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

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

Should Optimal Designers Worry About Consideration?

Consideration set formation using non-compensatory screening rules is a vital component of real purchasing decisions with decades of experimental validation. Marketers have recently developed statistical methods that can estimate quantitative choice models that include consideration set formation via non-compensatory screening rules. But is capturing consideration within models of choice important for design? This paper reports on a simulation study of a vehicle portfolio design when households screen over vehicle body style built to explore the importance of capturing consideration rules for optimal designers. We generate synthetic market share data, fit a variety of discrete choice models to the data, and then optimize design decisions using the estimated models. Model predictive power, design "error", and profitability relative to ideal profits are compared as the amount of market data available increases. We find that even when estimated compensatory models provide relatively good predictive accuracy, they can lead to sub-optimal design decisions when the population uses consideration behavior; convergence of compensatory models to non-compensatory behavior is likely to require unrealistic amounts of data; and modeling heterogeneity in non-compensatory screening is more valuable than heterogeneity in compensatory trade-offs. This supports the claim that designers should carefully identify consideration behaviors before optimizing product portfolios. We also find that higher model predictive power does not necessarily imply better design decisions; that is, different model forms can provide "descriptive" rather than "predictive" information that is useful for design.Comment: 5 figures, 26 pages. In Press at ASME Journal of Mechanical Design (as of 3/17/15

An Exact Method for Assortment Optimization under the Nested Logit Model

We study the problem of finding an optimal assortment of products maximizing the expected revenue, in which customer preferences are modeled using a Nested Logit choice model. This problem is known to be polynomially solvable in a specific case and NP-hard otherwise, with only approximation algorithms existing in the literature. For the NP-hard cases, we provide a general exact method that embeds a tailored Branch-and-Bound algorithm into a fractional programming framework. Contrary to the existing literature, in which assumptions are imposed on either the structure of nests or the combination and characteristics of products, no assumptions on the input data are imposed, and hence our approach can solve the most general problem setting. We show that the parameterized subproblem of the fractional programming scheme, which is a binary highly non-linear optimization problem, is decomposable by nests, which is a main advantage of the approach. To solve the subproblem for each nest, we propose a two-stage approach. In the first stage, we identify those products that are undoubtedly beneficial to offer, or not, which can significantly reduce the problem size. In the second stage, we design a tailored Branch-and-Bound algorithm with problem-specific upper bounds. Numerical results show that the approach is able to solve assortment instances with up to 5,000 products per nest. The most challenging instances for our approach are those in which the dissimilarity parameters of nests can be either less or greater than one

Consideration behavior and design decision making

Over the past decade, design engineering has developed a systematic framework to coordinate with consumer behavior models. Traditional consumer models applied in the past has mainly focused on the preference of compensatory trade-offs in the choice decisions. Recent marketing research has become interested in developing consumer models that are representative in that they reflect realistic human decision processes. One important example is consideration : the process of quickly screening out many available alternatives using non-compensatory rules before trading off the value of different feature combinations. Is capturing consideration important for design? This research investigates the impact of modeling consideration behavior to design engineering, aiming at constructing consideration models that can inform strategic decisions. The study includes several features absent in existing research: quantifying the mis-specifications of the underlying choice process, tailoring survey instruments for particular models, and exploring the models\u27 strategic value on product profitability and design feature differences. First, numerical methods are explored to address the discontinuity in the profit-oriented optimization problem introduced by the consideration models. Methods based on complementarity constraints, smoothing functions and genetic algorithms are implemented and evaluated with a vehicle design case study. Second, a simulation experiment based on synthetic market data compares consideration models and a variety of conventional choice models in the process of model estimation and design optimization. The simulation finds that even when estimated compensatory models provide relatively good predictive accuracy, they can lead to sub-optimal design decisions when the population uses consideration behavior; convergence of compensatory models to non-compensatory behavior is likely to require unrealistic amounts of data; modeling heterogeneity in non-compensatory screening is more valuable than heterogeneity in compensatory trade-offs. The synthetic experiment framework then further extends the comparison to include the survey design process guided by the different assumptions behind considerations and traditional models. A product line design case study reveals that even though both compensatory models and consideration models show robustness in profitability, using consideration models leads to optimal portfolios with higher feature diversity while reducing the risk of overestimating profits. Finally, the research explores how to use consideration models to analyze the market penetration of newly designed product in a case study of a consideration maximization problem. It is the hope that this research will arouse the attention of designers to the informative power of consideration models, expand the understanding of consumer behavior modeling from the predictive power in the marketing field to the strategic impacts to design decisions, and provide technical support to the future application of consideration models in design engineering

Intermodal commuter network planning

An intermodal commuter network is an integration of passenger transportation systems, or modes, to a single comprehensive system that provides connections among the various modes, and improved travel choices to users. In the system examined in this dissertation, commuters access their final destination via auto, rail, and intermodal auto-to-rail modes. There are numerous highway paths by which a commuter can reach the final destination. Once on the highway, the commuter can switch to rail at stations along the rail route. The commuter may also choose to walk to the rail station closest to the trip\u27s origin. The main focus of this dissertation is the development of models that can estimate traffic volumes and travel costs on intermodal networks. The particular approach used in the models is demand and supply equilibrium where transportation flows are impacted by the performance of the transportation facilities. Several optimization models are formulated based on sound mathematical and economic principles, and their equilibrium conditions are derived and stated clearly. A rigorous analysis of the mathematical properties of the models proves that these conditions are satisfied from the model solutions. The objective of these models is to alleviate some of the deficiencies encountered in the urban transportation planning process. A methodological framework is proposed which utilizes the models to analyze and evaluate operating and pricing policies in intermodal networks. The framework is designed to answer questions of interest to transportation planners, and to investigate the trade-offs between reduction in travel time and the increased cost of capacity improvements. To link theory and practice, the models are applied, within the proposed framework, to the analysis of a real-world intermodal commuter network. Policies aimed at improving the service quality of the intermodal network are evaluated based on their benefits compared to existing conditions. The models are also used to design an optimal rail transit service by computing rail fares and headways to meet future demands. The results of the analysis can be used by transportation planners, decision makers, transit operators, and transportation system managers to find effective ways to alleviate congestion on transportation systems. To this end, this dissertation points to areas of future research to further improve the proposed models

