Abstract
This paper concerns the multi-period newsvendor problem. In this problem, the decision maker has to decide the order quantity of an item in the subsequent period in which the demand is usually unknown. No statistical assumptions are made about the unknown demand. We adopt an online learning method from the field of prediction with expert advice to study the non-stationary newsvendor problem. We propose newsvendor strategies for both real-valued and integer order quantities. Taking the non-stationary strategies that can switch between different order quantities as benchmark, we prove that our proposed strategies can guarantee that the newsvendor’s cumulative gains are almost as large as those of the best switching strategies with not too many switches. Simple computational experiments are further performed to illustrate the effectiveness of our strategies.
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Acknowledgments
This research was supported by the National Natural Science Foundation of China (No. 71301029), the Humanities and Social Science Foundation of the Ministry of Education of China (No. 11YJC630255 and No. 13YJC630234), the National Social Science Foundation of China (No. 11&ZD156), and the Engineering and Physical Sciences Research Council of the UK (No. EP/F002998/1 and CEReS). Part of this work was done when the first author was visiting Rutgers Business School—Newark and New Brunswick as a PhD student. This author would like to thank Khrystyna Bochkay for her helpful suggestions that greatly improved the presentation. The authors are grateful to the reviewers for many useful comments (in particular, for pointing out a gap in the proof of Theorem 2). The computational experiments in Sect. 5 have been carried out using MATLAB.
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Zhang, Y., Vovk, V. & Zhang, W. Probability-free solutions to the non-stationary newsvendor problem. Ann Oper Res 223, 433–449 (2014). https://doi.org/10.1007/s10479-014-1620-8
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DOI: https://doi.org/10.1007/s10479-014-1620-8