Dynamic Pricing through Sampling Based Optimization

In this paper we develop an approach to dynamic pricing that combines ideas from data-driven and robust optimization to address the uncertain and dynamic aspects of the problem. In our setting, a firm off ers multiple products to be sold over a fixed discrete time horizon. Each product sold consumes one or more resources, possibly sharing the same resources among di fferent products. The firm is given a fixed initial inventory of these resources and cannot replenish this inventory during the selling season. We assume there is uncertainty about the demand seen by the fi rm for each product and seek to determine a robust and dynamic pricing strategy that maximizes revenue over the time horizon. While the traditional robust optimization models are tractable, they give rise to static policies and are often too conservative. The main contribution of this paper is the exploration of closed-loop pricing policies for di fferent robust objectives, such as MaxMin, MinMax Regret and MaxMin Ratio. We introduce a sampling based optimization approach that can solve this problem in a tractable way, with a con fidence level and a robustness level based on the number of samples used. We will show how this methodology can be used for data-driven pricing or adapted for a random sampling optimization approach when limited information is known about the demand uncertainty. Finally, we compare the revenue performance of the di fferent models using numerical simulations, exploring the behavior of each model under diff erent sample sizes and sampling distributions.National Science Foundation (U.S.) (Grant 0556106-CMII)National Science Foundation (U.S.) (Grant 0824674-CMII)Singapore-MIT Allianc

Pricing and incentive design in applications of green technology subsidies and revenue management

Thesis (Ph. D.)--Massachusetts Institute of Technology, Sloan School of Management, Operations Research Center, 2012.Cataloged from PDF version of thesis.Includes bibliographical references (p. 139-147).This thesis addresses three issues faced by firms and policy-makers when deciding how to price products and properly incentivize consumers. In the first part of the thesis, we focus on a firm attempting to dynamically adjust prices to maximize profits when facing uncertain demand, as for example airlines selling flights or hotels booking rooms. In particular, we develop a robust sampling-based optimization framework that minimizes the worst-case regret and dynamically adjusts the price according to the realization of demand. We propose a tractable optimization model that uses direct demand samples, where the confidence level of this solution can be obtained from the number of samples used. We further demonstrate the applicability of this approach with a series of numerical experiments and a case study using airline ticketing data. In the second part of the thesis, we propose a model for the adoption of solar photovoltaic technology by residential consumers. Using this model, we develop a framework for policy makers to find optimal subsidy levels in order to achieve a desired adoption target. The technology adoption process follows a discrete choice model, which is reinforced by network effects such as information spread and learning-by-doing. We validate the model through an empirical study of the German solar market, where we estimate the model parameters, generate adoption forecasts and demonstrate how to solve the policy design problem. We use this framework to show that the current policies in Germany could be improved by higher subsidies in the near future and a faster phase-out of the subsidy program. In the third part of the thesis, we model the interaction between a government and an industry player in a two-period game setting under uncertain demand. We show how the timing of decisions will affect the production levels and the cost of the subsidy program. In particular, we show that when the government commits to a fixed policy, it signals to the supplier to produce more in the beginning of the horizon. Consequently, a flexible policy is on average more expensive for the government than a committed policy.by Ruben Lobel.Ph.D

The Impact of Demand Uncertainty on Consumer Subsidies for Green Technology Adoption

This paper studies government subsidies for green technology adoption while considering the manufacturing industry’s response. Government subsidies offered directly to consumers impact the supplier’s production and pricing decisions. Our analysis expands the current understanding of the price-setting newsvendor model, incorporating the external influence from the government, who is now an additional player in the system. We quantify how demand uncertainty impacts the various players (government, industry, and consumers) when designing policies. We further show that, for convex demand functions, an increase in demand uncertainty leads to higher production quantities and lower prices, resulting in lower profits for the supplier. With this in mind, one could expect consumer surplus to increase with uncertainty. In fact, we show that this is not always the case and that the uncertainty impact on consumer surplus depends on the trade-off between lower prices and the possibility of underserving customers with high valuations. We also show that when policy makers such as governments ignore demand uncertainty when designing consumer subsidies, they can significantly miss the desired adoption target level. From a coordination perspective, we demonstrate that the decentralized decisions are also optimal for a central planner managing jointly the supplier and the government. As a result, subsidies provide a coordination mechanism

