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Robust assortment optimization in revenue management under the multinomial logit choice model
"... We study robust formulations of assortment optimization problems under the multinomial logit choice model. The novel aspect of our formulations is that the true parameters of the logit model are assumed to be unknown, and we represent the set of likely parameter values by a compact uncertainty set. ..."
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Cited by 6 (1 self)
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We study robust formulations of assortment optimization problems under the multinomial logit choice model. The novel aspect of our formulations is that the true parameters of the logit model are assumed to be unknown, and we represent the set of likely parameter values by a compact uncertainty set. The objective is to find an assortment that maximizes the worst case expected revenue over all parameter values in the uncertainty set. We consider both static and dynamic settings. The static setting ignores inventory consideration, while in the dynamic setting, there is a limited initial inventory that must be allocated over time. We give a complete characterization of the optimal policy in both settings, show that it can be computed efficiently, and derive operational insights. We also propose a family of uncertainty sets that enables the decision maker to control the tradeoff between increasing the average revenue and protecting against the worst case scenario. Numerical experiments show that our robust approach, combined with our proposed family of uncertainty sets, is especially beneficial when there is significant uncertainty in the parameter values. When compared to other methods, our robust approach yields over 10 % improvement in the worst case performance, but it can also maintain comparable average revenue if average revenue is the performance measure of interest. 1.
List pricing versus dynamic pricing: Impact on the revenue risk
, 2008
"... We consider the problem of a firm selling multiple products that consume a single resource over a finite time period. The amount of the resource is exogenously fixed. We analyze the difference between a dynamic pricing policy and a list price capacity control policy. The dynamic pricing policy adjus ..."
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Cited by 3 (3 self)
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We consider the problem of a firm selling multiple products that consume a single resource over a finite time period. The amount of the resource is exogenously fixed. We analyze the difference between a dynamic pricing policy and a list price capacity control policy. The dynamic pricing policy adjusts prices steadily resolving the underlying problem every time step, whereas the list pricing policy sets static prices once but controls the capacity by allowing or preventing product sales. As steady price changes are often costly or unachievable in practice, we investigate the question of how much riskier it is to apply a list pricing policy rather than a dynamic pricing policy. We conduct several numerical experiments and compare expected revenue, standard deviation, and conditionalvalueatrisk between the pricing policies. The differences between the policies show that list pricing can be a useful strategy when dynamic pricing is costly or impractical.
Revenue management with incomplete demand information
 In J. J
"... Consider a seller who is endowed with a fixed number of units of a product that she can sell to a pricesensitive and stochastically arriving stream of consumers during a finite time horizon. The seller has incomplete demand information, that is, there are some characteristics of the demand process ..."
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Cited by 3 (0 self)
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Consider a seller who is endowed with a fixed number of units of a product that she can sell to a pricesensitive and stochastically arriving stream of consumers during a finite time horizon. The seller has incomplete demand information, that is, there are some characteristics of the demand process (e.g., the arrival rate or the price elasticity) that she does not know with certainty. The seller’s problem is to dynamically adjust the product’s price to maximize the expected revenues she can collect if no replenishment is possible during the selling season.
Risk Management Policies for Dynamic Capacity Control
, 2009
"... 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 timedependent and mod ..."
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Cited by 1 (1 self)
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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 timedependent and modeled by a random variable. The firm controls the revenue stream by allowing or denying customer requests for product classes. We investigate risksensitive policies in this setting, for which risk concerns are important for many nonrepetitive events and shorttime considerations. Analyzing several numerically riskaverse capacity control policies in terms of standard deviation and conditionalvalueatrisk, our results show that only a slight modification of the riskneutral solution is needed to apply a riskaverse policy. In particular, riskaverse policies which decision rules are functions depending only on the marginal values of the riskneutral policy perform well. The risk sensitivity of a policy only depends on the current state but it does not matter whether riskneutral or riskaverse decisions led to the state. From a practical perspective, the advantage is that a decision maker does not need to compute any riskaverse dynamic program. Risk sensitivity can be easily achieved by implementing riskaverse functional decision rules based on a riskneutral solution.
ROBUST REVENUE MANAGEMENT WITH LIMITED INFORMATION: THEORY AND EXPERIMENTS
, 2008
"... Revenue management (RM) problems with full probabilistic information are well studied. However, as RM practice spreads to new businesses and industries, there are more and more applications where no or only limited information is available. In that respect, it is highly desirable to develop models ..."
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Revenue management (RM) problems with full probabilistic information are well studied. However, as RM practice spreads to new businesses and industries, there are more and more applications where no or only limited information is available. In that respect, it is highly desirable to develop models and methods that rely on less information, and make fewer assumptions about the underlying uncertainty. On the other hand, a decision maker may not only lack data and accurate forecasting in a new application, but he may have objectives (e.g. guarantees on worstcase profits) other than maximizing the average performance of a system. This dissertation focuses on the multifare single resource (leg) RM problem with limited information. We only use lower and upper bounds (i.e. a parameter range), instead of any particular probability distribution or random process to characterize an uncertain parameter. We build models that guarantee a certain performance level under all possible realizations within the given bounds. Our methods are based on the regret criterion, where a decision maker compares his performance to a perfect hindsight (offline) performance. We use competitive analysis of online
Robust New Product Pricing
, 2015
"... We study the pricing decision for a monopolist launching a new innovation. At the time of launch, we assume that the monopolist has incomplete information about the true demand curve. Despite the lack of objective information the firm must set a retail price to maximize total profits. To model this ..."
