 165 (2004) · Zbl 1054.90027 · doi:10.1080/10556780410001657653 |
| [12] | P. Baptiste, Batching identical jobs,, Mathematical Methods of Operations Research, 52, 355 (2000) · Zbl 1023.90020 · doi:10.1007/s001860000088 |
| [13] | P. Baptiste, <em>Preemptive Scheduling of Identical Machines</em>,, Technical Report (2000) |
| [14] | P. Baptiste, On minimizing the weighted number of late jobs in unit execution time open shops,, European Journal of Operational Research, 149, 344 (2003) · Zbl 1127.90349 · doi:10.1016/S0377-2217(02)00759-2 |
| [15] | P. Baptiste, Ten notes on equal processing time scheduling,, 40R, 2, 111 (2004) · Zbl 1070.90041 · doi:10.1007/s10288-003-0024-4 |
| [16] | P. Baptiste, <em>A Constraint Based Approach to Minimize the Weighted Number of Late Jobs on Parallel Machines</em>,, Technical Report 2000/228 (2000) |
| [17] | O. J. Boxma, Minimizing the expected weighted number of tardy jobs in stochastic flow shops,, Operations Research Letters, 5, 119 (1986) · Zbl 0633.90028 · doi:10.1016/0167-6377(86)90084-2 |
| [18] | P. Brucker, <em>Scheduling Algorithms</em>,, Springer - Verlag (1995) · Zbl 0839.90059 |
| [19] | P. Brucker, <em>Complexity Results for Scheduling Problems,</em>, 2011 |
| [20] | P. Brucker, Complexity results for single-machine problems with positive finish-start time-lags,, Computing, 63, 299 (1999) · Zbl 0946.90026 · doi:10.1007/s006070050036 |
| [21] | P. Brucker, Polynomial algorithms for resource - constrainted and multiprocessor task scheduling problems,, European Journal of Operational Research, 90, 214 (1996) · Zbl 0916.90144 |
| [22] | P. Brucker, Complexity results for flowshop and open shop problems with transportation delays,, Annals of Operations Research, 129, 81 (2004) · Zbl 1056.90057 · doi:10.1023/B:ANOR.0000030683.64615.c8 |
| [23] | P. Brucker, Complexity results for parallel machine problems with a single server,, Journal of Scheduling, 5, 429 (2002) · Zbl 1040.90016 · doi:10.1002/jos.120 |
| [24] | P. Brucker, Scheduling a batching machine,, Journal of Scheduling, 1, 31 (1998) · Zbl 0909.90172 · doi:10.1002/(SICI)1099-1425(199806)1:1<31::AID-JOS4>3.0.CO;2-R |
| [25] | P. Brucker, How useful are preemptive schedule?,, Operations Research Letters, 31, 129 (2003) · Zbl 1041.90015 · doi:10.1016/S0167-6377(02)00220-1 |
| [26] | P. Brucker, Scheduling unit time open shops to minimize the weighted number of late jobs,, Operations Research Letters, 14, 245 (1993) · Zbl 0793.90028 · doi:10.1016/0167-6377(93)90088-X |
| [27] | P. Brucker, Complexity of scheduling problems with multi-purpose machines,, Annals of Operations Research, 70, 57 (1997) · Zbl 0890.90089 · doi:10.1023/A:1018950911030 |
| [28] | P. Brucker, On the complexity of two machine job-shop scheduling with regular objective functions,, OR Spektrum, 19, 5 (1997) · Zbl 0892.90097 · doi:10.1007/BF01539799 |
| [29] | R. L. Bulfin, Minimizing the weighted number of tardy jobs on a two-machine flow shop,, Computers and Operational Research, 30, 1887 (2003) · Zbl 1047.90020 · doi:10.1016/S0305-0548(02)00114-4 |
| [30] | O. Cepek, A quadratic time algorithm to maximize the number of just-in-time jobs on identical parallel machines,, Computers and Operational Research, 32, 3265 (2005) · Zbl 1178.90139 · doi:10.1016/j.cor.2004.05.011 |
| [31] | C. L. Chen, Iterated hybrid metaheuristics algorithms for unrelated parallel machines problem with unequal ready times and sequence-dependent setup times,, The International Journal of Advanced Manufacturing Technology, 60, 693 (2012) |