The Role of Surge Pricing on a Service Platform with Self-Scheduling Capacity

Recent platforms, like Uber and Lyft, offer service to consumers via “self-scheduling” providers who decide for themselves how often to work. These platforms may charge consumers prices and pay providers wages that both adjust based on prevailing demand conditions. For example, Uber uses a “surge pricing” policy, which pays providers a fixed commission of its dynamic price. With a stylized model that yields analytical and numerical results, we study several pricing schemes that could be implemented on a service platform, including surge pricing. We find that the optimal contract substantially increases the platform’s profit relative to contracts that have a fixed price or fixed wage (or both), and although surge pricing is not optimal, it generally achieves nearly the optimal profit. Despite its merits for the platform, surge pricing has been criticized because of concerns for the welfare of providers and consumers. In our model, as labor becomes more expensive, providers and consumers are better off with surge pricing because providers are better utilized and consumers benefit both from lower prices during normal demand and expanded access to service during peak demand. We conclude, in contrast to popular criticism, that all stakeholders can benefit from the use of surge pricing on a platform with self-scheduling capacity

The Impact of Demand Uncertainty on Consumer Subsidies for Green Technology Adoption

This paper studies government subsidies for green technology adoption while considering the manufacturing industry’s response. Government subsidies offered directly to consumers impact the supplier’s production and pricing decisions. Our analysis expands the current understanding of the price-setting newsvendor model, incorporating the external influence from the government, who is now an additional player in the system. We quantify how demand uncertainty impacts the various players (government, industry, and consumers) when designing policies. We further show that, for convex demand functions, an increase in demand uncertainty leads to higher production quantities and lower prices, resulting in lower profits for the supplier. With this in mind, one could expect consumer surplus to increase with uncertainty. In fact, we show that this is not always the case and that the uncertainty impact on consumer surplus depends on the trade-off between lower prices and the possibility of underserving customers with high valuations. We also show that when policy makers such as governments ignore demand uncertainty when designing consumer subsidies, they can significantly miss the desired adoption target level. From a coordination perspective, we demonstrate that the decentralized decisions are also optimal for a central planner managing jointly the supplier and the government. As a result, subsidies provide a coordination mechanism

Dynamic Pricing Through Data Sampling

Abstract In this paper we study a dynamic pricing problem, where a firm offers a product to be sold over a fixed time horizon. The firm has a given initial inventory level, but there is uncertainty about the demand for the product in each time period. The objective of the firm is to determine a robust and dynamic pricing strategy that maximizes revenue over the entire selling season. We develop a tractable optimization model that directly uses demand data, therefore creating a practical decision tool. Furthermore, we provide theoretical performance guarantees for this sampling-based solution, based on the number of samples used. Finally, we compare the revenue performance of our model using numerical simulations, exploring the behavior of the model with different robust objectives, sample sizes, and sampling distributions. This modeling approach could be particularly important for risk-averse managers with limited access to historical data or information about the demand distribution

The impact of demand uncertainty on consumer subsidies for green technology adoption. Management Sci., forthcoming

This paper studies government subsidies for green technology adoption while considering the manufacturing industry's response. Government subsidies offered directly to consumers impact the supplier's production and pricing decisions. Our analysis expands the current understanding of the price-setting newsvendor model, incorporating the external influence from the government who is now an additional player in the system. We quantify how demand uncertainty impacts the various players (government, industry and consumers) when designing policies. We further show that for convex demand functions, an increase in demand uncertainty leads to higher production quantities and lower prices, resulting in lower profits for the supplier. With this in mind, one could expect consumer surplus to increase with uncertainty. In fact, we show this is not always the case and the uncertainty impact on consumer surplus depends on the trade-off between lower prices and the possibility of under-serving customers with high valuations. We also show that when policy makers such as governments ignore demand uncertainty when designing consumer subsidies, they can significantly miss the desired adoption target level. From a coordination perspective, we demonstrate that the decentralized decisions are also optimal for a central planner managing jointly the supplier and the government. As a result, subsidies provide a coordination mechanism