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Problem definition: Inspired by new developments in dynamic spectrum access, we study the dynamic pricing of wireless Internet access when demand and capacity (bandwidth) are stochastic. Academic/practical relevance: The demand for wireless Internet access has increased enormously. However, the spectrum available to wireless service providers is limited. The industry has, thus, altered conventional license-based spectrum access policies through unlicensed spectrum operations. The additional spectrum obtained through these operations has stochastic capacity. Thus, the pricing of this service by the service provider has novel challenges. The problem considered in this paper is, therefore, of high practical relevance and new to the academic literature. Methodology: We study this pricing problem using a Markov decision process model in which customers are posted dynamic prices based on their bandwidth requirement and the available capacity. Results: We characterize the structure of the optimal pricing policy as a function of the system state and of the input parameters. Because it is impossible to solve this problem for practically large state spaces, we propose a heuristic dynamic pricing policy that performs very well, particularly when the ratio of capacity to demand rate is low. Managerial implications: We demonstrate the value of using a dynamic heuristic pricing policy compared with the myopic and optimal static policies. The previous literature has studied similar systems with fixed capacity and has characterized conditions under which myopic policies perform well. In contrast, our setting has dynamic (stochastic) capacity, and we find that identifying good state-dependent heuristic pricing policies is of greater importance. Our heuristic policy is computationally more tractable and easier to implement than the optimal dynamic and static pricing policies. It also provides a significant performance improvement relative to the myopic and optimal static policies when capacity is scarce, a condition that holds for the practical setting that motivated this research.
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A model for wind farm management with option interactions
Abstract A renewable energy site can expand its power generation capacity by an endogenous amount but may also want to shut down to save on fixed operating costs and interest payments if the market prospects deteriorate. We model such circumstances and derive managerial implications that help us explain real‐world conundrums, illustrating the intricate interactions between the operational decision to build up capacity and the financial decision to exit an industry. Shutting down may be delayed in the hope of expanding capacity upon recovery; an expansion may also be delayed in the presence of a valuable exit option. Numerical extensions provide further managerial insights. In particular, the presence of fixed or proportional financing costs may lead the firm to delay its expansion decision, but the scale of investment will only be affected by proportional costs. If herding behavior causes equipment prices to increase (respectively, decrease) when electricity prices are high (respectively, low), managers should invest earlier (respectively, later) and more (respectively, less) while equipment prices are low (respectively, high). Furthermore, although volume swings (due to capacity decommissionings and expansions) are marked in a homogeneous industry (when the default and expansion thresholds are reached), heterogeneity in the population of wind farms smooths out such effects.
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- Award ID(s):
- 1905449
- PAR ID:
- 10372252
- Publisher / Repository:
- SAGE Publications
- Date Published:
- Journal Name:
- Production and Operations Management
- Volume:
- 31
- Issue:
- 7
- ISSN:
- 1059-1478
- Format(s):
- Medium: X Size: p. 2853-2871
- Size(s):
- p. 2853-2871
- Sponsoring Org:
- National Science Foundation
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