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Abstract: Consider a risk-averse decision maker in the setting of a single-leg dynamic revenue management problem with revenue controlled by limiting capacity for a fixed set of prices. Instead of focussing on maximising the expected revenue, the decision maker has the main objective of minimising the risk of failing to achieve a given target revenue. Interpreting the revenue management problem in the framework of finite Markov decision processes, we augment the state space of the risk-neutral problem definition and change the objective function to the probability of failing a certain specified target revenue. This enables us to obtain a dynamic programming solution that generates the policy minimising the risk of not attaining this target revenue. We compare this solution with recently proposed risk-sensitive policies in a numerical study and discuss advantages and limitations.
|Copy reference link||DOI: 10.1016/j.dss.2016.01.003|
Abstract: Revenue management (RM) is making a significant impact on pricing research and practice, from aviation and hospitality industries to retailing. However, empirical data conditions in retail are distinct to other industries, in particular in the large number of products within and across categories. To set profitable static prices with established RM models, the data is often simplified by data pruning (the exclusion of subsets of data that are deemed irrelevant or unsuitable) and data aggregation (the combination of disparate data points). However, the impact of such data preprocessing, despite being ubiquitous in retailing, is insufficiently considered in current RM research. This could induce potential sources of bias for the demand model estimates, as well as subsequent effects on the price optimization system, the optimized price set, and the profit maxima, which have not yet been investigated. This paper empirically studies the impact of two commonly used data preprocessing techniques in retail RM, data pruning and data aggregation, using simulated and empirical retail scanner data. We numerically assess potential biases introduced by data preprocessing using a systems perspective in estimating a two-stage demand model, the resulting price elasticities, optimized price sets, and the ensuing profit that it yields. Results show that both data aggregation and data pruning bias demand model estimates, albeit with different effect, but both produce less profitable price sets than unbiased reference solutions. The results demonstrate the practical importance of data preprocessing as a cause for estimation bias and suboptimal pricing in retail price optimization systems.
|Copy reference link||DOI: doi:http://dx.doi.org/10.1016/j.cor.2014.12.004|
Abstract: Abstract Consider a dynamic decision making model under risk with a fixed planning horizon, namely the dynamic capacity control model. The model describes a firm, operating in a monopolistic setting and selling a range of products consuming a single resource. Demand for each product is time-dependent and modeled by a random variable. The firm controls the revenue stream by allowing or denying customer requests for product classes. We investigate risk-sensitive policies in this setting, for which risk concerns are important for many non-repetitive events and short-time considerations. Numerically analysing several risk-averse capacity control policies in terms of standard deviation and conditional-value-at-risk, our results show that only a slight modification of the risk-neutral solution is needed to apply a risk-averse policy. In particular, risk-averse policies which decision rules are functions depending only on the marginal values of the risk-neutral policy perform well. From a practical perspective, the advantage is that a decision maker does not need to compute any risk-averse dynamic program. Risk sensitivity can be easily achieved by implementing risk-averse functional decision rules based on a risk-neutral solution.
|Copy reference link||DOI: doi:http://dx.doi.org/10.1016/j.ijpe.2015.03.027|
Abstract: Abstract Consider a single-leg dynamic revenue management problem with fare classes controlled by capacity in a risk-averse setting. The revenue management strategy aims at limiting the down-side risk, and in particular, value-at-risk. A value-at-risk optimised policy offers an advantage when considering applications which do not allow for a large number of reiterations. They allow for specifying a confidence level regarding undesired scenarios. We introduce a computational method for determining policies which optimises the value-at-risk for a given confidence level. This is achieved by computing dynamic programming solutions for a set of target revenue values and combining the solutions in order to attain the requested multi-stage risk-averse policy. We reduce the state space used in the dynamic programming in order to provide a solution which is feasible and has less computational requirements. Numerical examples and comparison with other risk-sensitive approaches are discussed.
|Copy reference link||DOI: 10.1111/j.1937-5956.2012.01345.x|
Abstract: The network choice revenue management problem models customers as choosing from an offer set, and the firm decides the best subset to offer at any given moment to maximize expected revenue. The resulting dynamic program for the firm is intractable and approximated by a deterministic linear program called the CDLP which has an exponential number of columns. However, under the choice-set paradigm when the segment consideration sets overlap, the CDLP is difficult to solve. Column generation has been proposed but finding an entering column has been shown to be NP-hard. In this study, starting with a concave program formulation called SDCP that is based on segment-level consideration sets, we add a class of constraints called product constraints (σPC), that project onto subsets of intersections. In addition, we propose a natural direct tightening of the SDCP called inline image, and compare the performance of both methods on the benchmark data sets in the literature. In our computational testing on the data sets, 2PC achieves the CDLP value at a fraction of the CPU time taken by column generation. For a large network our 2PC procedure runs under 70 seconds to come within 0.02% of the CDLP value, while column generation takes around 1 hour; for an even larger network with 68 legs, column generation does not converge even in 10 hours for most of the scenarios while 2PC runs under 9 minutes. Thus we believe our approach is very promising for quickly approximating CDLP when segment consideration sets overlap and the consideration sets themselves are relatively small.
