Paper
Robust Discrete Pricing Optimization via Multiple-Choice Knapsack Reductions
Authors
Zi Yuan Eric Shao
Abstract
We study a discrete portfolio pricing problem that selects one price per product from a finite menu under margin and fairness constraints. To account for demand uncertainty, we incorporate a budgeted robust formulation that controls conservatism while remaining computationally tractable. By reducing the problem to a Multiple-Choice Knapsack Problem (MCKP), we identify structural properties of the LP relaxation, in particular upper-hull filtering and greedy filling over hull segments, that yield an exact solution method for the LP relaxation of the fixed-parameter subproblems. For the resulting fixed-parameter subproblems, we show that the integrality gap is bounded additively by a single-item hull jump, and that the corresponding relative gap decays as O(1/n) under standard boundedness and linear-growth assumptions. Numerical experiments on synthetic portfolios and a stylized retail case study with economically calibrated parameters are consistent with these bounds and indicate that robust margin protection can be achieved with less than 1 percent nominal revenue loss on the instances tested.
Metadata
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Raw Data (Debug)
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"raw_xml": "<entry>\n <id>http://arxiv.org/abs/2603.18653v1</id>\n <title>Robust Discrete Pricing Optimization via Multiple-Choice Knapsack Reductions</title>\n <updated>2026-03-19T09:18:09Z</updated>\n <link href='https://arxiv.org/abs/2603.18653v1' rel='alternate' type='text/html'/>\n <link href='https://arxiv.org/pdf/2603.18653v1' rel='related' title='pdf' type='application/pdf'/>\n <summary>We study a discrete portfolio pricing problem that selects one price per product from a finite menu under margin and fairness constraints. To account for demand uncertainty, we incorporate a budgeted robust formulation that controls conservatism while remaining computationally tractable. By reducing the problem to a Multiple-Choice Knapsack Problem (MCKP), we identify structural properties of the LP relaxation, in particular upper-hull filtering and greedy filling over hull segments, that yield an exact solution method for the LP relaxation of the fixed-parameter subproblems. For the resulting fixed-parameter subproblems, we show that the integrality gap is bounded additively by a single-item hull jump, and that the corresponding relative gap decays as O(1/n) under standard boundedness and linear-growth assumptions. Numerical experiments on synthetic portfolios and a stylized retail case study with economically calibrated parameters are consistent with these bounds and indicate that robust margin protection can be achieved with less than 1 percent nominal revenue loss on the instances tested.</summary>\n <category scheme='http://arxiv.org/schemas/atom' term='math.OC'/>\n <published>2026-03-19T09:18:09Z</published>\n <arxiv:comment>28 pages, 10 figures. Code available at https://github.com/eric939/robust_mckp</arxiv:comment>\n <arxiv:primary_category term='math.OC'/>\n <author>\n <name>Zi Yuan Eric Shao</name>\n </author>\n </entry>"
}