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Scheduling problems with partially ordered jobs

  • Scheduling Problems on a Single Machine
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Abstract

Scheduling problems with given precedence constraints (with partially ordered jobs) are considered. A review of the results obtained in this area by the members of Minsk Scheduling Theory school created by V.S. Tanaev is done.

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References

  1. Tanaev, V.S. and Shkurba, V.V., Vvedenie v teoriyu raspisanii (Introduction to the Scheduling Theory), Moscow: Nauka, 1975.

    Google Scholar 

  2. Tanaev, V.S., Gordon, V.S., and Shafransky, Ya.M., Teoriya raspisanii. Odnostadiinye sistemy (Scheduling Theory. Single-stage Systems) Moscow: Nauka, 1984.

    Google Scholar 

  3. Tanaev, V.S., Gordon, V.S., and Shafransky, Y.M., Scheduling Theory. Single-Stage Systems, Dordrecht: Kluwer, 1994.

    MATH  Google Scholar 

  4. Handbook of Scheduling: Algorithms, Models and Performance Analysis, Leung, J.Y.-T., Ed., Boca Raton: CRC Press, 2004.

    MATH  Google Scholar 

  5. Lawler, E.L., Lenstra, J.K., Rinnooy Kan, A.H.G., and Shmoys, D.B., Sequencing and Scheduling: Algorithms and Complexity, in Handbooks in Operations Research and Management Science, Vol. 4, Logistics of Production and Inventory, Graves, S.C., Rinnooy Kan, A.H.G., and Zipkin, P.H., Eds., Amsterdam: North-Holland, 1993, pp. 445–522.

    Google Scholar 

  6. Chen, B., Potts, C.N., and Woeginger, G.J., A Review on Machine Scheduling: Complexity, Algorithms and Approximability, in Handbook of Combinatorial Optimization, Du, D.-Z. and Pardalos, P.M., Eds., Dordrecht: Kluwer, 1998, pp. 21–169.

    Google Scholar 

  7. Lawler, E.L., Optimal Sequencing of a Single Machine Subject to Precedence Constraints, Manage. Sci., 1973, vol. 19, pp. 544–546.

    Article  MATH  Google Scholar 

  8. Lenstra, J.K., Rinnooy Kan, A.H.G., and Brucker, P., Complexity of Machine Scheduling Problems, Ann. Discrete Math., 1977, vol. 1, pp. 343–362.

    Article  MathSciNet  Google Scholar 

  9. Gordon, V.S., Deterministic Servicing System with Minimax Optimality Criterion and Partially Ordered Set of Requests, Avtomat. Tekhn. Podgotovki Proizvodstva, 1977, vol. 4, pp. 70–75.

    Google Scholar 

  10. Gordon, V.S. and Tanaev, V.S., On the Minimax Scheduling Theory Problems with Single Machine, Izv. Akad. Nauk BSSR, Ser. Fiz.-Mat. Nauk, 1983, no. 3, pp. 3–9.

  11. Baker, K.R., Lawler, E.L., Lenstra, J.K., and Rinnooy Kan, A.H.G., Preemptive Scheduling of a Single Machine to Minimize Maximum Cost Subject to Release Dates and Precedence Constraints, Oper. Res., 1983, vol. 31, pp. 381–386.

    Article  Google Scholar 

  12. Gordon, V.S., Parallel Algorithm of Minimization of the Maximal Penalty for Request Servicing by a Single Machine, Izv. Ross. Akad. Nauk, Tekh. Kibern., 1989, no. 3, pp. 181–186.

  13. Gordon, V.S., Parallel Algorithms to Solve the Scheduling Theory Problems, Autom. Remote Control, 1992, no. 5, pp. 97–106.

  14. Shafransky, Ya.M., Optimization of Deterministic Systems of Servicing with Tree-like Partial Order, Izv. Akad. Nauk BSSR, Ser. Fiz.-mat. Nauk, 1978, no. 2, pp. 119.

  15. Tanaev, V.S., Some Optimizable Functions of Single-stage Production, Dokl. Akad. Nauk BSSR, 1965, vol. 9, no. 1, pp. 11–14.

    MathSciNet  Google Scholar 

  16. Tanaev, V.S., On the Scheduling Theory, Dokl. Akad. Nauk BSSR, 1964, vol. 8, no. 12, pp. 792–794.

    MATH  MathSciNet  Google Scholar 

  17. Gordon, V.S. and Tanaev, V.S., Deterministic Systems of Servicing with Single Machine, Tree-like Request Ordering, and Exponential Penalty Functions, in Vychisl. Tekhnika v Mashinostroenii, Minsk: Inst. Tekhn. Kibern. Akad. Nauk BSSR, 1973, pp. 3–10.