| [32] | C. L. Chen, Complexity of single machine multicriteria scheduling problems,, European Journal of Operational Research, 70, 115 (1993) · Zbl 0795.90032 |
| [33] | Z. Chen, Solving parallel machine scheduling problems by column generation,, INFORMS Journal on Computing, 11, 78 (1999) · Zbl 1034.90506 · doi:10.1287/ijoc.11.1.78 |
| [34] | Z. L. Chen, Exact algorithms for scheduling multiple families of jobs on parallel machines,, Naval Research Logistics, 50, 823 (2003) · Zbl 1044.90033 · doi:10.1002/nav.10091 |
| [35] | T. C. E. Cheng, Survey of scheduling research involving due date assignment,, European Journal of Operational Research, 38, 156 (1989) · Zbl 0658.90049 · doi:10.1016/0377-2217(89)90100-8 |
| [36] | T. C. E. Cheng, A review of flowshop scheduling research with setup times,, Production and Operations Management, 9, 262 (2000) |
| [37] | T. C. E. Cheng, Customer Order Scheduling on Multiple Facilities,, Private Communication (2006) |
| [38] | T. C. Chiang, Using a family of critical ratio-based approaches to minimize the number of tardy jobs in the job shop with sequence dependent setup times,, European Journal of Operational Research, 196, 78 (2009) · Zbl 1156.90359 |
| [39] | B. C. Choi, Maximizing the weighted number of just-in-time jobs in flowshop scheduling,, Journal of Scheduling, 10, 237 (2007) · Zbl 1168.90431 · doi:10.1007/s10951-007-0030-z |
| [40] | H. S. Choi, A branch and bound algorithm for two stage flow shops: minimizing the number of tardy jobs,, Journal of the Korean Institute of Industrial Engineers, 33, 213 (2007) |
| [41] | H. S. Choi, Scheduling algorithms to minimize the number of tardy jobs in two-stage hybrid flow shops,, Computers and Industrial Engineering, 56, 113 (2009) |
| [42] | C. Chu, Heuristic procedure for minimizing makespan and the number of required pallets,, European Journal of Operational Research, 86, 491 (1995) · Zbl 0913.90163 |
| [43] | R. W. Conway, <em>Theory of Scheduling</em>,, Addison-Wesley (1967) · Zbl 1058.90500 |
| [44] | F. D. Croce, Minimizing tardy jobs in a flowshop with common due date,, European Journal of Operational Research, 120, 375 (2000) · Zbl 0949.90040 · doi:10.1016/S0377-2217(99)00164-2 |
| [45] | S. Dauzère-Pérès, <em>Using Lagrangean Relaxation to Minimize the (Weighted) Number of Late Jobs on a Single Machine</em>,, National Contribution IFORS 1999 (1999) · Zbl 1030.90030 |
| [46] | C. Desprez, A genetic algorithm for minimizing the weighted number of tardy jobs,, Proceedings of IEEE, 1271 (2006) |
| [47] | C. Desprez, Minimizing the weighted number of tardy jobs in a hybrid flow shop with genetic algorithm,, International Journal of Computer Integrated Manufacturing, 22, 745 (2009) |
| [48] | M. J. Dessouky, Scheduling identical jobs on uniform parallel machines,, Statistica Neerlandica, 44, 115 (1990) · Zbl 0716.90053 · doi:10.1111/j.1467-9574.1990.tb01276.x |
| [49] | E. Dhouib, Minimizing the number of tardy jobs in a permutation flowshop scheduling problem with setup times and time lags constraints,, Journal of Mathematical Modelling and Algorithms in Operations Research, 12, 85 (2013) · Zbl 1311.90045 |
| [50] | J. Du, Minimizing the number of late jobs on unrelated machines,, Operations Research Letter, 10, 153 (1991) · Zbl 0734.90042 · doi:10.1016/0167-6377(91)90032-K |
| [51] | J. Du, Minimizing the number of late jobs with release time constraint,, Journal of Combinatorial Mathematics and Combinatorial Computing, 11, 97 (1992) · Zbl 0764.90043 |
