Optimization of two-level discount values using queueing tandem model with feedback M. Shklennik, S. P. Moiseeva, A. N. Moiseev
Material type:
ArticleContent type: Текст Media type: электронный Subject(s): оптимизация | математические модели | компаниииGenre/Form: статьи в сборниках Online resources: Click here to access online
In:
Information Technologies and Mathematical Modelling. Queueing Theory and Applications : 17th International Conference, ITMM 2018, named after A. F. Terpugov and 12th Workshop on Retrial Queues and Related Topics, WRQ 2018, Tomsk, Russia, September 10-15, 2018 : selected papers P. 321-332Abstract: The trading company model with two levels of discount is considered in the paper. The problem of choosing the optimal discount values is solved. The mathematical model of the company is formulated in the form of an infinite-server queueing tandem with feedback at the second stage. The analytical form of generating function of multi-dimensional joint probability distribution of the number of purchases is obtained. Analytical expressions are found for the mean and variance of the company’s profit. Optimal discount values are obtained for the case when the probabilities of repeated purchases linearly depend on the value of discounts.
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The trading company model with two levels of discount is considered in the paper. The problem of choosing the optimal discount values is solved. The mathematical model of the company is formulated in the form of an infinite-server queueing tandem with feedback at the second stage. The analytical form of generating function of multi-dimensional joint probability distribution of the number of purchases is obtained. Analytical expressions are found for the mean and variance of the company’s profit. Optimal discount values are obtained for the case when the probabilities of repeated purchases linearly depend on the value of discounts.
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