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1.
    
We study the classic assortment optimization problem in which a retailer seeks the revenue maximizing set of products to offer to each arriving customer. This study relates two variants of this assortment problem: the space constrained assortment problem, in which the retailer has a limit on the total space of the offered assortment, and the fixed cost assortment problem, in which the retailer incurs a fixed cost for each offered product. In particular, we develop an approximation scheme for the space constrained problem for any random utility choice model that only relies on the ability to solve the corresponding fixed cost assortment problem. We then apply this technique to give a constant factor approximation scheme for the space constrained assortment problem under a classical model for vertically differentiated products. Last, we present computational results to show the efficacy of this approach.  相似文献   

2.
    
This paper considers random coefficients binary choice models. The main goal is to estimate the density of the random coefficients nonparametrically. This is an ill‐posed inverse problem characterized by an integral transform. A new density estimator for the random coefficients is developed, utilizing Fourier–Laplace series on spheres. This approach offers a clear insight on the identification problem. More importantly, it leads to a closed form estimator formula that yields a simple plug‐in procedure requiring no numerical optimization. The new estimator, therefore, is easy to implement in empirical applications, while being flexible about the treatment of unobserved heterogeneity. Extensions including treatments of nonrandom coefficients and models with endogeneity are discussed.  相似文献   

3.
    
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 , 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.  相似文献   

4.
    
Traditional discrete‐choice models assume buyers are aware of all products for sale. In markets where products change rapidly, the full information assumption is untenable. I present a discrete‐choice model of limited consumer information, where advertising influences the set of products from which consumers choose to purchase. I apply the model to the U.S. personal computer market where top firms spend over $2 billion annually on advertising. I find estimated markups of 19% over production costs, where top firms advertise more than average and earn higher than average markups. High markups are explained to a large extent by informational asymmetries across consumers, where full information models predict markups of one‐fourth the magnitude. I find that estimated product demand curves are biased toward being too elastic under traditional models. I show how to use data on media exposure to improve estimated price elasticities in the absence of micro ad data.  相似文献   

5.
有关股票价格行为的研究大多数基于价格连续变化的假定.但最小报价单位引起的价格离散性导致价格变化并不连续.依据排序Probit模型原理,建立价格离散选择Probit模型,并利用高频数据,在价格离散奈件下对中国股市价格行为特征进行考察.实证结果表明:股票价格变化具有"报价回复"和"路径依赖"特征;高市值股票对股市整体走势反映迅速,市场信息能很快被融入到价格中;交易规模对价格变动存在持久的正的影响,非对称信息对股票价格的影响超过了流动性等其它暂时性因素的影响.交易时间间隔对股票价格变化没有显著影响.买卖价差越大、交易间隔越长,股价变动的波动性就越大.  相似文献   

6.
    
We develop a new nonparametric approach for discrete choice and use it to analyze the demand for health insurance in the California Affordable Care Act marketplace. The model allows for endogenous prices and instrumental variables, while avoiding parametric functional form assumptions about the unobserved components of utility. We use the approach to estimate bounds on the effects of changing premiums or subsidies on coverage choices, consumer surplus, and government spending on subsidies. We find that a $10 decrease in monthly premium subsidies would cause a decline of between 1.8% and 6.7% in the proportion of subsidized adults with coverage. The reduction in total annual consumer surplus would be between $62 and $74 million, while the savings in yearly subsidy outlays would be between $207 and $602 million. We estimate the demand impacts of linking subsidies to age, finding that shifting subsidies from older to younger buyers would increase average consumer surplus, with potentially large impacts on enrollment. We also estimate the consumer surplus impact of removing the highly-subsidized plans in the Silver metal tier, where we find that a nonparametric model is consistent with a wide range of possibilities. We find that comparable mixed logit models tend to yield price sensitivity estimates toward the lower end of the nonparametric bounds, while producing consumer surplus impacts that can be both higher and lower than the nonparametric bounds depending on the specification of random coefficients.  相似文献   

7.
    
Estimating structural models is often viewed as computationally difficult, an impression partly due to a focus on the nested fixed‐point (NFXP) approach. We propose a new constrained optimization approach for structural estimation. We show that our approach and the NFXP algorithm solve the same estimation problem, and yield the same estimates. Computationally, our approach can have speed advantages because we do not repeatedly solve the structural equation at each guess of structural parameters. Monte Carlo experiments on the canonical Zurcher bus‐repair model demonstrate that the constrained optimization approach can be significantly faster.  相似文献   

8.
    