| [52] | S. French, <em>Sequencing and Scheduling: An Introduction to the Mathematics of the Job Shop</em>,, Ellis Harwood (1982) · Zbl 0479.90037 |
| [53] | G. Galambos, Minimizing the weighted number of late jobs in uet open shops,, Zeitschrift fur Operations Research ZOR - Methematical Methods of Operations Research, 41, 109 (1995) · Zbl 0830.90071 · doi:10.1007/BF01415068 |
| [54] | M. R. Garey, Strong NP-completeness results: motivation, examples and implications,, Journal of the Association for Computing Machinery, 25, 499 (1978) · Zbl 0379.68035 · doi:10.1145/322077.322090 |
| [55] | M. R. Garey, <em>Computers and Intractability, A Guide to the Theory of NP Completeness</em>,, Freeman (1979) · Zbl 0411.68039 |
| [56] | A. A. Gladky, On complexity of minimizing weighted number of late jobs in unit time open shops,, Discrete Applied Mathematics, 74, 197 (1997) · Zbl 0872.90047 · doi:10.1016/S0166-218X(97)81448-5 |
| [57] | R. L. Graham, Optimization and approximation in deterministic sequencing and scheduling: A survey,, Annals of Discrete Mathematics, 5, 287 (1979) · Zbl 0411.90044 · doi:10.1016/S0167-5060(08)70356-X |
| [58] | E. Gersl, A note: Maximizing the weighted number of just-in-time jobs on a proportionate flowshop,, Information Procesing Letters, 115, 159 (2015) · Zbl 1302.90081 · doi:10.1016/j.ipl.2014.09.004 |
| [59] | S. Guirchoun, Complexity results for parallel machine scheduling problems with a server in computer systems,, In:Processings of the 2nd Multidisciplinary International Conference on Scheduling: Theory and Application, 232 (2005) |
| [60] | J. N. D. Gupta, <em>Integrating Job Selection and Scheduling in a Flowshop</em>,, Working Paper (1994) |
| [61] | J. N. D. Gupta, Two machine flow shop to minimize number of tardy jobs,, Journal of Operational Research Society, 48, 212 (1997) · Zbl 0888.90090 |
| [62] | J. N. D. Gupta, Minimizing tardy jobs in a two-stage hybrid flowshop,, International Journal of Production Research, 36, 2397 (1998) · Zbl 0945.90567 |
| [63] | N. G. Hall, Parallel machine scheduling with a common server,, Discrete Applied Mathematics, 102, 223 (2000) · Zbl 0972.90031 · doi:10.1016/S0166-218X(99)00206-1 |
| [64] | A. M. A. Hariri, A branch and bound algorithm to minimize number of late jobs in a permutation flow shop,, European Journal of Operational Research, 38, 228 (1989) · Zbl 0674.90048 · doi:10.1016/0377-2217(89)90108-2 |
| [65] | K. Hiraishi, Scheduling of parallel identical machines to maximize the weighted number of just-in-time jobs,, Computers and Operations Research, 29, 841 (2002) · Zbl 0999.68029 · doi:10.1016/S0305-0548(00)00086-1 |
| [66] | J. C. Ho, Minimizing the number of tardy jobs for m parallel machines,, European Journal of Operational Research, 84, 343 (1995) · Zbl 0927.90047 |
| [67] | J. C. Ho, Flowshop Scheduling with Dominant machine,, Computers and Operations Research, 22, 237 (1995) · Zbl 0826.90064 |
| [68] | H. Hoogeveen, Multicriteria scheduling,, European Journal of Operational Research, 167, 592 (2005) · Zbl 1154.90458 · doi:10.1016/j.ejor.2004.07.011 |
| [69] | H. L. Huang, Concurrent open shop problem to minimize the weighted number of late jobs,, Multiprocessor Scheduling: Theory and Applications, 215 (2007) |
| [70] | A. S. Jain, Deterministic job shop scheduling: Past, present and future,, European Journal of Operational Research, 113, 390 (1999) · Zbl 0938.90028 |
