The Pricing War Continues: On Competitive Multi-Item Pricing

We study a game with \emph{strategic} vendors who own multiple items and a single buyer with a submodular valuation function. The goal of the vendors is to maximize their revenue via pricing of the items, given that the buyer will buy the set of items that maximizes his net payoff. We show this game may not always have a pure Nash equilibrium, in contrast to previous results for the special case where each vendor owns a single item. We do so by relating our game to an intermediate, discrete game in which the vendors only choose the available items, and their prices are set exogenously afterwards. We further make use of the intermediate game to provide tight bounds on the price of anarchy for the subset games that have pure Nash equilibria; we find that the optimal PoA reached in the previous special cases does not hold, but only a logarithmic one. Finally, we show that for a special case of submodular functions, efficient pure Nash equilibria always exist

Strategic Remanufacturing Decision in a Supply Chain with an External Local Remanufacturer

This paper develops a model for remanufacturing decisions in a two-stage supply chain with one manufacturer, one retailer and one external local remanufacturer, who collects used products and then reproduces them into a new one if the manufacturer does not join in remanufacturing process. This paper is different from most of the extant studies about remanufacturing because they consider decisions of firms rather than supply chains. We mainly focus on the remanufacturing strategy of the manufacturer when there is a local remanufacturer. We derive the equilibrium results for all players and do some comparative studies under different cases. We find that product substitutability can invert the effect of manufacturer’s extension decision on the retailer’s profit. We also consider the effect of channel structure by comparing the decentralized channel with the centralized channel. We find that the manufacturer has a higher incentive to extend its product line in the centralized channel than the decentralized channel; and the competition can strengthen its motivation to extend the line

Analysis of Methodological Presumptions for Optimisation of Marketing Programmes

The analysis focuses on researches on optimisation of marketing programmes conducted over the last decade. On one hand, methods and models suggested by the researchers as well as results obtained by experimental modelling do not comply with contemporary marketing needs and therefore can hardly be used in practice. On the other hand, they are treated as a significant basis for the development of methodological research. Given the results of the analysis, the systemic guidelines were designed. The guidelines were concretised according to specifications based on three models required for marketing programme optimisation. The presentation of the specifications is based on fundamental determinants for the content and composition of models, which are as follow: practice requirements, existing methodological assumptions and methods for applied decision

An Integrated Framework For Configurable Product Assortment Planning

A manufacturer\u27s assortment is the set of products or product configurations that the company builds and offers to its customers. While the literature on assortment planning is growing in recent years, it is primarily aimed at non-durable retail and grocery products. In this study, we develop an integrated framework for strategic assortment planning of configurable products, with a focus on the highly complex automotive industry. The facts that automobiles are highly configurable (with the number of buildable configurations running into thousands, tens of thousands, and even millions) with relatively low sales volumes and the stock-out rates at individual dealerships (even with transshipments) are extremely high, pose significant challenges to traditional assortment planning models. This is particularly the case for markets such as the U.S. that mostly operate in a make-to-stock (MTS) environment. First, we study assortment planning models that account for exogenous demand models and stock-out based substitution while considering production and manufacturing complexity costs and economies-of-scale. We build a mathematical model that maximizes the expected profit for an Original Equipment Manufacturer (OEM) and is a mixed-integer nonlinear problem. We suggest using linear lower/upper bounds that will be solved through a Modified-Branch and Bound procedure and compare the results with commercial mixed-integer nonlinear solvers and show superiority of the proposed method in terms of solution quality as well as computational speed. We then build a modeling framework that identifies the optimal assortment for a manufacturer of automotive products under environmental considerations, in particular, Corporate Average Fuel Economy (CAFE) requirements as well as life-cycle Greenhouse Gas (GHG) emission constraints. We present a numerical experiment consisting of different vehicle propulsion technologies (conventional, Diesel, and hybrid) and study the optimal shares of different technologies for maximizing profitability under different target levels of CAFE requirements. Finally, we develop assortment planning formulations that can jointly identify optimal packages and stand-alone options over different series of the product model. Our numerical experiment reveals that product option packaging has a considerable effect on managing product complexity and profitability

Optimization Of Strategic Planning Processes For Configurable Products: Considerations For Global Supply, Demand, And Sustainability Issues

The assortment planning problem is to decide on the set of products that a retailer or manufacturer will offer to its customers to maximize profitability. While assortment planning research has been expanding in recent years, the current models are inadequate for the needs of a configurable product manufacturer. In particular, we address assortment planning for an automobile manufacturer. We develop models to integrate assortment planning and supply chain management, designed for use by a large automaker in its strategic planning phase. Our model utilizes a multinomial logit model transformed into a mixed integer linear program through the Charnes-Cooper transformation. It is able to scale to problems that contain thousands of configurations to possibly be offered, a necessity given the number of possible configurations an automaker can build. In addition, most research in assortment planning contains simplified costs associated with product complexity. We model a full supply chain and give a rich treatment of the complexity associated with product complexity. We believe that our model can significantly aid automotive manufacturers to balance their product complexity with supply chain complexity, thus increasing profitability. In addition, we study the effect of packaging on the assortment and supply chain of an automaker. We develop a new model for mathematically expressing the effect that packaging has on the way in which customers choose products. Packaging significantly complicates the search space of the assortment planning problem. We introduce a heuristic method based on our packaging model that speeds up the solve times of the models while finding reasonably good solutions. Finally, we extend our initial model to study the effects of sustainability requirements on an automaker\u27s assortment and supply chain. We introduce constraints on the vehicle program average fuel economy, greenhouse gas emissions in the supply chain, and greenhouse gas emissions in the product use phase. We dive deep into each case to glean insights about how automakers can change their decision-making process to balance making their companies more sustainable with profit maximization. While all the examples discussed are from the automotive industry, the models developed can be adapted to address assortment planning for other types of configurable products (e.g., computers, printers, phones)

