Maxime C. Cohen

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. This paper was accepted by Yossi Aviv, operations management .

Feature-based Dynamic Pricing

We consider the problem faced by a firm that receives highly differentiated products in an online fashion and needs to price them in order to sell them to its customer base. Products are described by vectors of features and the market value of each product is linear in the values of the features. The firm does not initially know the values of the different features, but it can learn the values of the features based on whether products were sold at the posted prices in the past. This model is motivated by a question in online advertising, where impressions arrive over time and can be described by vectors of features. We first consider a multi-dimensional version of binary search over polyhedral sets, and show that it has exponential worst-case regret. We then propose a modification of the prior algorithm where uncertainty sets are replaced by their Lowner-John ellipsoids. We show that this algorithm has a worst-case regret that is quadratic in the dimensionality of the feature space and logarithmic in the time horizon.

The Impact of Linear Optimization on Promotion Planning

Sales promotions are important in the fast-moving consumer goods FMCG industry due to the significant spending on promotions and the fact that a large proportion of FMCG products are sold on promotion. This paper considers the problem of planning sales promotions for an FMCG product in a grocery retail setting. The category manager has to solve the promotion optimization problem POP for each product, i.e., how to select a posted price for each period in a finite horizon so as to maximize the retailers profit. Through our collaboration with Oracle Retail, we developed an optimization formulation for the POP that can be used by category managers in a grocery environment. Our formulation incorporates business rules that are relevant, in practice. We propose general classes of demand functions including multiplicative and additive, which incorporate the post-promotion dip effect, and can be estimated from sales data. In general, the POP formulation has a nonlinear objective and is NP-hard. We then propose a linear integer programming IP approximation of the POP. We show that the IP has an integral feasible region, and hence can be solved efficiently as a linear program LP. We develop performance guarantees for the profit of the LP solution relative to the optimal profit. Using sales data from a grocery retailer, we first show that our demand models can be estimated with high accuracy, and then demonstrate that using the LP promotion schedule could potentially increase the profit by 3%, with a potential profit increase of 5% if some business constraints were to be relaxed. The online appendix is available at https://doi.org/10.1287/opre.2016.1573

Consumer Subsidies with a Strategic Supplier: Commitment vs. Flexibility

Governments use consumer incentives to promote green technologies (e.g., solar panels and electric vehicles). Our goal in this paper is to study how policy adjustments over time will interact with production decisions from the industry. 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 affects the risk-sharing between government and supplier, ultimately affecting the cost of the subsidy program. In particular, we show that when the government commits to a fixed policy, it encourages the supplier to produce more at the beginning of the horizon. Consequently, a flexible subsidy policy is on average more expensive, unless there is a significant negative demand correlation across time periods. However, we show that the variance of the total sales is lower in the flexible setting, implying that the governments additional spending reduces adoption level uncertainty. In addition, we show that for flexible policies, the supplier is better-off in terms of expected profits whereas the consumers can either benefit or not depending on the price elasticity of demand. Finally, we test our insights with a numerical example calibrated on data from a solar subsidy program.

DESIGNING PRICE INCENTIVES IN A NETWORK WITH SOCIAL INTERACTIONS

The recent ubiquity of social networks allows firms to collect vast amount of data on their customers and on their social interactions. We consider a setting where a monopolist sells an indivisible good to consumers who are embedded in a social network. This an important problem as sellers can use available data to design and send targeted promotions that account for social externality effects and ultimately increase their profits. We capture the interactions among consumers using a broad class of non-linear utility models. This class extends the existing models by explicitly capturing externalities from subsets of agents (communities or groups) and includes several existing models as special cases (e.g., full information version of the triggering model). Assuming complete information about the interactions, we model the optimal pricing problem as a two-stage game. First, the firm designs prices to maximize profits and then consumers choose whether or not to purchase the item. Under positive network externalities, we show the existence of a pure Nash equilibrium that is preferred by both the seller and the buyers. Using duality theory and integer programming techniques, we reformulate the problem into a linear mixed-integer program (MIP). We derive efficient ways to optimally solve the MIP using its linear programming relaxation for two pricing strategies: discriminative and uniform. Finally, we propose two intuitive heuristic algorithms to solve the problem for which we derive worst-case parametric performance bounds. We draw interesting insights on the structure of the optimal prices and the sellers profit. In particular, we quantify the effect on prices when using a non-linear utility model relative to a linear model and identify settings when it is beneficial to offer a price below cost to influential agents. Finally, we extend our model and results to the case where the seller offers incentives (in addition to prices) to solicit actions so as to ensure network externality effects.

Dynamic Pricing Through Data Sampling

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 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. We show numerically that regret-based objectives can perform well when compared with average revenue maximization. This modeling approach could be particularly important for risk-averse managers with limited access to historical data or information about the true demand distribution. Finally, we provide theoretical performance guarantees for this sampling-based solution.

Competition and Externalities in Green Technology Adoption

In this paper, we study the effects of competition among multiple suppliers who sell green technology products, such as electric vehicles. The government offers consumer subsidies to encourage the product adoption. We consider a setting where suppliers adjust production and price depending on the level of subsidies offered by the government. Our analysis expands the understanding of symmetric and asymmetric competition, incorporating the external influence of the government who is now an additional player in the system. We quantify how competition impacts the consumers, the suppliers as well as the government relative to the monopolistic setting where all the products are jointly produced from a single firm. In other words, we quantify who benefits from the competition and under what conditions. Our model incorporates demand uncertainty as well as positive externalities. We first compare different government objectives and determine that the magnitude of the externalities plays a key role in selecting the right objective. We then show that the effects of competition may differ depending on the demand uncertainty, the suppliers asymmetry and the magnitude of the externalities. When externalities are relatively small, we show that competition hurts the suppliers and benefits the government. However, it does not always benefit all the consumers, as it is usually the case in classical competition settings. We also show that in a market with large externalities, consumers, unlike the government, are always better-off in a competitive environment. Finally, we test our model and validate our insights using publicly available data from the electric vehicle industry, which is becoming increasingly competitive.

