101. Dynamic Pricing to Minimize Maximum Regret
- Author
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Hans Kellerer, Zhi-Long Chen, and Nicholas G. Hall
- Subjects
050208 finance ,021103 operations research ,Linear programming ,05 social sciences ,0211 other engineering and technologies ,Regret ,02 engineering and technology ,Interval (mathematics) ,Management Science and Operations Research ,Upper and lower bounds ,Industrial and Manufacturing Engineering ,Microeconomics ,Management of Technology and Innovation ,0502 economics and business ,Dynamic pricing ,Economics ,Econometrics ,Probability distribution ,Revenue ,Time complexity - Abstract
We consider a dynamic pricing problem that involves selling a given inventory of a single product over a short, two-period selling season. There is insufficient time to replenish inventory during this season, hence sales are made entirely from inventory. The demand for the product is a stochastic, nonincreasing function of price. We assume interval uncertainty for demand, that is, knowledge of upper and lower bounds but not a probability distribution, with no correlation between the two periods. We minimize the maximum total regret over the two periods that results from the pricing decisions. We consider a dynamic model where the decision maker chooses the price for each period contingent on the remaining inventory at the beginning of the period, and a static model where the decision maker chooses the prices for both periods at the beginning of the first period. Both models can be solved by a polynomial time algorithm that solves systems of linear inequalities. Our computational study demonstrates that the prices generated by both our models are insensitive to errors in estimating the demand intervals. Our dynamic model outperforms our static model and two classical approaches that do not use demand probability distributions, when evaluated by maximum regret, average relative regret, variability, and risk measures. Further, our dynamic model generates a total expected revenue which closely approximates that of a maximum expected revenue approach which requires demand probability distributions.
- Published
- 2016
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