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We study the pricing decision for a monopolist launching a new innovation. At the time of launch, we assume that the monopolist has incomplete information about the true demand curve. Despite the lack of objective information the firm must set a retail price to maximize total profits. To model this environment, we develop a novel twoperiod nonBayesian framework, where the monopolist sets the price in each period based only on a nonparametric set of all feasible demand curves. Optimal prices are dynamic as prices in any period allow the firm to learn about demand and improve future pricing decisions. Our main results show that the direction of dynamic introductory prices (versus static) depends on the type of heterogeneity in the market. We find (1) when consumers have homogeneous preferences, introductory dynamic price is higher than the static price (2) when consumers have heterogeneous preferences and the monopolist has no exante information, the introductory dynamic price is the same as the static price and (3) when consumers have heterogeneous preferences and the monopolist has exante information, the introductory dynamic price is lower than the static price. Further, the degree of this initial reduction increases with the amount of heterogeneity in the exante information.
INFORMS doi 10.1287/xxxx.0000.0000 c © 0000 INFORMS Intertemporal Pricing under Minimax Regret
, 2015
"... We consider the pricing problem faced by a monopolist who sells a product to a population of consumers over a finite time horizon. Customers are heterogeneous along two dimensions: (i) willingnesstopay for the product and (ii) arrival time during the selling season. We assume that the seller knows ..."
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We consider the pricing problem faced by a monopolist who sells a product to a population of consumers over a finite time horizon. Customers are heterogeneous along two dimensions: (i) willingnesstopay for the product and (ii) arrival time during the selling season. We assume that the seller knows only the support of the customers ’ valuations and do not make any other distributional assumptions about customers’ willingnesstopay or arrival times. We consider a robust formulation of the seller’s pricing problem which is based on the minimization of her worstcase regret, a framework first proposed by Bergemann and Schlag (2008) in the context of static pricing. We consider two distinct cases of customers ’ purchasing behavior: myopic and strategic customers. For both of these cases, we characterize optimal price paths. For myopic customers, the regret is determined by the price at a critical time. Depending on the problem parameters, this critical time will be either the end of the selling season or it will be a time that equalizes the worstcase regret generated by undercharging customers and the worstcase regret generated by customers waiting for the price to fall. The optimal pricing strategy is not unique except at the critical time. For strategic consumers, we develop a robust mechanism design approach to compute an optimal policy. Depending on the problem parameters, the optimal policy might lead some consumers to wait until the end of the selling season and might price others out of the market. Under strategic customers, the optimal price equalizes the
A Network Airline Revenue Management Framework Based on Decomposition by Origins and Destinations
"... Abstract: We propose a framework for solving airline revenue management problems on large networks. This framework is based on a mathematical programming model that decomposes the network into origindestination pairs so that each pair can be treated as a single flight leg problem. We first discuss ..."
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Abstract: We propose a framework for solving airline revenue management problems on large networks. This framework is based on a mathematical programming model that decomposes the network into origindestination pairs so that each pair can be treated as a single flight leg problem. We first discuss that the proposed framework is quite generic in the sense that not only several wellknown models from the literature fit into this framework but also many single flight leg models can be easily extended to a network setting through the prescribed construction. Then, we formally analyze the structure of the overall mathematical programming model and establish its relationship with other models frequently used in practice. The application of the proposed framework is illustrated through two examples based on static and dynamic singleleg models, respectively. These illustrative examples are then benchmarked against several existing methods on a set of reallife network problems acquired from a major European airline.
Seat Inventory Control with Limited Demand Information
"... In this paper, we consider the classical single resource (leg) problem in revenue management for the case where demand information is limited. Our approach employs a competitive analysis, which guarantees a certain performance level under all possible input sequences where the only information avail ..."
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In this paper, we consider the classical single resource (leg) problem in revenue management for the case where demand information is limited. Our approach employs a competitive analysis, which guarantees a certain performance level under all possible input sequences where the only information available consists of lower and/or upper bounds on demand. We consider both competitive ratio and absolute regret performance criteria. We derive the best possible static policies whose booking limits remain constant throughout the booking horizon, under the various models we analyze. We prove that the optimal policies have the form of nested protection levels. We also show how dynamic policies, whose booking limits may be adjusted at any time based on the history of bookings, can be obtained. We provide extensive computational experiments and compare our methods to existing ones. The results of the experiments demonstrate the effectiveness of these new robust methods. 1
CUSTOMERCENTRIC REVENUE MANAGEMENT IN
"... Manufacturing providers aim not only for a revenue maximizing allocation of their limited production capacity but also for the establishment of longterm customer relations. Due to longterm contracts and strategic reference customers, users of traditional revenue management systems already account ..."
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Manufacturing providers aim not only for a revenue maximizing allocation of their limited production capacity but also for the establishment of longterm customer relations. Due to longterm contracts and strategic reference customers, users of traditional revenue management systems already account for varying worthiness of clients, and intuitively ignore or override booking control suggestions, such as order’s denial or pricing level, in order not to endanger customer relations. So with a view to a holistic approach, the integration of both management concepts, each of decisive competitive impact, is advised. However, an implemented ITsystem, that provides the revenue analyst with greater insights, higher accuracy, quality and trust in decision process, is still missing in manufacturing industry. This reflects the common frustration of managers and analysts in practice when dealing with