Journal of Scheduling

, Volume 15, Issue 4, pp 403–418 | Cite as

Vyacheslav Tanaev: contributions to scheduling and related areas

  • V. S. Gordon
  • M. Y. Kovalyov
  • G. M. Levin
  • Y. M. Shafransky
  • Y. N. Sotskov
  • V. A. Strusevich
  • A. V. Tuzikov
Article

Abstract

This paper discusses several areas of research conducted by Vyacheslav Tanaev (1940–2002), mainly on scheduling. His contribution to the parametric decomposition of optimization problems is also addressed. For each area we focus on the most important results obtained by V.S. Tanaev and trace how his research has been advanced.

Keywords

Scheduling Sequencing Permutation Priority-generating function Symmetric function Mixed graph Parametric decomposition 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Aizenshtat, V. S. (1963). Multi-operator cyclic processes. Doklady Akademii Nauk BSSR, 7(4), 224–227 (in Russian). Google Scholar
  2. Al-Anzi, F., Sotskov, Yu. N., Allahverdi, A., & Andreev, G. (2006). Using mixed graph coloring to minimize total completion time in job shop scheduling. Mathematics of Computation, 182, 1137–1148. Google Scholar
  3. Alyushkevich, V. B., & Sotskov, Yu. N. (1989). Stability in the problems of production planning. Vestsi Akademii Navuk BSSR. Seryya Fizika-Matematychnykh Navuk, 3, 102–107 (in Russian). Google Scholar
  4. Baker, K. R. (1974). Introduction to sequencing and scheduling. New York: Wiley. Google Scholar
  5. Baker, K. R., Lawler, E. L., Lenstra, J. K., & Rinnooy Kan, A. H. G. (1983). Preemptive scheduling of a single machine to minimize maximum cost subject to release dates and precedence constraints. Operations Research, 31(2), 381–386. Google Scholar
  6. Barkan, S. A., & Tanaev, V. S. (1970). On constructing class schedules. Vestsi Akademii Navuk BSSR. Seryya Fizika-Matematychnykh Navuk, 1, 76–81 (in Russian). Google Scholar
  7. Blazewicz, J. (1976). Scheduling dependent tasks with different arrival times to meet deadlines. In E. Gelenbe & H. Beilner (Eds.), Modelling and Performance Evaluation of Computer Systems (pp. 57–65). Amsterdam: North Holland. Google Scholar
  8. Blazewicz, J., Ecker, K. H., Pesch, E., Schmidt, G., & Weglarz, J. (2007). Handbook on scheduling. Berlin: Springer. Google Scholar
  9. Blokh, A. S., & Tanaev, V. S. (1966). Multioperator processes. Vestsi Akademii Navuk BSSR. Seryya Fizika-Matematychnykh Navuk, 2, 5–11 (in Russian). Google Scholar
  10. Brucker, P., Knust, S., Cheng, T. C. E., & Shakhlevich, N. V. (2004). Complexity results for flow-shop and open-shop scheduling problems with transportation delays. Annals of Operations Research, 129(1–4), 81–106. Google Scholar
  11. Christofides, N., & Beasley, J. E. (1984). Period routing problem. Networks, 14(2), 237–256. Google Scholar
  12. Coffman, E. G., & Graham, R. L. (1972). Optimal scheduling for two-processor systems. Acta Informatica, 1(3), 200–213. Google Scholar
  13. Conway, R. W., Maxwell, W. L., & Miller, L. W. (1967). Theory of scheduling. Reading: Addison-Wesley. Google Scholar
  14. Dantzig, G. B., & Wolfe, P. (1960). Decomposition principle for linear programs. Operations Research, 8(1), 101–112. Google Scholar
  15. Dantzig, G. B., Blattner, W., & Rao, M. R. (1967). Finding a cycle in a graph with minimum cost to time ratio with application to a ship routing problem. In P. Rosenstiehl (Ed.), Theory of graphs (pp. 77–84). Paris/New York: Dunod/Gordon & Breach. Google Scholar
  16. Dawande, M., Geismer, H. N., Sethi, S. P., & Sriskandarajah, C. (2005). Sequencing and scheduling in robotic cells: Recent developments. Journal of Scheduling, 8(5), 387–426. Google Scholar
  17. Dilworth, R. P. (1950). A decomposition for partially ordered sets. Annals of Mathematics, 51, 161–166. Google Scholar
  18. Dolgui, A., Levin, G., & Louly, M. A. (2005). Decomposition approach for a problem of lot-sizing and sequencing under uncertainties. International Journal of Computer Integrated Manufacturing, 18(5), 376–385. Google Scholar
