Two-phase branch and bound algorithm for robotic cells rescheduling considering limited disturbance. (English) Zbl 1348.90331

Summary: This paper addresses a robotic cell rescheduling problem and focuses on trade-off between the total completion time of all jobs and the disturbance of a reschedule. We first define and measure the disturbance of a reschedule as the deviation of completion time of the jobs already scheduled between the reschedule and the initial schedule. To guarantee the steady performance of the system, we consider a special case that the processing sequence of the jobs already scheduled cannot be changed. The addressed rescheduling problem is transformed into a series of deterministic local scheduling problems with the objective of minimizing the total completion time of all jobs provided that the disturbance is within a given limit. A two-phase branch and bound algorithm is developed to efficiently solve the local scheduling problems. To improve the efficiency of the search procedure, a dynamic enumeration mechanism is applied to eliminate redundant constraints. Furthermore, two search strategies are proposed to direct the search procedure toward finding an optimal solution and a near-optimal solution. Finally, computational results demonstrate the efficiency of our algorithm.


90B35 Deterministic scheduling theory in operations research
68T40 Artificial intelligence for robotics
90C57 Polyhedral combinatorics, branch-and-bound, branch-and-cut
Full Text: DOI


[1] Levner, E.; Kats, V.; ALP, D.; Cheng, TCE., Complexity of cyclic scheduling problems: a state-of-the-art survey, Comput Ind Eng, 59, 2, 352-361 (2010)
[2] Levner, E.; Kats, V.; Levit, V. E., An improved algorithm for cyclic flowshop scheduling in a robotic cell, Eur J Oper Res, 97, 3, 500-508 (1997) · Zbl 0919.90088
[3] Levner, E.; Kogan, K.; Levin, I., Scheduling a two-machine robotic cell: a solvable case, Ann Oper Res, 57, 1, 217-232 (1995) · Zbl 0831.90075
[4] Kogan, K.; Levner, E., A polynomial algorithm for scheduling small-scale manufacturing cells served by multiple robots, Comput Oper Res, 25, 1, 53-62 (1998) · Zbl 0907.90183
[5] Kats, V.; Levner, E., A faster algorithm for 2-cyclic robotic scheduling with a fixed robot route and interval processing times, Eur J Oper Res, 209, 1, 51-56 (2011) · Zbl 1208.90067
[6] Kats, V.; Levner, E., A strongly polynomial algorithm for no-wait cyclic robotic flowshop scheduling, Oper Res Lett, 21, 4, 171-179 (1997) · Zbl 0892.90101
[7] Kats, V.; Levner, E., Minimizing the number of robots to meet a given cyclic schedule, Ann Oper Res, 69, 209-226 (1997) · Zbl 0880.90075
[8] Yih, Y., Algorithm for hoist scheduling problems, Int J Prod Res, 32, 3, 501-516 (1994) · Zbl 0903.90095
[9] Chen, H.; Chu, C.; Proth, J. M., Cyclic scheduling of a hoist with time window constraints, IEEE Trans Robot Autom, 14, 1, 144-152 (1998)
[10] Chauvet, F.; Levner, E.; Meyzin, L. K.; Proth, J-M., On-line scheduling in a surface treatment system, Eur J Oper Res, 120, 2, 382-392 (2000) · Zbl 0949.90038
[11] Akturk, M. S.; Gorgulu, E., Match-up scheduling under a machine breakdown, Eur J Oper Res, 112, 1, 81-97 (1999) · Zbl 0937.90029
[12] Hall, N. G.; Potts, C. N., Rescheduling for new orders, Oper Res, 52, 3, 440-453 (2004) · Zbl 1165.90456
[13] Hall, N. G.; Potts, C. N., Rescheduling for job unavailability, Oper Res, 58, 3, 746-755 (2010) · Zbl 1231.90196
[14] Qi, X.; Bard, J. F.; Yu, G., Disruption management for machine scheduling: the case of SPT schedules, Int J Prod Econ, 103, 1, 166-184 (2006)
[15] Ballestin, F.; Leus, R., Meta-heuristics for stable scheduling on a single machine, Comput Oper Res, 35, 7, 2175-2192 (2008) · Zbl 1177.90142
[16] Yildiz, S.; Karasan, O. E.; Akturk, M. S., An analysis of cyclic scheduling problems in robot centered cells, Comput Oper Res, 39, 6, 1290-1299 (2012) · Zbl 1251.90205
[17] Fazel Zarandi, M. H.; Mosadegh, H.; Fattahi, M., Two-machine robotic cell scheduling problem with sequence-dependent setup times, Comput Oper Res, 40, 5, 1420-1434 (2012) · Zbl 1352.90037
[18] Che, A.; Hu, H.; Chabrol, M.; Gourgand, M., A polynomial algorithm for multi-robot 2-cyclic scheduling in a no-wait robotic cell, Comput Oper Res, 38, 9, 1275-1285 (2011) · Zbl 1208.90056
