In this paper, the problem of program performance scheduling with accepting strategy is studied. Considering the uncertainty of actual situation, the duration of a program is expressed as a bounded interval. Firstly, we decide which programs are accepted. Secondly, the risk preference coefficient of the decision maker is introduced. Thirdly, the min-max robust optimization model of the uncertain program show scheduling is built to minimize the performance cost and determine the sequence of these programs. Based on the above model, an effective algorithm for the original problem is proposed. The computational experiment shows that the performance’s cost (revenue) will increase (decrease) with decision maker’s risk aversion.
References
[1]
Cheng, T.C.E., Diamond, J.E. and Lin, B.M.T. (1993) Optimal Scheduling in Film Production to Minimize Talent Hold Cost. Journal of Optimization Theory and Applications, 79, 479-492. https://doi.org/10.1007/BF00940554
[2]
Nordström, A.L. and Tufekci, S. (1994) A Genetic Algorithm for the Talent Scheduling Problem. Computers & Operations Research, 21, 927-940.
https://doi.org/10.1016/0305-0548(94)90021-3
[3]
Bomsdorf, F. and Derigs, U. (2008) A Model, Heuristic Procedure and Decision Support System for Solving the Movie Shoot Scheduling Problem. OR Spectrum, 30, 751-772. https://doi.org/10.1007/s00291-007-0103-6
[4]
Garcia De La Banda, M., Stuckey, P.J. and Chu, G. (2011) Solving Talent Scheduling with Dynamic Programming. INFORMS Journal on Computing, 23, 120-137.
https://doi.org/10.1287/ijoc.1090.0378
[5]
Wang, S.Y., Chuang, Y.T. and Lin, B.M.T. (2016) Minimizing Talent Cost and Operating Cost in Film Production. Journal of Industrial and Production Engineering, 33, 17-31.
[6]
Qin, H., Zhang, Z.Z., Lim, A., et al. (2016) An Enhanced Branch-and-Bound Algorithm for the Talent Scheduling Problem. European Journal of Operational Research, 250, 412-426. https://doi.org/10.1016/j.ejor.2015.10.002
[7]
Sakulsom, N. and Tharmmaphornphilas, W. (2014) Scheduling a Music Performance Problem with Unequal Music Piece Length. Computers & Industrial Engineering, 70, 20-30. https://doi.org/10.1016/j.cie.2013.12.017
[8]
Zhen, L., Liu, B. and Wang, W.C. (2017) Scheduling of Performance with Mixing Piece Length. Journal of Systems Management, 26, 850-856.
[9]
Wang, Y. and Tang, J.F. (2016) A Two-Stage Robust Optimization Method for Solving Surgery Scheduling Problem. Journal of Systems Engineering, 31, 431-440.
[10]
Xu, X.Q., Cui, W.T., Lin, J. and Qian, Y.J. (2013) Robust Identical Parallel Machines Scheduling Model Based on Min-Max Regret Criterion. Journal of Systems Engineering, 28, 729-737.
[11]
Qiu, R.Z. and Huang X.Y. (2011) A Robust Supply Chain Coordination Model Based on Minimax Regret Criterion. Journal of Systems Management, 20, 296-302.
[12]
Zhang, L., Chen, T. and Huang, J. (2014) Emergency Network Model and Algorithm Based on Min-Max Regret Robust Optimization. Chinese Journal of Management Science, 22, 131-139.
[13]
Bertsimas, D. and Sim, M. (2004) The Price of Robustness. Operations Research, 52, 35-53. https://doi.org/10.1287/opre.1030.0065
[14]
Bertsimas, D. and Sim, M. (2003) Robust Discrete Optimization and Network Flows. Mathematical Programming, 98, 49-71. https://doi.org/10.1007/s10107-003-0396-4
[15]
Charalambous, C. and Conn, A.R. (1978) An Efficient Method to Solve the Minimax Problem Directly. SIAM Journal on Numerical Analysis, 15, 162-187.
https://doi.org/10.1137/0715011
[16]
Yao, E.Y., He, Y. and Cheng, S.P. (2001) Mathematical Planning and Combination Optimization. Zhejiang University Press, Hangzhou, 31-35.
[17]
Liu, H. (2013) MATLAB R2012a Completely Self-Study. Electronic Industry Press, Beijing.