  19. Dolgui, A., Finel, B., Guschinskaya, O., Guschinsky, N., Levin, G., & Vernadat, F. (2006a). Balancing large-scale machining lines with multi-spindle heads using decomposition. International Journal of Production Research, 44(18–19), 4105–4120. Google Scholar
  20. Dolgui, A., Guschinsky, N., & Levin, G. (2006b). A decomposition method for transfer line life cycle cost optimization. Journal of Mathematical Modeling and Algorithms, 5, 215–238. Google Scholar
  21. Dolgui, A., Guschinsky, N., & Levin, G. (2007). Optimisation of power transmission systems using a multilevel decomposition approach. RAIRO–Operations Research, 41, 213–229. Google Scholar
  22. Dolgui, A., Guschinskaya, O., Guschinsky, N., & Levin, G. (2008a). Decision making and support tools for design of machining systems. In F. Adam & P. Humphreys (Eds.), Encyclopedia of decision making and decision support technologies (pp. 155–164). Hershey: Idea Group Inc. Google Scholar
  23. Dolgui, A., Guschinsky, N., & Levin, G. (2008b). Decision making and support tools for design of transmission systems. In F. Adam & P. Humphreys (Eds.), Encyclopedia of decision making and decision support technologies (pp. 165–175). Hershey: Idea Group Inc. Google Scholar
  24. Emelichev, V. A., Girlich, E. N., Nikulin, Y. V., & Podkopaev, D. P. (2002). Stability and regularization radius of vector problems of integer linear programming. Optimization, 51(4), 645–676. Google Scholar
  25. Ermoliev, Y. G., & Ermolieva, L. G. (1972). Method of parametric decomposition. Kibernetika, 1, 66–69. Google Scholar
  26. Ford, L. R. Jr., & Fulkerson, D. R. (1962). Flows in networks. Princeton: Princeton University Press. Google Scholar
  27. Gladky, A. A., Shafransky, Y. M., & Strusevich, V. A. (2004). Flow shop scheduling problems under machine-dependent precedence constraints. Journal of Combinatorial Optimization, 8, 13–28. Google Scholar
  28. Gordon, V. S., & Shafransky, Y. M. (1977). On a class of scheduling problems with partially ordered jobs. In Proceedings of the 4-th all-union conference on theoretical cybernetics problems, Novosibirsk, August 30–September 1 (pp. 101–103) (in Russian). Google Scholar
  29. Gordon, V. S., & Shafransky, Y. M. (1978a). Optimal ordering with series-parallel precedence constraints. Doklady Akademii Nauk BSSR, 22(3), 244–247 (in Russian). Google Scholar
  30. Gordon, V. S., & Shafransky, Y. M. (1978b). The decomposition approach to minimizing functions over a set of permutations of partially ordered elements. In Proceedings of the 5-th all-union conference of complex system control (pp. 51–56). Alma-Ata (in Russian). Google Scholar
  31. Gordon, V. S., & Shafransky, Y. M. (1978c). On optimal ordering with series-parallel precedence constraints. Vestsi Akademii Navuk BSSR. Seryya Fizika-Matematychnykh Navuk, 5, 135 (in Russian). Google Scholar
  32. Gordon, V. S., & Strusevich, V. A. (1999). Earliness penalties on a single machine subject to precedence constraints: SLK due date assignment. Computers & Operations Research, 26, 157–177. Google Scholar
  33. Gordon, V. S., & Tanaev, V. S. (1971). Single-machine deterministic scheduling with step functions of penalties. In Computers in engineering (pp. 3–8). Minsk (in Russian). Google Scholar
  34. Gordon, V. S., & Tanaev, V. S. (1973a). Single-machine deterministic scheduling with tree-like ordered jobs and exponential penalty functions. In Computers in engineering (pp. 3–10). Minsk (in Russian). Google Scholar
  35. Gordon, V. S., & Tanaev, V. S. (1973b). Preemptions in deterministic systems with parallel machines and different release dates of jobs. In Optimization of systems of collecting, transfer and processing of analogous and discrete data in local information computing systems. Materials of the 1st joint Soviet-Bulgarian seminar. Institute of Engineering Cybernetics of Academy of Sciences of BSSR—Institute of Engineering Cybernetics of Bulgarian Academy of Sciences (pp. 36–50). Minsk (in Russian). Google Scholar
  36. Gordon, V. S., & Tanaev, V. S. (1973c). Due dates in single-stage deterministic scheduling. In Optimization of systems of collecting, transfer and processing of analogous and discrete data in local information computing systems. Materials of the 1st joint Soviet-Bulgarian seminar, Institute of Engineering Cybernetics of Academy of Sciences of BSSR—Institute of Engineering Cybernetics of Bulgarian Academy of Sciences (pp. 54–58). Minsk (in Russian). Google Scholar