Overcommitment in Cloud Services Bin packing with Chance Constraints

This paper considers a traditional problem of resource allocation, scheduling jobs on machines. One such recent application is cloud computing, where jobs arrive in an online fashion with capacity requirements and need to be immediately scheduled on physical machines in data centers. It is often observed that the requested capacities are not fully utilized, hence offering an opportunity to employ an overcommitment policy, i.e., selling resources beyond capacity. Setting the right overcommitment level can induce a significant cost reduction for the cloud provider, while only inducing a very low risk of violating capacity constraints. We introduce and study a model that quantifies the value of overcommitment by modeling the problem as a bin packing with chance constraints. We then propose an alternative formulation that transforms each chance constraint into a submodular function. We show that our model captures the risk pooling effect and can guide scheduling and overcommitment decisions. We also develop a family of online algorithms that are intuitive, easy to implement and provide a constant factor guarantee from optimal. Finally, we calibrate our model using realistic workload data, and test our approach in a practical setting. Our analysis and experiments illustrate the benefit of overcommitment in cloud services, and suggest a cost reduction of 1.5% to 17% depending on the providers risk tolerance.

Coopetition and Profit Sharing for Ride-Sharing Platforms

On-demand ride-hailing platforms totally changed the way people commute and travel for short distances. Within the online ride-hailing market, a recent trend emerged on several platforms: ride-sharing or carpooling services. Several ride-hailing platforms offer an option which allows passengers heading in the same direction to be matched to the same vehicle and share their ride. In such a service, riders cannot select the people they are sharing with but instead an algorithm will match several riders to the same vehicle. For example, in NYC, one can find at least three such services: uberPOOL, Lyft Line, and Via. One of the main arguments for sharing a ride is the low price paid by the rider. In response to this recent market trend of on-demand ride-sharing platforms, taxi companies started to also offer on-demand services via mobile platforms to better fit in today’s economy. For example, in several cities, taxi rides can now be directly ordered from a smartphone application and the payment (including the tip) can either be completed via the application or in person. One such platform based in the U.S. is Curb. On their website, one can read: “Curb is the #1 taxi app in the US that connects you to fast, convenient and safe rides in 65 cities (50,000 Cabs – 100,000 Drivers).” In the last two years, several partnerships between ride-hailing platforms have emerged. One such example is the partnership between Curb and Via in NYC. Via offers an affordable fare for riders who are willing to carpool, whereas Curb offers a private taxi ride while charging the meter price plus an additional fixed fee per trip. One can definitely view these two platforms as competitors. Yet, they decided to collaborate and engage in a unique partnership. More precisely, on June 6, 20171, both platforms started to offer a joint service through a profit sharing contract, under which Curb and Via each earn a certain portion of the net profit from the joint service. This type of partnerships is sometimes referred to as coopetition, a term coined to describe cooperative competition. The new joint service introduced by Curb and Via in NYC allows users to book a shared taxi from either platform. For example, when a user requests a ride through the Via smartphone application, s/he may be offered to ride with a nearby available taxi (this option is called Shared Taxi). Then, the rider can either accept the Shared Taxi or decline by requesting a regular Via ride. Shared Taxi fares are calculated using the meter price and paid directly to the 1The partnership between Curb and Via in NYC was the topic of extensive media coverage. See for example: https://www.nytimes.com/2017/06/06/nyregion/new-york-yellow-taxis-ridesharing.html, https://techcrunch.com/2017/06/06/curb-and-via-bring-ride-sharing-to-nycs-yellow-taxis/ and https://qz.com/999132/can-shared-rides-save-the-iconic-new-york-city-yellow-cab/Two-sided platforms have become omnipresent (e.g., ride-sharing and on-demand delivery services). In this context, firms compete not only for customers but also for flexible self-scheduling workers who can work for multiple platforms. We consider a setting where two-sided platforms simultaneously choose prices and wages to compete for both sides of the market. We assume that customers and workers each follow an endogenous Multinomial Logit choice model that accounts for network effects. In our model, the behavior of an agent depends not only on the price or wage set by the platform, but also on the strategic interactions among agents on both sides of the market. We show that a unique equilibrium exists and that it can be computed using a tatonnement scheme. The proof technique for the competition between two-sided platforms is not a simple extension of the traditional (one-sided) setting and involves different arguments. Armed with this result, we study the impact of coopetition between two-sided platforms, that is, the business strategy of cooperating with competitors. Motivated by recent practice in the ride-sharing industry, we analyze a setting where two competing platforms engage in a profit sharing contract by introducing a new joint service. We show that a well-designed profit sharing contract (e.g., under Nash bargaining) will benefit every party in the market (both platforms, riders, and drivers).

Pricing with Limited Knowledge of Demand

How should a firm price a new product for which little is known about demand? We propose a pricing rule that can be used if the firm can estimate (even roughly) the maximum price it can charge and still expect to sell some units, and the firm need not know in advance the quantity it will sell. The rule is simple: Set price as though the demand curve were linear. We show that if the true demand curve is one of many commonly used demand functions, or even a more complex function, and if marginal cost is known and constant, the firm can expect its profit to be close to what it would earn if it knew the true demand curve. We derive analytical performance bounds for a variety of demand functions, calculate expected profit performance for randomly generated demand curves, and evaluate the welfare implications of our pricing rule.