Inter-Temporal Price Constraints in Dynamic Pricing: Performance Guarantees Under Price Monotonicity and Promotion Fatigue
Abstract
We study dynamic pricing problems under inter-temporal price constraints. We have resources with limited capacities. At each time period, we decide which products to make available and what prices to charge for the available products. The sale probability for a product depends on its price. If we make a sale for a product, then we collect a revenue reflecting the price and consume the capacities of a combination of resources. We work with two types of inter-temporal constraints. In price monotonicity, the prices charged for a product at different time periods have to be monotone. In promotion fatigue, we can discount a product at most once over each time interval of a fixed length. Computing the optimal policy is intractable. We use fluid approximations to construct policies. Traditionally, policies from fluid approximations make randomized decisions at each time period by following an optimal solution to the fluid approximation, but such randomized decisions easily violate price monotonicity or promotion fatigue constraints. We develop policies that sample price paths according to an optimal solution to the fluid approximation, while satisfying the inter-temporal constraints. Letting cmin be the smallest initial capacity of a resource and L be the maximum number of resources used by a product, our policies have a performance guarantee of max{ 1/8L, 1/2 − √((log cmin)/(2 cmin)) − L/cmin}. Thus, under large resource capacities, our policies are guaranteed to obtain at least half of the optimal total expected revenue. The latter performance guarantee is tight in the sense that no policy can, in general, obtain more than half of the optimal objective value of the fluid approximation even under large resource capacities. We unify our approach to open the path for extensions to other inter-temporal price constraints.
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BibTeX
@misc{li2026intertemporal,
title = {{Inter-Temporal Price Constraints in Dynamic Pricing: Performance Guarantees Under Price Monotonicity and Promotion Fatigue}},
author = {Weiyuan Li and Paat Rusmevichientong and Huseyin Topaloglu},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.28451},
eprint = {2609.28451},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.28451},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - Inter-Temporal Price Constraints in Dynamic Pricing: Performance Guarantees Under Price Monotonicity and Promotion Fatigue
AU - Weiyuan Li
AU - Paat Rusmevichientong
AU - Huseyin Topaloglu
PY - 2026
DA - 2026/09/23
PB - arXiv
DO - 10.48550/arxiv.2609.28451
UR - https://arxiv.org/abs/2609.28451
AB - We study dynamic pricing problems under inter-temporal price constraints. We have resources with limited capacities. At each time period, we decide which products to make available and what prices to charge for the available products. The sale probability for a product depends on its price. If we make a sale for a product, then we collect a revenue reflecting the price and consume the capacities of a combination of resources. We work with two types of inter-temporal constraints. In price monotonicity, the prices charged for a product at different time periods have to be monotone. In promotion fatigue, we can discount a product at most once over each time interval of a fixed length. Computing the optimal policy is intractable. We use fluid approximations to construct policies. Traditionally, policies from fluid approximations make randomized decisions at each time period by following an optimal solution to the fluid approximation, but such randomized decisions easily violate price monotonicity or promotion fatigue constraints. We develop policies that sample price paths according to an optimal solution to the fluid approximation, while satisfying the inter-temporal constraints. Letting c_min be the smallest initial capacity of a resource and L be the maximum number of resources used by a product, our policies have a performance guarantee of max{ 1/8L, 1/2 − √((log c_min)/(2 c_min)) − L/c_min}. Thus, under large resource capacities, our policies are guaranteed to obtain at least half of the optimal total expected revenue. The latter performance guarantee is tight in the sense that no policy can, in general, obtain more than half of the optimal objective value of the fluid approximation even under large resource capacities. We unify our approach to open the path for extensions to other inter-temporal price constraints.
ER -