On the product line selection problem under attraction choice models of consumer behavior

Product line design (PLD) involves important decisions at the interface of operations and marketing that are very costly to implement and change, and, simultaneously, determinant for market success. To evaluate the financial performance of a product line, a number of mathematical programming approaches have been proposed. Problem formulations are typically mixed or pure integer non-linear optimization models that are intractable for exact solution - in particular when empirically supported consumer choice models are incorporated. In this note, we present an exact approach for determining a profit-maximizing product line with continuous prices when consumers choose among available products according to a general and widely applied attraction choice model including the MNL, the BTL, the MCI, and approximately the first choice model. In particular, we show how to efficiently exploit the structural properties resulting from attraction models when consumer behavior is (a) modelled at the aggregate level or (b) disaggregated into customer segments in such a way that each segment can be offered a customized price - a strategy that firms more and more engage in, recognizing it to be not only very profitable but also implementable in the era of e-business. Under these assumptions, we can transform the standard MINLP formulation of the PLD problem into a more convenient convex MIP that can be solved globally with current solvers even for large instances with ten-thousands of products in reasonable time. Therefore our work contributes by accommodating a new trend increasingly encountered in practice and by providing an efficient exact approach to profit-driven PLD for real-world applications.Pricing Product line design

The Rank Pricing Problem with Ties

In the Rank Pricing Problem (RPP), a firm intends to maximize its profit through the pricing of a set of products to sell. Customers are interested in purchasing at most one product among a subset of products. To do so, they are endowed with a ranked list of preferences and a budget. Their choice rule consists in purchasing the highest-ranked product in their list and whose price is below their budget. In this paper, we consider an extension of RPP, the Rank Pricing Problem with Ties (RPPT), in which we allow for indifference between products in the list of preferences of the customers. Considering the bilevel structure of the problem, this generalization differs from the RPP in that it can lead to multiple optimal solutions for the second level problems associated to the customers. In such cases, we look for pessimistic optimal solutions of the bilevel problem : the customer selects the cheapest product. We present a new three-indexed integer formulation for RPPT and introduce two resolution approaches. In the first one, we project out the customer decision variables, obtaining a reduced formulation that we then strengthen with valid inequalities from the former formulation. Alternatively, we follow a Benders decomposition approach leveraging the separability of the problem into a master problem and several subproblems. The separation problems to include the valid inequalities to the master problem dynamically are shown to reduce to min-cost flow problems. We finally carry out extensive computational experiments to assess the performance of the resolution approaches

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

Tractable multi-product pricing under discrete choice models

Thesis (Ph. D.)--Massachusetts Institute of Technology, Sloan School of Management, Operations Research Center, 2013.Cataloged from PDF version of thesis.Includes bibliographical references (pages 199-204).We consider a retailer offering an assortment of differentiated substitutable products to price-sensitive customers. Prices are chosen to maximize profit, subject to inventory/ capacity constraints, as well as more general constraints. The profit is not even a quasi-concave function of the prices under the basic multinomial logit (MNL) demand model. Linear constraints can induce a non-convex feasible region. Nevertheless, we show how to efficiently solve the pricing problem under three important, more general families of demand models. Generalized attraction (GA) models broaden the range of nonlinear responses to changes in price. We propose a reformulation of the pricing problem over demands (instead of prices) which is convex. We show that the constrained problem under MNL models can be solved in a polynomial number of Newton iterations. In experiments, our reformulation is solved in seconds rather than days by commercial software. For nested-logit (NL) demand models, we show that the profit is concave in the demands (market shares) when all the price-sensitivity parameters are sufficiently close. The closed-form expressions for the Hessian of the profit that we derive can be used with general-purpose nonlinear solvers. For the special (unconstrained) case already considered in the literature, we devise an algorithm that requires no assumptions on the problem parameters. The class of generalized extreme value (GEV) models includes the NL as well as the cross-nested logit (CNL) model. There is generally no closed form expression for the profit in terms of the demands. We nevertheless how the gradient and Hessian can be computed for use with general-purpose solvers. We show that the objective of a transformed problem is nearly concave when all the price sensitivities are close. For the unconstrained case, we develop a simple and surprisingly efficient first-order method. Our experiments suggest that it always finds a global optimum, for any model parameters. We apply the method to mixed logit (MMNL) models, by showing that they can be approximated with CNL models. With an appropriate sequence of parameter scalings, we conjecture that the solution found is also globally optimal.by Philipp Wilhelm Keller.Ph.D