[19] Brauner, N., Identical part production in cyclic robotic cells: concepts, overview and open questions, Discrete Appl Math, 156, 13, 2480-2492 (2008) · Zbl 1152.90429
[20] Alcaide, D.; Chu, C.; Kats, V.; Levner, E.; Sierksma, G., Cyclic multiple-robot scheduling with time-window constraints using a critical path approach, Eur J Oper Res, 177, 1, 147-162 (2007) · Zbl 1111.90033
[21] Paul, H. J.; Bierwirth, C.; Kopfer, H., A heuristic scheduling procedure for multi-item hoist production lines, Int J Prod Econ, 105, 1, 54-69 (2007)
[22] Lei, L.; Liu, Q., Optimal cyclic scheduling of a robotic processing line with two-product and time-window constraints, INFOR, 39, 2, 185-199 (2001) · Zbl 1518.90026
[24] Zhou, Z.; Che, A.; Yan, P., A mixed integer programming approach for multi-cyclic robotic flowshop scheduling with time window constraints, Appl Math Modell., 36, 8, 3621-3629 (2012) · Zbl 1252.90029
[25] Leung, J. M.Y.; Zhang, G.; Yang, X.; Mak, R.; Lam, K., Optimal cyclic multi-hoist scheduling: a mixed integer programming approach, Oper Res, 52, 6, 965-976 (2004) · Zbl 1165.90460
[26] Liu, J.; Jiang, Y.; Zhou, Z., Cyclic scheduling of a single hoist in extended electroplating lines: a comprehensive integer programming solution, IIE Trans (Inst Ind Eng), 34, 10, 905-914 (2002)
[27] Phillips, L. W.; Unger, P. S., Mathematical programming solution of a hoist scheduling program, AIIE Trans, 8, 2, 219-225 (1976)
[28] Che, A.; Chu, C., Cyclic hoist scheduling in large real-life electroplating lines, OR Spectrum, 29, 3, 445-470 (2007) · Zbl 1173.90400
[29] Che, A.; Zhou, Z.; Chu, C.; Chen, H., Multi-degree cyclic hoist scheduling with time window constraints, Int J Pro Res, 49, 19, 5679-5693 (2011)
[30] Lei, L.; Wang, T. J., Determining optimal cyclic hoist schedules in a single-hoist electroplating line, IIE Trans (Inst Ind Eng), 26, 2, 25-33 (1994)
[31] Ng, W. C., A branch and bound algorithm for hoist scheduling of a circuit board production line, Int J Flex Manuf Syst, 8, 1, 45-65 (1996)
[32] Sharpiro, G. W.; Nuttle, H. L., Hoist scheduling for a PCB electroplating facility, IIE Trans Inst Ind Eng, 20, 2, 157-167 (1988)
[33] Brauner, N.; Finke, G.; Lehoux-Lebacque, V.; Potts, C.; Whitehead, J., Scheduling of coupled tasks and one-machine no-wait robotic cells, Comput Oper Res, 36, 2, 301-307 (2009) · Zbl 1157.90406
[34] Crama, Y.; Van De Klundert, J., Cyclic scheduling of identical parts in a robotic cell, Oper Res, 45, 6, 952-965 (1997) · Zbl 0895.90113
[35] Hall, N. G.; Kamoun, H.; Sriskandarajah, C., Scheduling in robotic cells: complexity and steady state analysis, Eur J Oper Res, 109, 1, 43-65 (1998) · Zbl 0949.90041
[36] Dawande, M.; Geismar, H. N.; Sethi, S. P.; Sriskandarajah, C., Sequencing and scheduling in robotic cells: recent developments, J Scheduling, 8, 5, 387-426 (2005) · Zbl 1123.90020
[37] Manier, M. A.; Bloch, C., A classification for hoist scheduling problems, Int J Flex Manuf Syst, 15, 1, 37-55 (2003)
[38] Bean, J. C.; Birge, J. R.; Mittenthal, J.; Noon, C. E., Matchup scheduling with multiple resources, release dates and disruptions, Oper Res, 39, 3, 470-483 (1991) · Zbl 0742.90041
[39] Akturk, M.; Atamtuk, A.; Gurel, S., Parallel machine match-up scheduling with manufacturing cost considerations, J Sched, 13, 1, 95-110 (2010) · Zbl 1185.90064
[40] Wu, S. D.; Storer, R. H.; Pei-Chann, C., One-machine rescheduling heuristics with efficiency and stability as criteria, Comput Oper Res, 20, 1, 1-14 (1993) · Zbl 0759.90049
[41] Unal, A. T.; Uzsoy, R.; Kiran, A., Rescheduling on a single machine with part-type dependent setup times and deadlines, Ann Oper Res, 70, 0, 93-113 (1997) · Zbl 0889.90092
[43] Zhao, C.; Fu, J.; Xu, Q., Real-time dynamic hoist scheduling for multistage material handling process under uncertainties, AIChE J, 59, 2, 465-482 (2012)
[44] Escudero, L. F.; Guignard, M.; Malik, K., A Lagrangian relax-and-cut approach for the sequential ordering problem with precedence relationships, Ann Oper Res, 50, 1, 219-237 (1994) · Zbl 0833.90068
[45] Gambardella, L. M.; Dorigo, M., An ant colony system hybridized with a new local search for the sequential ordering problem, INFORMS J Computing, 12, 3, 237-255 (2000) · Zbl 1040.90570
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