  37. Gordon, V. S., & Tanaev, V. S. (1983). On minmax problems of scheduling theory for a single machine. Vestsi Akademii Navuk BSSR. Seryya Fizika-Matematychnykh Navuk, 3, 3–9 (in Russian). Google Scholar
  38. Gordon, V. S., & Tanaev, V. S. (2001). Scheduling decisions for the systems with deadlines. In Z. Binder (Ed.), Proceedings of the 2nd IFAC/IFIP/IEEE conference, management and control of production and logistics (vol. 2, pp. 687–690). Elmsford: Pergamon. Google Scholar
  39. Gordon, V. S., Proth, J.-M., & Strusevich, V. A. (2005). Single machine scheduling and due date assignment under series-parallel precedence constraints. Central European Journal of Operations Research, 13, 15–35. Google Scholar
  40. Gordon, V. S., Potts, C. N., Strusevich, V. A., & Whitehead, J. D. (2008). Single machine scheduling models with deterioration and learning: Handling precedence constraints via priority generation. Journal of Scheduling, 11, 357–370. Google Scholar
  41. Graham, R. L., Lawler, E. L., Lenstra, J. K., & Rinnooy Kan, A. H. G. (1979). Optimization and approximation in deterministic scheduling: a survey. Annals of Discrete Mathematics, 5, 287–326. Google Scholar
  42. Guschinskaya, O., Dolgui, A., Guschinsky, N., & Levin, G. (2008). A heuristic multi-start decomposition approach for optimal design of serial machining lines. European Journal of Operational Research, 189(3), 902–913. Google Scholar
  43. Guschinsky, N. N., & Levin, G. M. (1987). Two-level optimization of a composite function and its application to a problem of path optimization in a graph. Vestsi Akademii Navuk BSSR. Seryya Fizika-Matematychnykh Navuk, 3, 3–9 (in Russian). Google Scholar
  44. Guschinsky, N. N., & Levin, G. M. (1991). Minimization of a monotone superposition of recurrent-monotone functions over the set of parametrized paths in a digraph. Sistemy Modelirovaniya, 17, 167–178 (in Russian). Google Scholar
  45. Guschinsky, N. N., Levin, G. M., & Tanaev, V. S. (1991). Parametric decomposition of problems of minimizing composite functions on parametrized paths in a digraph. Soviet Journal of Computer and Systems Sciences, 29(6), 31–42 (translated from Russian, Izvestiya AN SSSR. Seria Tekhnicheskaya Kibernetika, 1990). Google Scholar
  46. Guschinsky, N. N., Levin, G. M., & Dolgui, A. B. (2006). Decision support for design of power transmissions. Minsk: Belaruskaya Navuka (in Russian). Google Scholar
  47. Hansen, P., Kuplinsky, J., & de Werra, D. (1997). Mixed graph colorings. Mathematical Methods of Operational Research, 45, 145–160. Google Scholar
  48. Hardy, G. H., Littlewood, J. E., & Polya, G. (1934). Inequalities. London: Cambridge University Press. Google Scholar
  49. Horn, W. A. (1972). Single-machine job sequencing with treelike precedence ordering and linear delay penalties. SIAM Journal of Applied Mathematics, 23, 189–202. Google Scholar
  50. Horn, W. A. (1974). Some simple scheduling algorithms. Naval Research Logistics Quarterly, 21(1), 177–185. Google Scholar
  51. Hu, T. C. (1961). Parallel sequencing and assembly line problems. Operations Research, 9, 841–848. Google Scholar
  52. Jackson, J. R. (1955). Scheduling a production line to minimize maximum tardiness (Research Report 43, Management Science Research Project). University of California, Los Angeles, USA. Google Scholar
  53. Janiak, A., & Kovalyov, M. Y. (2006). Scheduling in a contaminated area: a model and polynomial algorithms. European Journal of Operational Research, 173, 125–132. Google Scholar
  54. Janiak, A., Shafransky, Y. M., & Tuzikov, A. (2001). Sequencing with ordered criteria, precedence and group technology constraints. Informatica, 12(1), 61–88. Google Scholar
  55. Johnson, S. M. (1954). Optimal two- and three-stage production schedules with setup times included. Naval Research Logistics Quarterly, 1, 61–68. Google Scholar