| [71] | A. Janiak, Algorithms for parallel processor scheduling with distinct due windows and unit-time jobs,, Bulletin of the Polish Academy of Sciences Technical Sciences, 57, 209 (2009) |
| [72] | F. Jolai, A hybrid memetic algorithm for maximizing the weighted number of just-in-time jobs on unrelated parallel machines,, Journal of Intelligence Manufacturing, 22, 247 (2011) |
| [73] | J. Josefowska, Scheduling shops to minimize the weighted number of late jobs,, Operations Research Letters, 10, 27 (1994) |
| [74] | J. Jungwattanaki, An evaluation of sequencing heuristics for flexible flowshop scheduling problems with unrelated parallel machines and dual criteria,, Otto-von-Guericke-Universitat Magdeburg, 1 (2005) |
| [75] | J. Jungwattanaki, Constructive tabu search algorithms for hybrid flowshop problems with unrelated parallel machines and setup times,, International Journal of Computational Science, 1, 204 (2007) |
| [76] | S. Knust, <em>Shop-scheduling problems with transportation</em>,, PhD Thesis (1999) · Zbl 0947.68013 |
| [77] | A. Krämer, <em>Scheduling Multi processor Tasks in Dedicated Processors</em>,, PhD Thesis (1995) · Zbl 1062.68531 |
| [78] | S. Kravchenko, Parallel machine problems with equal processing times: A survey,, J. Sched., 14, 435 (2011) · Zbl 1280.90058 · doi:10.1007/s10951-011-0231-3 |
| [79] | S. A. Kravchenko, Minimizing the number of late jobs for the two-machine unit-time job shop scheduling problem,, Discrete Applied Mathematics, 98, 209 (2000) · Zbl 0947.90046 · doi:10.1016/S0166-218X(99)00165-1 |
| [80] | S. A. Kravchenko, On the complexity of minimizing the number of late jobs in unit time open shop,, Discrete Applied Mathematics, 100, 127 (2000) · Zbl 0971.90030 · doi:10.1016/S0166-218X(99)00202-4 |
| [81] | W. Kubiak, A note on the complexity of open shop scheduling problems,, INFOR, 29, 284 (1991) · Zbl 0778.90027 |
| [82] | A. Lann, A note on the maximum number of on-time jobs on parallel identical machines,, Computers and Operations Research, 30, 1745 (2003) · Zbl 1039.90016 · doi:10.1016/S0305-0548(02)00084-9 |
| [83] | E. L. Lawler, Preemptive scheduling of two uniform machines to minimize the number of late jobs,, Operations Research, 37, 314 (1989) · Zbl 0672.90071 · doi:10.1287/opre.37.2.314 |
| [84] | E. L. Lawler, A functional equation and its applications to resource allocation and sequencing problems,, Management Science, 16, 77 (1969) · Zbl 0184.23303 |
| [85] | E. L. Lawler, <em>Efficient Implementation of Dynamic Programming Algorithms for Sequencing Problems</em>,, Report BW 106/79 (1979) · Zbl 0416.90036 |
| [86] | E. L. Lawler, Recent results in the theory of machine scheduling,, In: A. Bachem, 202 (1983) · Zbl 0547.90042 |
| [87] | E. L. Lawler, Erratum: Minimizing maximum lateness in a two-machine open shop,, Maths. Operations Research, 7 (1982) · Zbl 0497.90036 · doi:10.1287/moor.7.4.635 |
| [88] | E. L. Lawler, Minimizing maximum lateness in a two-machine open shop,, Math. Operations Research, 6, 153 (1981) · Zbl 0496.90047 · doi:10.1287/moor.6.1.153 |
| [89] | E. L. Lawler, Sequencing and scheduling: Algorithms and complexity,, In: S.C. Graves, 445 (1993) |
| [90] | D. Lei, Multi-objective production scheduling: A survey,, International Journal of Advance Manufacturing Technology, 43, 926 (2009) |
| [91] | J. K. Lenstra, <em>Production Scheduling</em>,, Mathematisch Centrum (1977) |
| [92] | J. K. Lenstra, Complexity of machine scheduling problems,, Annals of Discrete Mathematics, 1, 343 (1977) · Zbl 0353.68067 |
