A comparison of control strategies applied to a pricing problem in retail

When sales of a product are affected by randomness in demand, retailers can use dynamic pricing strategies to maximise their profits. In this article the pricing problem is formulated as a stochastic optimal control problem, where the optimal policy can be found by solving the associated Bellman equ...

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Bibliographic Details
Published in:arXiv.org 2017-10
Main Authors: Riseth, Asbjørn N, Dewynne, Jeff N, Farmer, Chris L
Format: Article
Language:English
Subjects:
Algorithms
Computer simulation
Dynamic programming
Equivalence
Feedback control
Optimal control
Optimization
Pricing
Pricing policies
Randomness
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Summary:When sales of a product are affected by randomness in demand, retailers can use dynamic pricing strategies to maximise their profits. In this article the pricing problem is formulated as a stochastic optimal control problem, where the optimal policy can be found by solving the associated Bellman equation. The aim is to investigate Approximate Dynamic Programming algorithms for this problem. For realistic retail applications, modelling the problem and solving it to optimality is intractable. Thus practitioners make simplifying assumptions and design suboptimal policies, but a thorough investigation of the relative performance of these policies is lacking. To better understand such assumptions, we simulate the performance of two algorithms on a one-product system. It is found that for more than half of the realisations of the random disturbance, the often-used, but approximate, Certainty Equivalent Control policy yields larger profits than an optimal, maximum expected-value policy. This approximate algorithm, however, performs significantly worse in the remaining realisations, which colloquially can be interpreted as a more risk-seeking attitude by the retailer. Another policy, Open-Loop Feedback Control, is shown to work well as a compromise between the Certainty Equivalent Control and the optimal policy.
ISSN:2331-8422