A simultaneous two-dimensionally constraint disaggregate trip generation, distribution and mode choice model - Theory and application for a Swiss national model

The Swiss federal government has asked the IVT, ETH Zürich in collaboration with the TU Dresden and Emch+Berger, Zürich to estimate origin-destination matrices by mode and purpose for the year 2000. The zoning system employing about 3’000 zones of very uneven size required a solution algorithm which is fast, but also able to model generation, distribution and mode choice simultaneously, while addressing the different data availability for traffic within, destined for and passing through the country. The EVA algorithm developed by Lohse (1997) was adapted for this purpose. The key proper-ties of the algorithm are its disaggregate description of demand, its use of appropriate logit-type models for the demand distribution, while maintaining the known marginal distributions of the matrices generated. This last point is of particular importance in a large scale planning applica-tion such as the one at hand. The algorithm calculates trip production and attractions by zone using activity pairs. The 17 ac-tivity pairs distinguished are the combinations of two activities, such as home-work or work-leisure. The relevant daily rates are derived for each of the 17 activity pairs from the 2000 Swiss National Travel Survey (Bundesamt für Statistik and Bundesamt für Raumentwicklung, 2001). The zonal attractivity is defined separately for each trip purpose. In addition to the common variables, such as employment or population, detailed descriptions of education places, shop-ping or leisure facilities, overnight accommodations, shopping centres etc. are employed (see Tschopp, Keller and Axhausen, 2003 for the data). The combined destination and mode choice models estimated for the different traveller types and activity pairs are based on the Swiss National Travel survey (RP data), but incorporates re-sults from a prior SP study on mode and route choice (Vrtic and Axhausen, 2004). The different zone sizes and the different levels of data available required the formulation of new additional models for the transit traffic passing through Switzerland and the traffic originat-ing outside, respectively leaving the country The matching network models for public transport and road traffic were implemented using VISUM 9.0 of PTV AG, Karlsruhe. The timetable based assignment considers all scheduled train services plus the relevant interurban bus services, in particular in rural areas. The paper has three main parts: the first main part derives and describes for the first time the EVA algorithm in English, including the solution method used. The second part summarizes the results of choice model estimation using the generalised cost elasticities of demand by purpose and traveller type. The third part assesses the quality of the results. These assessments are based on two independently derived matrices, which are available for rail-travel from on board - counts and for commuters from the 2000 national census. In addition, we compare the assign-ment results with the available cross section counts. The conclusions discuss computing times, accuracy and issues for further research.

EQUITY AND EFFICIENCY IN MULTI-MODAL TRANSPORTATION SYSTEMS

The land-use pattern for many cities is a central business district surrounded by sprawling suburbs. This pattern can lead to an inefficient and congestion-prone transportation system due to a reliance on automobiles, because high-capacity transit is not efficient in low-density areas where insufficient travelers can access transit. This also poses an equity concern as the monetary cost of faster and more expensive travel disproportionately burdens low income travelers. This dissertation presents a deterministic approximation of a discrete choice model for mixed access and mainline transportation modes, meaning that travelers may use different modes to access a mainline system, such as transit. The purpose is to provide a tractable computationally efficient model to address the first/last mile problem using a system-wide pricing policy that can account for heterogeneous values of time; a problem that is difficult to solve efficiently using a stochastic model. The model is structured for a catchment area around a central access point for a mainline mode, approximating choice by comparing modal utility costs. The underlying utility model accommodates both fixed prices (e.g., parking, fixed tolls, and fares) and distance-based unit prices (e.g. taxi fare, bike-share, and distance tolls) that may be set in a coordinated way with respect to value of time. Using numerical analysis, the deterministic model achieved results within 4% accuracy of a stochastic logit-based model, and within 6\% of measured values. The final model achieved a 57% reduction in generalized travel time and improved the Gini inequity measure from 0.21 to 0.03

Constrained Assortment Optimization under the Cross-Nested Logit Model

We study the assortment optimization problem under general linear constraints, where the customer choice behavior is captured by the Cross-Nested Logit model. In this problem, there is a set of products organized into multiple subsets (or nests), where each product can belong to more than one nest. The aim is to find an assortment to offer to customers so that the expected revenue is maximized. We show that, under the Cross-Nested Logit model, the assortment problem is NP-hard, even without any constraints. To tackle the assortment optimization problem, we develop a new discretization mechanism to approximate the problem by a linear fractional program with a performance guarantee of $\frac{1 - \epsilon}{1+\epsilon}$, for any accuracy level $\epsilon>0$. We then show that optimal solutions to the approximate problem can be obtained by solving mixed-integer linear programs. We further show that our discretization approach can also be applied to solve a joint assortment optimization and pricing problem, as well as an assortment problem under a mixture of Cross-Nested Logit models to account for multiple classes of customers. Our empirical results on a large number of randomly generated test instances demonstrate that, under a performance guarantee of 90%, the percentage gaps between the objective values obtained from our approximation methods and the optimal expected revenues are no larger than 1.2%