| [93] | J. Y. T. Leung, Scheduling orders for multiple product types with due dates related objectives,, European Journal of Operational Research, 168, 370 (2006) · Zbl 1099.90541 · doi:10.1016/j.ejor.2004.03.030 |
| [94] | J. Y. T. Leung, Heuristic for minimizing the number of late jobs on two processors,, International Journal on Foundations of Computer Science, 5, 261 (1995) · Zbl 0830.68010 |
| [95] | C. L. Li, Single machine scheduling to minimize the weighted number of early and tardy agreeable jobs,, Computers and Operations Research, 22, 205 (1995) · Zbl 0812.90068 |
| [96] | C. L. Li, A heuristic for parallel machine scheduling with agreeable due dates to minimize the number of late jobs,, Computers and Operations Research, 22, 277 (1995) · Zbl 0827.90075 |
| [97] | B. M. T. Lin, Parallel machine batch scheduling to minimize the maximum lateness and the number of tardy jobs,, International Journal of Production Economics, 91, 121 (2004) |
| [98] | B. M. T. Lin, Customer order scheduling to minimize the number of late jobs,, European Journal of Operational Research, 183, 944 (2007) · Zbl 1180.90128 |
| [99] | B. M. T. Lin, Scheduling in the two-machine flow shop with due date constraints,, Journal of Production Economics, 70, 117 (2001) |
| [100] | R. Linn, Hybrid flow shop scheduling. a survey,, Computers and Industrial Engineering, 37, 57 (1999) |
| [101] | C. Y. Liu, Scheduling open shops with unit execution times to minimize functions of due dates,, Operations Research, 36, 553 (1988) · Zbl 0652.90063 · doi:10.1287/opre.36.4.553 |
| [102] | M. Liu, Scheduling algorithm based on evolutionary computing in identical parallel machine production line,, Robotics and Computer Integrated Manufacturing, 19, 401 (2003) |
| [103] | E. Lodree, A new rule for minimizing the weighted number of tardy jobs in dynamic flow shops,, European Journal of Operational Research, 159, 258 (2004) · Zbl 1065.90039 · doi:10.1016/S0377-2217(03)00404-1 |
| [104] | R. M’Hallah, Minimizing the weighted number of tardy jobs on parallel processors,, European Journal of Operational Research, 160, 471 (2005) · Zbl 1067.90047 · doi:10.1016/j.ejor.2003.06.027 |
| [105] | M. Mathirajan, A literature review, classification and simple meta-analysis on scheduling of batch processors in semi-conductor,, International Journal of Advance Manufacturing Technology, 29, 990 (2006) |
| [106] | M. Middendorf, Transversal graphs for partially ordered sets: Sequencing, merging and scheduling problems,, Journal of Combinatorial Optimization, 3, 417 (1999) · Zbl 0962.90019 · doi:10.1023/A:1009827520712 |
| [107] | J. M. Moore, An n job, one machine sequencing algorithm for minimizing the number of late jobs,, Management Science, 15, 102 (1968) · Zbl 0164.20002 |
| [108] | G. Mosheiov, Minimizing the number of tardy jobs on a proportionate flowshop with general position-dependent processing times,, Computers and Operational Research, 39, 1601 (2012) · Zbl 1251.90172 · doi:10.1016/j.cor.2011.09.011 |
| [109] | G. Mosheiov, Minimum weighted number of tardy jobs on m-machine flow-shop,, European Journal of Operational Research, 201, 404 (2010) · Zbl 1175.90184 · doi:10.1016/j.ejor.2009.03.018 |
| [110] | A. Nagar, Multiple and bicriteria scheduling: A literature survey,, European Journal of Operational Research, 81, 88 (1995) · Zbl 0913.90178 |
