Static Pricing Problems under Mixed Multinomial Logit Demand

Price differentiation is a common strategy for many transport operators. In this paper, we study a static multiproduct price optimization problem with demand given by a continuous mixed multinomial logit model. To solve this new problem, we design an efficient iterative optimization algorithm that asymptotically converges to the optimal solution. To this end, a linear optimization (LO) problem is formulated, based on the trust-region approach, to find a "good" feasible solution and approximate the problem from below. Another LO problem is designed using piecewise linear relaxations to approximate the optimization problem from above. Then, we develop a new branching method to tighten the optimality gap. Numerical experiments show the effectiveness of our method on a published, non-trivial, parking choice model

A review of choice-based revenue management : theory and methods

Over the last fifteen years, the theory and practice of revenue management has experienced significant developments due to the need to incorporate customer choice behavior. In this paper, we portray these developments by reviewing the key literature on choice-based revenue management, specifically focusing on methodological publications of availability control over the years 2004–2017. For this purpose, we first state the choice-based network revenue management problem by formulating the underlying dynamic program, and structure the review according to its components and the resulting inherent challenges. In particular, we first focus on the demand modeling by giving an overview of popular choice models, discussing their properties, and describing estimation procedures relevant to choice-based revenue management. Second, we elaborate on assortment optimization, which is a fundamental component of the problem. Third, we describe recent developments on tackling the entire control problem. We also discuss the relation to dynamic pricing. Finally, we give directions for future research

Automobile Prices in Market Equilibrium with Unobserved Price Discrimination

In markets where sellers are able to price discriminate, individuals pay different prices that may be unobserved by the econometrician. This paper considers the structural estimation of a demand and supply model à la Berry et al. (1995) with such price discrimination and limited information on prices taking the form of, e.g., observing list prices from catalogues or average prices. Within this framework, identification is achieved by using supply-side conditions, provided that the marginal costs of producing and selling the goods do not depend on the characteristics of the buyers. The model can be estimated by GMM using a nested fixed point algorithm that extends BLP’s algorithm to our setting. We apply our methodology to estimate the demand and supply in the French new automobile market. Our results suggest that discounting arising from price discrimination is important. The average discount is estimated to be 9.6%, with large variation depending on buyers’ characteristics and cars’ specifications. Our results are consistent with other evidence on transaction prices in France

Dynamic pricing under customer choice behavior for revenue management in passenger railway networks

Revenue management (RM) for passenger railway is a small but active research field with an increasing attention during the past years. However, a detailed look into existing research shows that most of the current models in theory rely on traditional RM techniques and that advanced models are rare. This thesis aims to close the gap by proposing a state-of-the-art passenger railway pricing model that covers the most important properties from practice, with a special focus on the German railway network and long-distance rail company Deutsche Bahn Fernverkehr (DB). The new model has multiple advantages over DB’s current RM system. Particularly, it uses a choice-based demand function rather than a traditional independent demand model, is formulated as a network model instead of the current leg-based approach and finally optimizes prices on a continuous level instead of controlling booking classes. Since each itinerary in the network is considered by multiple heterogeneous customer segments (e.g., differentiated by travel purpose, desired departure time) a discrete mixed multinomial logit model (MMNL) is applied to represent demand. Compared to alternative choice models such as the multinomial logit model (MNL) or the nested logit model (NL), the MMNL is significantly less considered in pricing research. Furthermore, since the resulting deterministic multi-product multi-resource dynamic pricing model under the MMNL turns out to be non- linear non-convex, an open question is still how to obtain a globally optimal solution. To narrow this gap, this thesis provides multiple approaches that make it able to derive a solution close to the global optimum. For medium-sized networks, a mixed-integer programming approach is proposed that determines an upper bound close to the global optimum of the original model (gap < 1.5%). For large-scale networks, a heuristic approach is presented that significantly decreases the solution time (by factor up to 56) and derives a good solution for an application in practice. Based on these findings, the model and heuristic are extended to fit further price constraints from railway practice and are tested in an extensive simulation study. The results show that the new pricing approach outperforms both benchmark RM policies (i.e., DB’s existing model and EMSR-b) with a revenue improvement of approx. +13-15% over DB’s existing approach under a realistic demand scenario. Finally, to prepare data for large-scale railway networks, an algorithm is presented that automatically derives a large proportion of necessary data to solve choice-based network RM models. This includes, e.g., the set of all meaningful itineraries (incl. transfers) and resources in a network, the corresponding resource consumption and product attribute values such as travel time or number of transfers. All taken together, the goal of this thesis is to give a broad picture about choice-based dynamic pricing for passenger railway networks