  56. Karp, R. M. (1978). A characterization of the minimum cycle mean in a digraph. Discrete Mathematics, 23, 309–311. Google Scholar
  57. Karp, R. M., & Orlin, J. B. (1981). Parametric shortest path algorithms with an application to cyclic staffing. Discrete Applied Mathematics, 3(1), 37–45. Google Scholar
  58. Kladov, G. K., & Livshitz, E. M. (1968). On a scheduling problem to minimize the total penalty. Kibernetika, 6, 99–100 (in Russian). Google Scholar
  59. Kolen, A. W. J., Lenstra, J. K., Papadimitriou, C. H., & Spieksma, F. C. R. (2007). Interval scheduling: a survey. Naval Research Logistics, 54, 530–543. Google Scholar
  60. Kornai, J., & Liptak, T. (1965). Two-level planning. Econometrica, 33, 141–169. Google Scholar
  61. Kovalyov, M. Y., & Shafransky, Y. M. (1998). Uniform machine scheduling of unit-time jobs subject to resource constraints. Discrete Applied Mathematics, 84, 253–257. Google Scholar
  62. Kovalyov, M. Y., & Tuzikov, A. V. (1994). Sequencing groups of jobs on a single machine subject to precedence constraints. Applied Mathematics and Computer Science, 4(4), 635–641. Google Scholar
  63. Kovalyov, M. Y., Shafransky, Y. M., Strusevich, V. A., Tanaev, V. S., & Tuzikov, A. V. (1989). Approximation scheduling algorithms: a survey. Optimization, 20(6), 859–878. Google Scholar
  64. Kovalyov, M. Y., Ng, C. T., & Cheng, T. C. E. (2007). Fixed interval scheduling: models, applications, computational complexity and algorithms. European Journal of Operational Research, 178, 331–342. Google Scholar
  65. Kruger, K., Sotskov, Yu. N., & Werner, F. (1998). Heuristic for generalized shop scheduling problems based on decomposition. International Journal of Production Research, 36(11), 3013–3033. Google Scholar
  66. Lambin, N. V., & Tanaev, V. S. (1970). On circuit-free orientation of mixed graphs. Doklady Akademii Nauk BSSR, 14(9), 780–781 (in Russian). Google Scholar
  67. Laporte, G., & Osman, I. H. (1995). Routing problems: a bibliography. Annals of Operation Research, 61(1), 227–262. Google Scholar
  68. Leont’ev, V. K. (1975). Stability of the traveling salesman problem. Zhurnal Vychislitel’noj Matematiki i Matematicheskoj Fiziki, 15(4), 1298–1309 (in Russian). Google Scholar
  69. Levin, G. M. (1980). Towards optimization of functions recursively defined over weakly normalized sets of permutations. Vestsi Akademii Navuk BSSR. Seryya Fizika-Matematychnykh Navuk, 5, 9–14. Google Scholar
  70. Levin, G. M., & Tanaev, V. S. (1968). On a class of problems of combinatorial optimization. Vestsi Akademii Navuk BSSR. Seryya Fizika-Matematychnykh Navuk, 5, 30–35 (in Russian). Google Scholar
  71. Levin, G. M., & Tanaev, V. S. (1970). On the theory of optimization over a set of permutations. Doklady Akademii Nauk BSSR, 14(7), 588–590 (in Russian). Google Scholar
  72. Levin, G. M., & Tanaev, V. S. (1974a). Parametric decomposition of extremal problems. Vestsi Akademii Navuk BSSR. Seryya Fizika-Matematychnykh Navuk, 4, 24–29 (in Russian). Google Scholar
  73. Levin, G. M., & Tanaev, V. S. (1974b). Towards the theory of parametric decomposition of extremal problems. Doklady Akademii Nauk BSSR, 18(10), 883–885 (in Russian). Google Scholar
  74. Levin, G. M., & Tanaev, V. S. (1977). On parametric decomposition of extremal problems. Kibernetika, 3, 123–128 (in Russian). Google Scholar
  75. Levin, G. M., & Tanaev, V. S. (1978). Decomposition methods in optimization of design decisions. Minsk: Nauka i Tekhnika (in Russian). Google Scholar
  76. Levin, G. M., & Tanaev, V. S. (1998). Parametric decomposition of optimization problems. Vestsi Akademii Navuk BSSR. Seryya Fizika-Matematychnykh Navuk, 4, 121–131 (in Russian). Google Scholar
  77. Levin, G. M., & Tanaev, V. S. (2002). Extended parametric decomposition of optimization problems: some properties and applications. Iskusstvenny Intellekt, 2, 4–10 (in Russian). Google Scholar
  78. Levin, G. M., Guschinsky, N. N., & Burdo, E. I. (2004). Optimization of transmission parameters of a cascade-reproduction structure. Vestsi NAN of Belarus. Seryya Fizika-Matematychnykh Navuk, 2, 114–120. Google Scholar
