A Stochastic Optimization Model for Consecutive Promotion
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Bibliographic record
Abstract
AbstractNowadays in business environment, marketing competitiveness is as demanding as ever. To survive under keen competitions, industries must keep acquiring customers and make them loyal while maximizing profit from their service subscription or product purchasing. Intensive research works have been done in answering when and what kind of promotions should be used under limited marketing communication resources to maintain a perpetual generation of revenue. In this paper, we investigate the advantages in consecutive promotion based on the framework of the model proposed in Ching et al. [1]. The customers' behavior is modelled by using a Markov chain and we aim at maximizing the expected profit using stochastic dynamic programming. We find that a multi-period promotion strategy is better than the strategy of applying several single-period promotions in our tested examples.Keywords: Consecutive promotioncustomer behaviorMarkov processstochastic dynamic programming Additional informationNotes on contributorsHo-Yin LeungHo-Yin Leung M.Phil. student at the Department of Mathematics, the University of Hong Kong. He got his B.Sc. in Mathematics, the University of Hong Kong with first class honour. He was in the Dean's honour list for three years (2005-2007) and he got the following scholarships: CV Starr Scholarships (2007), HSBC Hong Kong Scholarship (2006) and the Koo Shui Ting Memorial Scholarship (2005-2007). He also obtained the following academic prizes: Alan John Ellis Prizes in Mathematics (2005), B.Sc. Class of 1971 Prize (2006), Ho Sin Hang Price in Science (2007) and Wong Yung Chow Prize in Mathematics (2006). His research interests are stochastic process and modelling with applications.Wai-Ki ChingWai-Ki Ching lecturer at the Department of Mathematics, the University of Hong Kong. He obtained his B.Sc. (1991) and M.Phil. (1994) degrees in Mathematics from the University of Hong Kong. He then obtained his Ph.D. degree in Systems Engineering and Engineering Management (1998) from the Chinese University of Hong Kong and was a visiting post-doc fellow at the Judge Business School of the Cambridge University (1999-2000). He has previously taught at the Hong Kong Polytechnic University and the University of Science and Technology. Before joining his Alma Mater, he was a lecturer at the University of Southampton (2000-2001). His research interests include data modelling, optimization algorithms, systems engineering and bioinformatics.Issic K.C. LeungIssic K.C. Leung lecturer at the University of Macau for two years (1990-1992) after he had obtained his Bachelor and Master degrees from the University of Manitoba, Canada (1990). He then studied further and graduated with his Ph.D. in Mathematics from the Flinders University of South Australia (1996) at there he was awarded the Flinders University Research Scholarship (1993-1996). He was a senior market analyst in PCCW, one of the giants in the telecom industry in Hong Kong, for many years before he became an assistant professor of mathematics education at the Hong Kong Institute of Education (2006-2008). His research interest is in mathematics in business modelling, quantitative methods in marketing analysis, mathematics education and teacher competence in mathematics.
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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it