| [111] | C. T. Ng, Concurrent Open Shop Scheduling to Minimize the Weighted Number of Tardy Jobs,, Journal of Scheduling, 6, 405 (2003) · Zbl 1027.90033 · doi:10.1023/A:1024284828374 |
| [112] | H. Ohta, A heuristic job shop scheduling algorithm to minimize the total holding of completed and in-process products subject to no tardy jobs,, International Journal of Production Economics, 101, 19 (2006) |
| [113] | M. Park, Search heuristics for a parallel machine scheduling problem with ready times and due dates,, Computers Industrial Engineering, 33, 793 (1997) |
| [114] | C. N. Potts, Scheduling with batching: A review,, European Journal of Operational Research, 120, 228 (2000) · Zbl 0953.90028 · doi:10.1016/S0377-2217(99)00153-8 |
| [115] | C. N. Potts, Integrating scheduling with batching and lot-sizing: A review of algorithms and complexity,, Journal of Operations Research Society, 43, 395 (1992) · Zbl 0756.90050 |
| [116] | T. A. Reomer, A note on the complexity of the concurrent open shop problem,, Journal of Scheduling, 9, 389 (2006) · Zbl 1154.90484 · doi:10.1007/s10951-006-7042-y |
| [117] | A. H. G. Rinnooy Kan, <em>Machine Scheduling Problems: Classification, Complexity and Computations</em>,, Nijhoff (1976) · doi:10.1007/978-1-4613-4383-7 |
| [118] | A. J. Ruiz-Torres, Minimizing the number of tardy jobs in the flowshop problem with operational and resource flexibility,, Computers and Operational Research, 37, 282 (2010) · Zbl 1175.90190 · doi:10.1016/j.cor.2009.04.018 |
| [119] | A. J. Ruiz-Torres, Minimizing the number of late jobs for the permutation flowshop problem with secondary resources,, Computers and Operational Research, 35, 1227 (2008) · Zbl 1169.90361 · doi:10.1016/j.cor.2006.07.013 |
| [120] | A. J. Ruiz-Torres, Simulated annealing heuristics for the average flow time and number of tardy jobs bi-criteria identical parallel machine problem,, Computers and Industrial Engineering, 33, 257 (1997) |
| [121] | A. J. Ruiz-Torres, Scheduling uniform parallel machines subjected to a secondary resource to minimize the number of tardy jobs,, European Journal of Operational Research, 179, 302 (2007) · Zbl 1180.90136 |
| [122] | P. Senthilkumar, Literature review of single machine scheduling problem with uniform parallel machines,, Intelligent Information Management, 2, 457 (2010) |
| [123] | M. Sevaux, <em>VNS/TS for a Parallel Machine Scheduling Problem</em>,, MEC-VNS: 18th Mini Euro Conference pm VNS (2005) |
| [124] | M. Sevaux, Heuristics and metaheuristics for a parallel machine scheduling problem: A computational evaluation,, Proceedings of 4th Metaheuristics International Conference, 411 (2001) |
| [125] | D. Shabtay, Maximizing the weighted number of just-in-time jobs in several two machine scheduling systems,, Journal of Scheduling, 15, 39 (2012) · Zbl 1280.90070 · doi:10.1007/s10951-010-0204-y |
| [126] | D. Shabtay, A bicriteria approach to maximize the weighted number of just-in-time jobs and to minimize the total resource consumption cost in a two-machine flowshop scheduling system,, International Journal of Production Economics, 136, 67 (2012) |
| [127] | R. Sitters, Complexity of preemptive minsum scheduling on unrelated parallel machines,, Journal of Algorithms, 57, 37 (2005) · Zbl 1101.68430 · doi:10.1016/j.jalgor.2004.06.011 |
| [128] | Y. N. Sotskov, The complexity of shop scheduling problems with two or three jobs,, European Journal of Operational Research, 53, 326 (1991) · Zbl 0742.90046 |
| [129] | S. Sriram, Online Parallel Machine Scheduling with Hard Deadlines,, International Journal of Recent Trends in Engineering, 2, 263 (2009) |