  79. Levner, E., Kats, V., & De Pablo, D. A. L. (2007). Cyclic scheduling in robotic cells: an extension of basic models in machine scheduling theory. In E. Levner (Ed.), Multiprocessor scheduling: theory and applications Vienna: Itech Education and Publishing. Google Scholar
  80. Matyushkov, L. P., & Tanaev, V. S. (1967). A program generator for feasible schedules, I. In Computers in engineering (pp. 35–48). Minsk (in Russian). Google Scholar
  81. Matyushkov, L. P., & Tanaev, V. S. (1968). A program generator for feasible schedules, II. In Computers in engineering (pp. 12–28). Minsk (in Russian). Google Scholar
  82. McNaughton, R. (1959). Scheduling with deadlines and loss functions. Management Science, 6(1), 1–12. Google Scholar
  83. Megiddo, N. (1978). Combinatorial optimization with rational objective functions. In Proceedings of the 10th annual ACM symposium on theory of computing (pp. 1–12). San Diego. Google Scholar
  84. Mikhalevich, V. S. (1965a). Sequential algorithms of optimization and their application: I. Kibernetika, 1, 45–66. Google Scholar
  85. Mikhalevich, V. S. (1965b). Sequential algorithms of optimization and their application: II. Kibernetika, 2, 85–89 (in Russian). Google Scholar
  86. Monma, C. L., & Sidney, J. B. (1979). Sequencing with series-parallel precedence constraints. Mathematics of Operations Research, 4, 215–234. Google Scholar
  87. Orlin, J. B., & Ahuja, R. K. (1992). New scaling algorithms for the assignment and minimum mean cycle problems. Mathematical Programming, 54(1–3), 41–56. Google Scholar
  88. Potts, C. N., & Strusevich, V. A. (2009). Fifty years of scheduling: a survey of milestones. The Journal of the Operational Research Society, 60, S41–S68. Google Scholar
  89. Ries, B. (2007). Coloring some classes of mixed graphs. Discrete Applied Mathematics, 155, 1–6. Google Scholar
  90. Ries, B., & de Werra, D. (2008). On two coloring problems in mixed graphs. European Journal of Combinatorics, 29, 712–725. Google Scholar
  91. Romanovskii, I. V. (1964). Asymptotic recursive relations of dynamic programming and optimal stationary control. Doklady Akademii Nauk SSSR, 157(6), 1303–1306 (in Russian). Google Scholar
  92. Romanovskii, I. V. (1967). Optimization of stationary control of a discrete deterministic process. Kibernetika, 3, 66–78 (in Russian). Google Scholar
  93. Rothkopf, M. H. (1966). Scheduling independent tasks on parallel processors. Management Science, 12, 437–447. Google Scholar
  94. Roy, B., & Sussmann, B. (1964). Les problèmes d’ordonnancement avec contraintes disjonctives (Note DS No 9 bis.). SEMA, Montrouge. Google Scholar
  95. Shafransky, Y. M. (1978a). Optimization for deterministic scheduling systems with tree-like partial order. Vestsi Akademii Navuk BSSR. Seryya Fizika-Matematychnykh Navuk, 2, 119 (in Russian). Google Scholar
  96. Shafransky, Y. M. (1978b). On optimal sequencing for deterministic systems with tree-like partial order. Vestsi Akademii Navuk BSSR. Seryya Fizika-Matematychnykh Navuk, 2, 120 (in Russian). Google Scholar
  97. Shafransky, Y. M., & Strusevich, V. A. (1998). The open shop scheduling problem with a given sequence on one machine. Naval Research Logistics, 45, 705–731. Google Scholar
  98. Shakhlevich, N. V. (2005). Open shop unit-time scheduling problems with symmetric objective functions. 4OR, 3, 117–131. Google Scholar
  99. Shakhlevich, N. V., Sotskov, Yu. N., & Werner, F. (1996). Adaptive scheduling algorithm based on the mixed graph model. IEE Proceedings. Control Theory and Applications, 43(1), 9–16. Google Scholar
  100. Smith, W. E. (1956). Various optimizers for single stage production. Naval Research Logistics Quarterly, 3, 59–66. Google Scholar
  101. Sotskov, Yu. N. (1991). Stability of an optimal schedule. European Journal of Operational Research, 55, 91–102. Google Scholar
  102. Sotskov, Yu. N. (1997). Mixed multigraph approach to scheduling jobs on machines of different types. Optimization, 42, 245–280. Google Scholar
  103. Sotskov, Yu. N., & Alyushkevich, V. B. (1988). Stability of optimal orientation of the edges of a mixed graph. Doklady Akademii Nauk BSSR, 32(4), 108–111 (in Russian). Google Scholar
