Abstract
In this paper, we introduce the concept of “workload fence" into online machine rental and machine scheduling problems. With the knowledge of workload fence, online algorithms acquire the information of a finite number of first released jobs in advance. The concept originates from the frozen time fence in the domain of master scheduling in materials management. The total processing time of the jobs foreseen, corresponding to a finite number of jobs, is called workload fence, which is irrelevant to the job sequence. The remaining jobs in the sequence, however, can only become known on their arrival. This work aims to reveal whether the knowledge of workload fence helps to boost the competitive performance of deterministic online algorithms. For the online machine rental problem, we prove that the competitiveness of online algorithms can be improved with a sufficiently large workload fence. We further propose a best online algorithm for the corresponding scenario. For online parallel machine scheduling with workload fence, we give a positive answer to the above question for the case where the workload fence is equal to the length of the longest job. We also show that the competitiveness of online algorithms may not be improved even with a workload fence strictly larger than the largest length of a job. The results help one manager to make a better decision regarding the tradeoff between the performance improvement of online algorithms and the cost caused to acquire the knowledge of workload fence.
Similar content being viewed by others
Data Availability
No datasets were generated or analysed during the current study.
References
Albers S, Hellwig M (2012) Semi-online scheduling revisited. Theoret Comput Sci 443:1–9
Albers S, Hellwig M (2017) Online makespan minimization with parallel schedules. Algorithmica 78(2):492–520
Arnold TJR, Chapman SN, Clive LM (2012) Introduction to materials management, 7th edn. Prentice Hall
Angelelli E, Nagy ÁB, Speranza MG, Tuza Z (2007) Semi-online scheduling on three processors with known sum of the tasks. J Sched 10(4):263–269
Chai X, Li W (2018) Online scheduling with chain precedence constraints of equal-length jobs on parallel machines to minimize makespan. J Comb Optim 36(2):472–492
Chen C, Zhang HL, Xu YF (2020) Online machine minimization with lookahead. J Comb Optim. https://doi.org/10.1007/s10878-020-00633-w
Cheng TCE, Kellerer H, Kotov V (2005) Semi-on-line multiprocessor scheduling with given total processing time. Theoret Comput Sci 337:134–146
Dösa G, He Y (2004) Better online algorithms for scheduling with machine cost. SIAM J Comput 33(5):1035–1051
Dösa G, Tan ZY (2010) New upper and lower bound for online scheduling with machine cost. Discret Optim 7:125–135
Dösa G, Fuegenschuh A, Tan ZY, Tuza Z, Weske K (2019) Tight upper bounds for semi-online scheduling on two uniform machines with known optimum. CEJOR 27:1107–1130
Dunke F, Nickel S (2016) A general modeling approach to online optimization with lookahead. Omega 63:134–153
Dwibedy D, Mohanty R (2022) Semi-online scheduling: A survey. Comput. Oper. Res. 139:105646
Englert M, Oezmen D, Westermann M (2014) The power of reordering for online minimum makespan scheduling. SIAM J Comput 43(3):1220–1237
Englert M, Mezlaf D, Westermann M (2021) Online makespan scheduling with job migration on uniform machines. Algorithmica 83:3537–3566
Epstein L (2018) A survey on makespan minimization in semi-online environments. J Sched 21(3):269–284
Feigle U, Kern W, Turan G (1989) On the performance of on-line algorithms for partition problems. Acta Cybernet 9(2):107–119
Fung SPY, Poon CK, Zheng FF (2014) Improved randomized online scheduling of intervals and jobs. Theory Comput Syst 55(1):202–228
Graham RL (1966) Bounds for certain multiprocessing anomalies. Bell Syst Tech J 45:1563–1581
Guo S, Ma R, Zhang Y, Fan B (2021) A semi-online algorithm for single machine scheduling with rejection. Asia-Pacific J Oper Res 38(5):2140003
Hall NG, Posner ME, Potts CN (2021) Online production planning to maximize the number of on-time orders. Ann Oper Res 298(1):249–269