    Google Scholar 

  18. Shafransky, Ya.M., On Optimal Ordering in Deterministic Systems with Tree-like Partial Order of Servicing, Izv. Akad. Nauk BSSR, Ser. Fiz.-Mat. Nauk, 1978, no. 2, p. 120.

  19. Gordon, V.S. and Shafransky, Ya.M., Decomposition Approach to Function Minimization on the Set of Permutations of Partially Ordered Elements, in Proc. V All-Union Seminar on Control of Large Systems, Alma-Ata, 1978, pp. 51–56.

  20. Gordon, V.S. and Shafransky, Ya.M., On Optimal Ordering under Series-Parallel Precedence Constraints, Izv. Akad. Nauk BSSR, Ser. Fiz.-Mat. Nauk, 1978, no. 5, p. 135.

  21. Monma, C.L. and Sidney, J.B., Sequencing with Series-Parallel Precedence Constraints, Math. Oper. Res., 1979, vol. 4, pp. 215–234.

    Article  MATH  MathSciNet  Google Scholar 

  22. Lawler, E.L., Sequencing Jobs to Minimize Total Weighted Completion Time Subject to Precedence Constraints, Ann. Discret. Math., 1978, vol. 2, pp. 75–90.

    Article  MATH  MathSciNet  Google Scholar 

  23. Gordon, V.S. and Shafransky, Ya.M., Optimal Ordering for Series-Parallel Precedence Constraints, Dokl. Akad. Nauk BSSR, 1978, vol. 22, no. 3, pp. 244–247.

    MATH  MathSciNet  Google Scholar 

  24. Shafransky, Ya.M., On Minimization of Functions on the Set of Permutations of Partially Ordered Elements. I, II, Izv. Akad. Nauk BSSR, Ser. Fiz.-mat. Nauk, 1980, no. 5, p. 132; 1982, no. 1, p. 113.

  25. Shafransky, Ya.M., On One Property of the Priority-generating Functions, Izv. Akad. Nauk BSSR, Ser. Fiz.-Mat. Nauk, 1981, no. 6, pp. 15–18.

  26. Shafransky, Ya.M., On the Algorithm to Determine the Minimum of the Priority-generating Functions on Special Sets of Permutations. I, II, Izv. Akad. Nauk BSSR, Ser. Fiz.-mat. Nauk, 1982, no. 3, pp. 38–42; 1983, no. 1, pp. 15–20.

  27. Kovalyov, M.Ya., Domain of Convergence of One Algorithm of Minimization of the Priority-generating Functionals, in Algoritmy i programmy resheniya zadach optimizatsii (Algorithms and Programs to Solve Optimization Problems), Minsk: Inst. Tekhn. Kibern. Akad. Nauk BSSR, 1983, pp. 21–35.

    Google Scholar 

  28. Shafransky, Y.M. and Tuzikov, A.V., Construction of All Optimal Permutations under Precedence Constraints, Tr. Inst. Mat. NAN Belarus., Diskret. Mat., 2001, vol. 8, pp. 106–113.

    Google Scholar 

  29. Janiak, A., Shafransky, Y.M., and Tuzikov, A.V., Sequencing with Ordered Criteria, Precedence and Group Technology Constraints, Informatica, 2001, vol. 12, pp. 61–88.

    MATH  MathSciNet  Google Scholar 

  30. Gordon, V.S., Minimization of Cost Related with Variable Deadlines in the Problem of the Scheduling Theory with One Machine, Autom. Remote Control, 1992, no. 2, pp. 105–112.

  31. Gordon, V.S., A Note on Optimal Assignment of Slack Due-Dates in Single-Machine Scheduling, Eur. J. Oper. Res., 1993, vol. 70, pp. 311–315.

    Article  MATH  Google Scholar 

  32. Cheng, T.C.E. and Gordon, V.S., Optimal Assignment of Due-dates for Preemptive Single-machine Scheduling, Math. Comput. Modeling, 1994, vol. 20, pp. 33–40.

    Article  Google Scholar 

  33. Gordon, V.S. and Strusevich, V.A., Earliness Penalties on a Single Machine Subject to Precedence Constraints: SLK Due Date Assignment, Comput. Oper. Res., 1999, vol. 26, pp. 157–177.

    Article  MATH  MathSciNet  Google Scholar 

  34. Gordon, V.S., Proth, J.-M., and Strusevich, V., Single Machine Scheduling with Precedence Constraints and SLK Due Date Assignment, Oper. Res. Proc. 2003, Heidelberg: Springer, 2004, pp. 157–163.