  104. Sotskov, Yu. N., & Shakhlevich, N. V. (1995). NP-hardness of shop-scheduling problems with three jobs. Discrete Applied Mathematics, 59, 237–266. Google Scholar
  105. Sotskov, Yu. N., & Tanaev, V. S. (1974). On enumeration of the circuit-free digraphs generated by a mixed graph. Vestsi Akademii Navuk BSSR, Seryya Fizika-Matematychnykh Navuk, 2, 16–21 (in Russian). Google Scholar
  106. Sotskov, Yu. N., & Tanaev, V. S. (1976a). On one approach to enumeration of the circuit-free digraphs generated by a mixed graph. Vestsi Akademii Navuk BSSR, Seryya Fizika-Matematychnykh Navuk, 5, 99–102 (in Russian). Google Scholar
  107. Sotskov, Yu. N., & Tanaev, V. S. (1976b). A chromatic polynomial of a mixed graph. Vestsi Akademii Navuk BSSR, Seryya Fizika-Matematychnykh Navuk, 6, 20–23 (in Russian). Google Scholar
  108. Sotskov, Yu. N., & Tanaev, V. S. (1989). Construction of a schedule admissible for a mixed multi-graph. Vestsi Akademii Navuk BSSR, Seryya Fizika-Matematychnykh Navuk, 4, 94–98 (in Russian). Google Scholar
  109. Sotskov, Yu. N., & Tanaev, V. S. (1994). Scheduling theory and practice: Minsk group results. Intelligent Systems Engineering, 1, 1–8. Google Scholar
  110. Sotskov, Yu. N., Strusevich, V. A., & Tanaev, V. S. (1994). Mathematical models and methods of production planning. Minsk: Universitetskoe (in Russian). Google Scholar
  111. Sotskov, Yu. N., Leontev, V. K., & Gordeev, E. N. (1995). Some concepts of stability analysis in combinatorial optimization. Discrete Applied Mathematics, 58, 169–190. Google Scholar
  112. Sotskov, Yu. N., Sotskova, N. Yu., & Werner, F. (1997). Stability of an optimal schedule in a job shop. Omega, 25(4), 397–414. Google Scholar
  113. Sotskov, Yu. N., Tanaev, V. S., & Werner, F. (1998a). Stability radius of an optimal schedule: a survey and recent development. In Industrial applications of combinatorial optimization (pp. 72–108). Boston: Kluwer Academic. Google Scholar
  114. Sotskov, Yu. N., Wagelmans, A. P. M., & Werner, F. (1998b). On the calculation of the stability radius of an optimal or an approximate schedule. Annals of Operation Research, 83, 213–252. Google Scholar
  115. Sotskov, Yu. N., Dolgui, A., & Werner, F. (2001). Mixed graph coloring for unit-time job-shop scheduling. International Journal of Mathematical Algorithms, 2, 289–323. Google Scholar
  116. Sotskov, Yu. N., Tanaev, V. S., & Werner, F. (2002). Scheduling problems and mixed graph colorings. Optimization, 51(3), 597–624. Google Scholar
  117. Strusevich, V. A. (1997a). Multi-stage scheduling problems with precedence constraints. In C. Mitchell (Ed.), Applications of combinatorial mathematics (pp. 217–232). London: Oxford University Press. Google Scholar
  118. Strusevich, V. A. (1997b). Shop scheduling problems under precedence constraints. Annals of Operation Research, 69, 351–377. Google Scholar
  119. Suprunenko, D. A., Aizenshtat, V. S., & Metel’sky, A. S. (1962). A multistage technological process. Doklady Akademii Nauk BSSR, 6(9), 541–544 (in Russian). Google Scholar
  120. Tanaev, V. S. (1964a). On a flow shop scheduling problem with one operator. Inzhenerno-Fizicheskij Zhurnal, 3, 111–114 (in Russian). Google Scholar
  121. Tanaev, V. S. (1964b). On a scheduling problem. Vestsi Akademii Navuk BSSR. Seryya Fizika-Matematychnykh Navuk, 4, 128–131 (in Russian). Google Scholar
  122. Tanaev, V. S. (1964c). On scheduling theory. Doklady Akademii Nauk BSSR, 8(12), 792–794 (in Russian). Google Scholar
  123. Tanaev, V. S. (1965). Some objective functions of a single stage production. Doklady Akademii Nauk BSSR, 9(1), 11–14 (in Russian). Google Scholar
  124. Tanaev, V. S. (1967). On the number of permutations of n partially ordered elements. Doklady Akademii Nauk BSSR, 9(3), 208 (in Russian). Google Scholar
  125. Tanaev, V. S. (1968). A method to solve a discrete programming problem. Ekonomika i Matematicheskie Metody, 4(5), 776–782 (in Russian). Google Scholar
  126. Tanaev, V. S. (1973). Preemptions in deterministic scheduling systems with parallel identical machines. Vestsi Akademii Navuk BSSR. Seryya Fizika-Matematychnykh Navuk, 6, 44–48 (in Russian). Google Scholar