An explicit Nash equilibrium for a market share attraction game

In competitive marketing, the speed of generating the best price has become as critical as its reliability. In this study, we aim to design a practical marketing management tool. We consider a non-cooperative marketing environment with multiple substitute products, where total market size is moderately price-sensitive. The price-demand relations are determined by a market share attraction model, where the attraction of each product is a linear function of its price. The product's brand image is reflected in the parameters of this linear function. For the general case of multiple substitute products, we derive explicit expressions for the best-response functions. For the specific case of two substitute products, we derive closed form expressions for the prices at Nash equilibrium. These expressions help managers in changing their marketing instruments other than price, so as to obtain substantial individual profits. We show how our closed form Nash equilibrium enables the examination of the profit loss due to competition. Relevant for practice is the fact that our model can be easily calibrated. We provide a simple procedure for estimating the model parameters

Multiproduct Pricing Management and Design of New Service Products

In this thesis, we study price optimization and competition of multiple differentiated substitutable products under the general Nested Logit model and also consider the designing and pricing of new service products, e.g., flexible warranty and refundable warranty, under customers' strategic claim behavior. Chapter 2 considers firms that sell multiple differentiated substitutable products and customers whose purchase behavior follows the Nested Logit model, of which the Multinomial Logit model is a special case. In the Nested Logit model, customers make product selection decision sequentially: they first select a class or a nest of products and subsequently choose a product within the selected class. We consider the general Nested Logit model with product-differentiated price coefficients and general nest-heterogenous degrees. We show that the adjusted markup, which is defined as price minus cost minus the reciprocal of the price coefficient, is constant across all the products in each nest. When optimizing multiple nests of products, the adjusted nested markup is also constant within a nest. By using this result, the multi-product optimization problem can be reduced to a single-dimensional problem in a bounded interval, which is easy to solve. We also use this result to simplify the oligopolistic price competition and characterize the Nash equilibrium. Furthermore, we investigate its application to dynamic pricing and revenue management. In Chapter 3, we investigate the flexible monthly warranty, which offers flexibility to customers and allow them to cancel it at anytime without any penalty. Frequent technological innovations and price declines severely affect sales of extended warranties as product replacement upon failure becomes an increasingly attractive alternative. To increase sales and profitability, we propose offering flexible-duration extended warranties. These warranties can appeal to customers who are uncertain about how long they will keep the product as well as to customers who are uncertain about the product's reliability. Flexibility may be added to existing services in the form of monthly-billing with month-by-month commitments, or by making existing warranties easier to cancel, with pro-rated refunds. This thesis studies flexible warranties from the perspectives of both the customer and the provider. We present a model of the customer's optimal coverage decisions under the objective of minimizing expected support costs over a random planning horizon. We show that under some mild conditions the customer's optimal coverage policy has a threshold structure. We also show through an analytical study and through numerical examples how flexible warranties can result in higher profits and higher attach rates. Chapter 4 examines the designing and pricing of residual value warranty that refunds customers at the end of warranty period based on customers' claim history. Traditional extended warranties for IT products do not differentiate customers according to their usage rates or operating environment. These warranties are priced to cover the costs of high-usage customers who tend to experience more failures and are therefore more costly to support. This makes traditional warranties economically unattractive to low-usage customers. In this chapter, we introduce, design and price residual value warranties. These warranties refund a part of the upfront price to customers who have zero or few claims according to a pre-determined refund schedule. By design, the net cost of these warranties is lower for light users than for heavy users. As a result, a residual value warranty can enable the provider to price-discriminate based on usage rates or operating conditions without the need to monitor individual customers' usage. Theoretic results and numerical experiments demonstrate how residual value warranties can appeal to a broader range of customers and significantly increase the provider's profits