    Google Scholar 

  35. Gordon, V.S., Proth, J.-M., and Strusevich, V., Single Machine Scheduling and Due Date Assignment under Series-Parallel Precedence Constraints, Central Eur. J. Oper. Res., 2005, vol. 13, no. 1, pp. 15–35.

    MATH  MathSciNet  Google Scholar 

  36. Monma, C.L. and Sidney, J.B., Optimal Sequencing via Modular Decomposition: Characterization of Sequencing Functions, Math. Oper. Res., 1987, vol. 12, pp. 22–31.

    Article  MATH  MathSciNet  Google Scholar 

  37. Sidney, J.B. and Steiner, G., Optimal Sequencing by Modular Decomposition: Polynomial Algorithms, Oper. Res., 1986, vol. 34, pp. 606–612.

    Article  MATH  MathSciNet  Google Scholar 

  38. Gordon, V.S., Proth, J.-M., and Chu, C., A Survey of the State-of-the-art of Common Due Date Assignment and Scheduling, Eur. J. Oper. Res., 2002, vol. 139, pp. 1–25.

    Article  MATH  MathSciNet  Google Scholar 

  39. Gordon, V.S., Proth, J.-M., and Chu, C., Due Date Assignment And Scheduling: SLK, TWK and Other Due Date Assignment Models, Product. Plan. Control, 2002, vol. 13, pp. 117–132.

    Article  Google Scholar 

  40. Gordon, V., Proth, J.-M., and Strusevich, V., Scheduling with Due Date Assignment, in Handbook of Scheduling: Algorithms, Models and Performance Analysis, Leung, J.Y.-T., Ed., Boca Raton: CRC Press, 2004, pp. 1–22.

    Google Scholar 

  41. Gordon, V.S., Smotryaev, V.N., and Tarasevich, A.A., Construction of Optimal Schedules at Assigning the Due Dates, Informatika, 2004, no. 1, pp. 17–27.

  42. Mel’nikov, O.I. and Shafransky, Ya.M., Parametric Scheduling Theory, Kibernetika, 1979, no. 6, pp. 53–57.

  43. Janiak, A. and Kovalyov, M.Y., Scheduling in a Contaminated Area: A Model and Polynomial Algorithms, Eur. J. Oper. Res., 2006, vol. 173, pp. 125–132.

    Article  MATH  MathSciNet  Google Scholar 

  44. Gordon, V.S., Potts, C.N., Strusevich, V.A., and Whitehead, J.D., Single Machine Scheduling Models with Deterioration and Learning: Handling Precedence Constraints Via Priority Generation, J. Scheduling, 2008, vol. 11, pp. 357–370.

    Article  MATH  MathSciNet  Google Scholar 

  45. Wang, J.-B., Ng, C.T., and Cheng, T.C.E., Single-machine Scheduling with Deteriorating Jobs under a Series-Parallel Graph Constraint, Comput. Oper. Res., 2008, vol. 35, pp. 2684–2693.

    Article  MATH  MathSciNet  Google Scholar 

  46. Gordon, V. and Tanaev, V., Scheduling Decisions for the Systems with Deadlines, in IFAC IFIP / IEEE 2nd Conf. MCPL’2000, Grenoble, 2000, London: Pergamon, 2001, vol. 2, pp. 687–690.

    Google Scholar 

  47. Gordon, V., Finke, G., and Proth, J.-M., Scheduling with Due Dates and Deadlines, in Proc. 2002 IEEE Int. Sympos. Industr. Electron., L’Aquila, 2002, vol. 1, pp. 223–227.

    Google Scholar 

  48. Gordon, V., Proth, J.-M., and Strusevich, V., Single Machine Scheduling under Precedence Constraints and Due Date Assignment, in Proc. 9 Int. Workshop Project Management Sched., Nancy, 2004, pp. 132–134.

  49. Gordon, V., Proth, J.-M., and Strusevich, V., Scheduling and Due Date Assignment Problems of Minimizing Earliness Penalties under Precedence Constraints, in Proc. 7th Workshop Model. Algorithm. Planning Sched. Probl., Siena, 2005, pp. 148–150.

  50. Gordon, V., Dolgui, A., and Strusevich, V., Due Date Assignment and Scheduling under Special Conditions on Job Processing, Preprints 13th IFAC Sympos. Inform. Control Probl. Manufacturing, Moscow, 2009, pp. 520–525.

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Original Russian Text © V.S. Gordon, A.B. Dolgui, 2010, published in Avtomatika i Telemekhanika, 2010, No. 10, pp. 15–25.

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Gordon, V.S., Dolgui, A.B. Scheduling problems with partially ordered jobs. Autom Remote Control 71, 2029–2037 (2010). https://doi.org/10.1134/S0005117910100036

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