  127. Tanaev, V. S. (1975). Mixed (disjunctive) graphs in scheduling problems. In Large systems of information and control (p. 181). Sofia (in Russian). Google Scholar
  128. Tanaev, V. S. (1977a). On optimization of recursive functions on a set of permutations. Vestsi Akademii Navuk BSSR. Seryya Fizika-Matematychnykh Navuk, 3, 27–30 (in Russian). Google Scholar
  129. Tanaev, V. S. (Ed.) (1977b). Program library for solving extremal problems. Issue 1 (p. 1997). Minsk: Institute of Engineering Cybernetics (in Russian). Google Scholar
  130. Tanaev, V. S. (1979a). On optimal partitioning a finite set into subsets. Doklady Akademii Nauk BSSR, 23(1), 26–28 (in Russian). Google Scholar
  131. Tanaev, V. S. (Ed.) (1979b). Program library for solving extremal problems. Issue 2. Minsk: Institute of Engineering Cybernetics (in Russian). Google Scholar
  132. Tanaev, V. S. (Ed.) (1980). Algorithms and programs for solving optimization problems. Minsk: Institute of Engineering Cybernetics (in Russian). Google Scholar
  133. Tanaev, V. S. (Ed.) (1981). Methods and programs for solving extremal problems. Minsk: Institute of Engineering Cybernetics (in Russian). Google Scholar
  134. Tanaev, V. S. (Ed.) (1982). Methods and programs for solving extremal problems and related issues. Minsk: Institute of Engineering Cybernetics (in Russian). Google Scholar
  135. Tanaev, V. S. (Ed.) (1983). Algorithms and programs for solving optimization problems. Minsk: Institute of Engineering Cybernetics (in Russian). Google Scholar
  136. Tanaev, V. S. (Ed.) (1984). Complexity and methods for solving optimization problems. Minsk: Institute of Engineering Cybernetics (in Russian). Google Scholar
  137. Tanaev, V. S. (Ed.) (1985). Methods, algorithms and programs for solving extremal problems. Minsk: Institute of Engineering Cybernetics (in Russian). Google Scholar
  138. Tanaev, V. S. (1987). Decomposition and aggregation in mathematical programming problems. Minsk: Nauka i Technika (in Russian). Google Scholar
  139. Tanaev, V. S. (1988). Scheduling theory. Moscow: Znanie (in Russian). Google Scholar
  140. Tanaev, V. S. (Ed.) (1989). Methods for solving extremal problems. Minsk: Institute of Engineering Cybernetics (in Russian). Google Scholar
  141. Tanaev, V. S. (Ed.) (1990). Methods for solving extremal problems and related issues. Minsk: Institute of Engineering Cybernetics (in Russian). Google Scholar
  142. Tanaev, V. S. (Ed.) (1991). Extremal problems of optimal planning and design. Minsk: Institute of Engineering Cybernetics (in Russian). Google Scholar
  143. Tanaev, V. S. (1992). Symmetric functions in scheduling theory (single machine problems with the same job release dates). Vestsi Akademii Navuk BSSR. Seryya Fizika-Matematychnykh Navuk, 5–6, 97–101 (in Russian). Google Scholar
  144. Tanaev, V. S. (1993). Symmetric functions in scheduling theory (single machine problems with distinct job release dates). Vestsi Akademii Navuk BSSR. Seryya Fizika-Matematychnykh Navuk, 1, 84–87 (in Russian). Google Scholar
  145. Tanaev, V. S., & Gladky, A. A. (1994a). Symmetric functions in scheduling theory (identical machines problems with ordered set of jobs). Vestsi Akademii Navuk BSSR. Seryya Fizika-Matematychnykh Navuk, 4, 81–84 (in Russian). Google Scholar
  146. Tanaev, V. S., & Gladky, A. A. (1994b). Symmetric functions in scheduling theory (parallel machines systems) (Preprint 23). Minsk: Institute of Engineering Cybernetics. Google Scholar
  147. Tanaev, V. S., & Gordon, V. S. (1983). On scheduling to minimize the weighted number of late jobs. Vestsi Akademii Navuk BSSR. Seryya Fizika-Matematychnykh Navuk, 6, 3–9 (in Russian). Google Scholar
  148. Tanaev, V. S., & Levin, G. M. (1967). On optimal behavior of limited memory systems. Vestsi Akademii Navuk BSSR. Seryya Fizika-Matematychnykh Navuk, 3, 82–88 (in Russian). Google Scholar
  149. Tanaev, V. S., & Povarich, M. P. (1974). Synthesis of graph-schemes of decision-making. Minsk: Nauka i Technika. Google Scholar