| [130] | G. A. Süer, Minimizing the number of tardy jobs in multi-period cell loading problems,, Computers and Industrial Engineering, 33, 721 (1997) |
| [131] | G. A. Süer, <em>Minimizing the Number of Tardy Jobs in Identical Machine Scheduling,</em>, Proceedings of the 15th Conference on Computers and Industrial Engineering (1993) |
| [132] | G. A. Süer, Identical machine scheduling to minimize the number of tardy jobs when lost-splitting is allowed,, Computers Industrial Engineering, 33, 271 (1997) |
| [133] | S. C. Sung, <em>Just-In-Time Scheduling on Parallel Machines,</em>, The European Operational Research Conference (2001) |
| [134] | V. T’Kindt, Enumerating of pareto optima for a flowshop scheduling problem with two criteria,, Journal of Computing, 19, 64 (2007) · Zbl 1241.90058 · doi:10.1287/ijoc.1050.0167 |
| [135] | V. G. Timkorsky, Is a unit-time job shop not easier than identical parallel machines?,, Discrete Applied Mathematics, 85, 149 (1998) · Zbl 0908.90173 · doi:10.1016/S0166-218X(98)00032-8 |
| [136] | V. G. Timkorsky, Identical parallel machines vs. unit time shops and preemptions vs. chains in scheduling complexity,, European Journal of Operational Research, 149, 355 (2003) · Zbl 1030.90027 · doi:10.1016/S0377-2217(02)00767-1 |
| [137] | H. Ucar, A particle swarm optimization algorithm for permutation flow shop sequencing problem with the number of tardy jobs criterion,, Proceedings of 5th International Symposium of Intelligent Manufacturing Systems, 1110 (2006) |
| [138] | J. M. Van Den Akker, Parallel machine scheduling by column generation,, Operations Research, 47, 862 (1999) · Zbl 0979.90051 · doi:10.1287/opre.47.6.862 |
| [139] | M. Van der Akker, <em>Minimizing the Number of Tardy Jobs,</em> In J.Y.-T. Leung (Ed),, Handbook of Scheduling: Algorithms (2004) |
| [140] | F. Vargas-Nieto, <em>Scheduling a Thermal-Printed Label Manufacturing Plant Using an Evolutionary Algorithm,</em>, 19th Proceedings International Conference on Production Research (ICPR-19) (2007) |
| [141] | E. Wagneur, Open shops with job overlap,, European Journal of Operational Research, 71, 366 (1993) · Zbl 0797.90047 |
| [142] | I. L. Wang, Scheduling unrelated parallel machines in semiconductor manufacturing by problem reduction and local search heuristics,, Flexible Services and Manufacturing Journal, 25, 343 (2012) |
| [143] | J. B. Wang, No wait or no idle permutation flowshop scheduling with dominating machines,, Journal of Applied Mathematics and Computing, 17, 419 (2005) · Zbl 1138.90400 · doi:10.1007/BF02936066 |
| [144] | S. Webster, Scheduling groups of jobs on a single machine,, Operations Research, 43, 692 (1995) · Zbl 0857.90062 · doi:10.1287/opre.43.4.692 |
| [145] | S. Xiang, Solvable cases of permutation flowshop scheduling with dominating machines,, International Journal of Production Economics, 66, 53 (2000) |
| [146] | W. H. Yang, Survey of scheduling research involving setup times,, International Journal of Systems Sciences, 30, 143 (1999) · Zbl 0995.90037 |
| [147] | B. P. C. Yen, Single machine bicriteria scheduling: A survey,, Industrial Engineering: Theory, 10, 222 (2003) |
| [148] | W. K. Yeung, Two-machine flow shop scheduling with common due window to minimize weighted number of early and tardy jobs,, Naval Research Logistics, 56, 593 (2009) · Zbl 1183.90206 · doi:10.1002/nav.20356 |
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