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Scheduling two groups of jobs with incomplete information

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Abstract

In real world situations, most scheduling problems occur neither as complete off-line nor as complete on-line models. Most likely, a problem arises as an on-line model with some partial information. In this article, we consider such a model. We study the scheduling problem P(n 1,n 2), where two groups of jobs are to be scheduled. The first job group is available beforehand. As soon as all jobs in the first group are assigned, the second job group appears. The objective is to minimize the longest job completion time (makespan). We show a lower bound of 3/2 even for very special cases. Best possible algorithms are presented for a number of cases. Furthermore, a heuristic is proposed for the general case. The main contribution of this paper is to discuss the impact of the quantity of available information in designing an on-line algorithm. It is interesting to note that the absence of even a little bit information may significantly affect the performance of an algorithm.

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Author notes

  1. C. K. Wong

    Present address: On Watson Research Center, Yorktown Heights, NY, 10598, USA

Authors and Affiliations

  1. Department of Mathematics, Zhejiang University, Hangzhou, 310027, P.R. China

    Guochuan Zhang

  2. Department of Systems Engineering and Engineering Management, The Chinese University of Hong Kong, Shatin N.T., Hong Kong, China

    Xiaoqiang Cai

  3. Department of Computer Science and Engineering, The Chinese University of Hong Kong, Shatin N.T., Hong Kong, China

    C. K. Wong

Authors
  1. Guochuan Zhang
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  2. Xiaoqiang Cai
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  3. C. K. Wong
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Additional information

Research partially supported by a Hong Kong Government RGC Earmarked Grant. Ref. No. CUHK356/96E Part of this work was done while visiting The Chinese University of Hong Kong. Research partially supported by National 973 Fundamental Research Project of China and National Natural Science Foundation of China (19801032)

Part of this work was done while visiting The Chinese University of Hong Kong. Research partially supported by National 973 Fundamental Research Project of China and National Natural Science Foundation of China (19801032)

On leave from IBM T.J. Watson Research Center, Yorktown Heights, NY 10598, U.S.A

Guochuan Zhang is Professor of Department of Mathematics, Zhejiang University, China. He received his Ph.D. in Operations Research from Academia Sinica (Beijing) in 1995, and was awarded Alexander-von-Humboldt Research Fellowship in 2000. His current research interests are in on-line algorithms and approximation algorithms for hard optimization problems. He has published papers in journals such as Naval Research logistics, Operations Research Letters, Discrete Applied Mathematics, etc.

Xiaoqiang Cai is Professor and Chairman of the Department of Systems Engineering and Engineering Management, The Chinese University of Hong Kong. He received his Ph.D from Tsinghua University, Beijing, in 1988. His current research interests include scheduling models and applications, time-varying network optimization, and portfolio optimization. He has published over 50 papers in journals such as Management Science, Operations Research, Naval Research Logistics, IIE Transactions, IEEE Transactions, Discrete Applied Mathematics, European Journal of Operational Research, etc. He is on the editorial board of IIE Transactions on Scheduling and Logistics, Journal of Scheduling, and several other journals.

C.K. Wong is Professor of Computer Science and Engineering at The Chinese University of Hong Kong and served as Chairman of the Department of Computer Science and Engineering from 1995–1997. He received the B.A. degree (First Class Honors) in mathematics from University of Hong Kong in 1965, and the M.A. and Ph.D. degrees in mathematics from Columbia University in 1966 and 1970, respectively. He is a Fellow of the Institute of Electrical and Electronic Engineers (IEEE) and a Fellow of the Association for Computing Machinery (ACM). He had ever been Chair of the IEEE Computer Society Technical Committee, Editor of “IEEE Transactions on Computers”, Associate Editor of “IEEE Transactions on VLSI Systems, and an Editorial Board Member of the international journal “Fuzzy Sets and Systems” and “Networks”. He is also the founding Editor-in-Chief of the international journal “Algorithmica” and an Advisory Board Member of “ACM Journal of Experimental Algorithmics”. His current research is mainly focused on algorithms, in particular, VLSI design algorithms, Steiner tree problems in non-Euclidean metrics and scheduling problems in various settings. He holds four U.S. patents and has published more than 200 papers and two books. He received an Outstanding Invention Award, an Outstanding Technical Achievement Award and four Invention Achievement Awards from IBM. At the 1995 IEEE International Conference on Computer Design: VLSI in Computers & Processors (ICCD’ 95), he received a best paper award for his work on FPGA design.

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Zhang, G., Cai, X. & Wong, C.K. Scheduling two groups of jobs with incomplete information. J. Syst. Sci. Syst. Eng. 12, 73–81 (2003). https://doi.org/10.1007/s11518-006-0121-y

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  • DOI: https://doi.org/10.1007/s11518-006-0121-y

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