Imreh C (2006) Online scheduling with general machine cost functions. Electr Notes Discrete Math 157(9):2070–2077
Jiao CW, Feng Q (2021) Research on the parallel-batch scheduling with linearly lookahead model. J Ind Manag Optim 17(6):3551–3558
Jiao CW, Yuan JJ, Feng Q (2019) Online algorithms for scheduling unit length jobs on unbounded parallel-batch machines with linearly lookahead. Asia-Pacific J Oper Res 36(5):1950024
Karlin AR, Manasse MS, Rudolph L, Sleator DD (1988) Competitive snoopy caching. Algorithmica 3(1–4):79–119
Kellerer H, Kotov V, Gabay M (2015) An efficient algorithm for semi-online multiprocessor scheduling with given total processing time. J Sched 18(6):623–630
Khanafer A, Kodialam M, Puttaswamy KPN, (2013) The constrained Ski-Rental problem and its application to online cloud cost optimization. (2013) IEEE INFOCOM, 14–19 April 2013. Italy, Turin, pp 1492–1500
Lee K, Leung JYT, Pinedo ML (2013) Makespan minimization in online scheduling with machine eligibility. Ann Oper Res 204(1):189–222
Li WH, Yuan JJ, Yang SF (2014) Online scheduling of incompatible unit-length job families with lookahead. Theoret Comput Sci 543:120–125
Li WH, Yuan JJ (2015) An improved online algorithm for the online preemptive scheduling of equal-length intervals on a single machine with lookahead. Asia-Pacific J Oper Res 32(6):1–9
Lucarelli G, Thang NK, Srivastav A, Trystram D (2016) Online non-preemptive scheduling in a resource augmentation model based on duality. 24th Annual European Symposium on Algorithms (ESA 2016), 22-24 Aug 2016, Aarhus, Denmark, 17 pages
Mandelbaum M, Shabtay D (2011) Scheduling unit length jobs on parallel machines with lookahead information. J Sched 14:335–350
Nagy-Gyögy J, Imreh C (2007) Online scheduling with machine cost and rejection. Discret Appl Math 155(18):2546–2554
Pinson N, Spieksma FCR (2019) Online interval scheduling on two related machines: the power of lookahead. J Comb Optim 38(1):224–253
Ruiz-Torres AJ, López FJ, Wojciechowski PJ, Ho CJ (2010) Parallel machine scheduling problems considering regular measures of performance and machine cost. J Oper Res Soci 61(5):849–857
Shah A, Rajkumar A (2021) Sequential ski rental problem. 20th International Conference on Autonomous Agents and Multiagent Systems (AAMAS 2021), 3-7 May 2021, London, UK, 10 pages
Tan ZY, Zhang A (2013). Online and semi-online scheduling. In Pardalos P, Du DZ, Graham R (eds) Handbook of Combinatorial Optimization, Springer, New York, NY, https://doi.org/10.1007/978-1-4419-7997-1_2
Wang SF, Li J, Wang SQ (2020) Online algorithms for multi-shop ski renal with machine learned advice. 34th Conference on Neural Information Processing Systems (NeurIPS 2020) 6-12 Dec 2020, Vancouver, Canada, 11 pages
Wu BH, Bao W, Yuan D (2021) Competitive analysis for two-level ski-rental problem. 35th AAAI Conference on Artificial Intelligence (AAAI 2021) 2-9 Feb 2021, Online, pp. 12034-12041
Xu ZZ, Chen X, Xu XJ, Zhao XW, Dai J, Jia MF (2017) A look-ahead algorithm for online multiple workflow scheduling problem in heterogeneous systems. Concurr Eng Res Appl 25(4):331–342
Zhang XY, Ma R, Sun J, Zhang ZB (2020) Randomized selection algorithm for online stochastic unrelated machines scheduling. J Comb Optim. https://doi.org/10.1007/s10878-020-00542-y
Zheng FF, Cheng YC, Liu M, Xu YF (2013) Online interval scheduling on a single machine with finite lookahead. Comput Oper Res 40(1):180–191
Funding
This paper was supported by the National Natural Science Foundation of China (71771048, 71832001, and 72071144) and the Fundamental Research Funds for the Central Universities (2232018H-07).
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of interest
The authors have no relevant financial or non-financial interests to disclose.
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Zheng, F., Chen, Y., Liu, M. et al. Competitive analysis of online machine rental and online parallel machine scheduling problems with workload fence. J Comb Optim 44, 1060–1076 (2022). https://doi.org/10.1007/s10878-022-00882-x
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10878-022-00882-x