|Copy reference link||DOI: 10.1016/j.ejor.2011.09.028|
Abstract: One of the latest developments in network revenue management (RM) is the incorporation of customer purchase behavior via discrete choice models. Many authors presented control policies for the booking process that are expressed in terms of which combination of products to offer at a given point in time and given resource inventories. However, in many implemented RM systems—most notably in the hotel industry—bid price control is being used, and this entails the problem that the recommended combination of products as identified by these policies might not be representable through bid price control. If demand were independent from available product alternatives, an optimal choice of bid prices is to use the marginal value of capacity for each resource in the network. But under dependent demand, this is not necessarily the case. In fact, it seems that these bid prices are typically not restrictive enough and result in buy-down effects.We propose (1) a simple and fast heuristic that iteratively improves on an initial guess for the bid price vector; this first guess could be, for example, dynamic estimates of the marginal value of capacity. Moreover, (2) we demonstrate that using these dynamic marginal capacity values directly as bid prices can lead to significant revenue loss as compared to using our heuristic to improve them. Finally, (3) we investigate numerically how much revenue performance is lost due to the confinement to product combinations that can be represented by a bid price.The heuristic is not restricted to a particular choice model and can be combined with any method that provides us with estimates of the marginal values of capacity. In our numerical experiments, we test the heuristic on some popular networks examples taken from peer literature. We use a multinomial logit choice model which allows customers from different segments to have products in common that they consider to purchase. In most problem instances, our heuristic policy results in significant revenue gains over some currently available alternatives at low computational cost.
|Copy reference link||DOI: 10.1016/j.ejor.2011.06.033|
Abstract: We develop an approximate dynamic programming approach to network revenue management models with customer choice that approximates the value function of the Markov decision process with a non-linear function which is separable across resource inventory levels. This approximation can exhibit significantly improved accuracy compared to currently available methods. It further allows for arbitrary aggregation of inventory units and thereby reduction of computational workload, yields upper bounds on the optimal expected revenue that are provably at least as tight as those obtained from previous approaches. Computational experiments for the multinomial logit choice model with distinct consideration sets show that policies derived from our approach can outperform some recently proposed alternatives, and we demonstrate how aggregation can be used to balance solution quality and runtime.
|Copy reference link||DOI: 10.1080/00207543.2010.518991|
Abstract: One of the fundamental problems in operations management is determining the optimal investment in capacity. Capacity investment consumes resources and the decision, once made, is often irreversible. Moreover, the available capacity level affects the action space for production and inventory planning decisions directly. In this article, we address the joint capacitated lot-sizing and capacity-acquisition problems. The firm can produce goods in each of the finite periods into which the production season is partitioned. Fixed as well as variable production costs are incurred for each production batch, along with inventory carrying costs. The production per period is limited by a capacity restriction. The underlying capacity must be purchased up front for the upcoming season and remains constant over the entire season. We assume that the capacity acquisition cost is smooth and convex. For this situation, we develop a model which combines the complexity of time-varying demand and cost functions and of scale economies arising from dynamic lot-sizing costs with the purchase cost of capacity. We propose a heuristic algorithm that runs in polynomial time to determine a good capacity level and corresponding lot-sizing plan simultaneously. Numerical experiments show that our method is a good trade-off between solution quality and running time.
|Copy reference link||DOI: 10.1016/j.ijpe.2011.01.022|
Abstract: Lot-sizing and capacity planning are important supply chain decisions, and competition and cooperation affect the performance of these decisions. In this paper, we look into the dynamic lot-sizing and resource competition problem of an industry consisting of multiple firms. A capacity competition model combining the complexity of time-varying demand with cost functions and economies of scale arising from dynamic lot-sizing costs is developed. Each firm can replenish inventory at the beginning of each period in a finite planning horizon. Fixed as well as variable production costs incur for each production setup, along with inventory carrying costs. The individual production lots of each firm are limited by a constant capacity restriction, which is purchased up front for the planning horizon. The capacity can be purchased from a spot market, and the capacity acquisition cost fluctuates with the total capacity demand of all the competing firms. We solve the competition model and establish the existence of a capacity equilibrium over the firms and the associated optimal dynamic lot-sizing plan for each firm under mild conditions.
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Abstract: The railway industry offers similar revenue management opportunities to those found in the airline industry. The railway industry caters for the delivery and management of cargo as well as the transport of passengers. Unlike the airline industry, the railway industry has seen relatively little attention to revenue management problems.We provide an overview of the published literature for both passenger and freight rail revenue management. We include a summary of the some the available models and include some possible extensions. From the existing literature and talks with industry, it is clear that that there is room to exploit revenue management techniques in the railway industry, an industry that has revenues of $60 billion in the US and promises huge growth in Europe in the forthcoming years.
Prof. Dr. Joern Meissner
Tel: +49 40 328707-236
Fax: +49 40 328707-209