  150. Tanaev, V. S., & Shkurba, V. V. (1975). Introduction to scheduling theory. Moscow: Nauka (in Russian). Google Scholar
  151. Tanaev, V. S., Gordon, V. S., & Shafransky, Y. M. (1984a). Scheduling theory. Single-stage systems. Moscow: Nauka (in Russian); translated into English by Kluwer Academic Publishers, Dordrecht (1994). Google Scholar
  152. Tanaev, V. S., Levin, G. M., & Sannikova, A. K. (1984b). Program package for multi-step optimization (PP MODA). Minsk: Institute of Engineering Cybernetics. Google Scholar
  153. Tanaev, V. S., Gordon, V. S., Sotskov, Yu. N., Yanova, O. V., Shafransky, Y. M., Gorokh, O. V., & Baranovskaya, S. M. (1986a). A package of applied programs for solving sequencing problems (PAP RUPOR). Minsk: Institute of Engineering (in Russian). Google Scholar
  154. Tanaev, V. S., Levin, G. M., Rozin, B. M., & Sannikova, A. K. (1986b). A dialog system for synthesis of programs of multi-step optimization (MODA-7920). Minsk: Institute of Engineering (in Russian). Google Scholar
  155. Tanaev, V. S., Levin, G. M., Rozin, B. M., & Sannikova, A. K. (1986c). A dialog system for design of programs of multi-step optimization MODA-7906. Upravlyayushchie Sistemy i Machiny, 3, 95–99. Google Scholar
  156. Tanaev, V. S., Gordon, V. S., Sotskov, Yu. N., Yanova, O. V., Shafransky, Y. M., Gorokh, O. V., & Baranovskaya, S. M. (1987). A package of applied programs for solving sequencing problems (PAP RUPOR). Programs description. Minsk: Institute of Engineering (in Russian). Google Scholar
  157. Tanaev, V. S., Gordon, V. S., Sotskov, Yu. N., & Yanova, O. V. (1989a). A program package for solving scheduling theory problems. Upravlyayuschie Sistemy i Machiny, 4, 107–111 (in Russian). Google Scholar
  158. Tanaev, V. S., Sotskov, Yu. N., & Strusevich, V. A. (1989b). Scheduling theory. Multi-stage systems. Moscow: Nauka (in Russian); translated into English by Kluwer Academic Publishers, Dordrecht (1994). Google Scholar
  159. Tanaev, V. S., Kovalyov, M. Y., & Shafransky, Y. M. (1998). Scheduling theory. Group technologies. Minsk: Institute of Engineering (in Russian). Google Scholar
  160. Tuzikov, A. V., & Shafransky, Y. M. (1983). On problems of lexicographic minimization on a set of permutations. Vestsi Akademii Navuk BSSR, Seryya Fizika-Matematychnykh Navuk, 6, 115 (in Russian). Google Scholar
  161. Verina, L. F. (1985). Solution of some non-convex problems by reduction to convex mathematical programming. Vestsi Akademii Navuk BSSR. Seryya Fizika-Matematychnykh Navuk, 1, 13–18 (in Russian). Google Scholar
  162. Verina, L. F., & Levin, G. M. (1991). On a problem of optimization of a transfer function of network elements and its application to transmission design. Vestsi Akademii Navuk BSSR. Seryya Fizika-Matematychnykh Navuk, 2, 28–32 (in Russian). Google Scholar
  163. Verina, L. F., Levin, G. M., & Tanaev, V. S. (1988). Parametric decomposition of extremal problems—a general approach and some applications. Soviet Journal of Computer and Systems Sciences, 26(4), 137–148 (translated from Russian, Izvestiya AN SSSR. Seria Tekhnicheskaya Kibernetika). Google Scholar
  164. Verina, L. F., Levin, G. M., & Tanaev, V. S. (1995). Towards the theory of parametric decomposition and immersion of extremum problems. Doklady Akademii Nauk BSSR, 39(4), 9–12 (in Russian). Google Scholar
  165. Young, N. E., Tarjan, R. E., & Orlin, J. B. (1991). Faster parametric shortest path and minimum-balance algorithms. Networks, 21(2), 205–221. Google Scholar
  166. Zinder, Y. A. (1976). The priority solvability of a class of scheduling problems. In Problems of design of automated systems of production control (pp. 56–63). Kiev (in Russian). Google Scholar

Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  • V. S. Gordon
    • 1
  • M. Y. Kovalyov
    • 1
  • G. M. Levin
    • 1
  • Y. M. Shafransky
    • 1
  • Y. N. Sotskov
    • 1
  • V. A. Strusevich
    • 2
  • A. V. Tuzikov
    • 1
  1. 1.United Institute of Informatics ProblemsNational Academy of Sciences of BelarusMinskBelarus
  2. 2.School of Computing and Mathematical SciencesUniversity of GreenwichLondonUK

Personalised recommendations