We investigate the nature of price competition among firms that produce differentiated products and compete in markets that are limited in extent. We propose an instrumental variables series estimator for the matrix of cross price response coefficients, demonstrate that our estimator is consistent, and derive its asymptotic distribution. Our semiparametric approach allows us to discriminate among models of global competition, in which all products compete with all others, and local competition, in which products compete only with their neighbors. We apply our semiparametric estimator to data from U.S. wholesale gasoline markets and find that, in this market, competition is highly localized.  相似文献   

9.
    
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10.
    
This paper develops a tractable econometric model of optimal migration, focusing on expected income as the main economic influence on migration. The model improves on previous work in two respects: it covers optimal sequences of location decisions (rather than a single once‐for‐all choice) and it allows for many alternative location choices. The model is estimated using panel data from the National Longitudinal Survey of Youth on white males with a high‐school education. Our main conclusion is that interstate migration decisions are influenced to a substantial extent by income prospects. The results suggest that the link between income and migration decisions is driven both by geographic differences in mean wages and by a tendency to move in search of a better locational match when the income realization in the current location is unfavorable.  相似文献   

11.
    
This paper investigates the long‐term stock price effects and equity risk effects of supply chain disruptions based on a sample of 827 disruption announcements made during 1989–2000. Stock price effects are examined starting one year before through two years after the disruption announcement date. Over this time period the average abnormal stock returns of firms that experienced disruptions is nearly –40%. Much of this underperformance is observed in the year before the announcement, the day of the announcement, and the year after the announcement. Furthermore, the evidence indicates that firms do not quickly recover from the negative effects of disruptions. The equity risk of the firm also increases significantly around the announcement date. The equity risk in the year after the announcement is 13.50% higher when compared to the equity risk in the year before the announcement.  相似文献   

12.
    
Discrete‐choice models are widely used to model consumer purchase behavior in assortment optimization and revenue management. In many applications, each customer segment is associated with a consideration set that represents the set of products that customers in this segment consider for purchase. The firm has to make a decision on what assortment to offer at each point in time without the ability to identify the customer's segment. A linear program called the Choice‐based Deterministic Linear Program (CDLP) has been proposed to determine these offer sets. Unfortunately, its size grows exponentially in the number of products and it is NP‐hard to solve when the consideration sets of the segments overlap. The Segment‐based Deterministic Concave Program with some additional consistency equalities (SDCP+) is an approximation of CDLP that provides an upper bound on CDLP's optimal objective value. SDCP+ can be solved in a fraction of the time required to solve CDLP and often achieves the same optimal objective value. This raises the question under what conditions can one guarantee equivalence of CDLP and SDCP+. In this study, we obtain a structural result to this end, namely that if the segment consideration sets overlap with a certain tree structure or if they are fully nested, CDLP can be equivalently replaced with SDCP+. We give a number of examples from the literature where this tree structure arises naturally in modeling customer behavior.  相似文献   

13.
The ready‐to‐eat cereal industry is characterized by high concentration, high price‐cost margins, large advertising‐to‐sales ratios, and numerous introductions of new products. Previous researchers have concluded that the ready‐to‐eat cereal industry is a classic example of an industry with nearly collusive pricing behavior and intense nonprice competition. This paper empirically examines this conclusion. In particular, I estimate price‐cost margins, but more importantly I am able empirically to separate these margins into three sources: (i) that which is due to product differentiation; (ii) that which is due to multi‐product firm pricing; and (iii) that due to potential price collusion. The results suggest that given the demand for different brands of cereal, the first two effects explain most of the observed price‐cost margins. I conclude that prices in the industry are consistent with noncollusive pricing behavior, despite the high price‐cost margins. Leading firms are able to maintain a portfolio of differentiated products and influence the perceived product quality. It is these two factors that lead to high price‐cost margins.  相似文献   

14.
    
We propose a new methodology for structural estimation of infinite horizon dynamic discrete choice models. We combine the dynamic programming (DP) solution algorithm with the Bayesian Markov chain Monte Carlo algorithm into a single algorithm that solves the DP problem and estimates the parameters simultaneously. As a result, the computational burden of estimating a dynamic model becomes comparable to that of a static model. Another feature of our algorithm is that even though the number of grid points on the state variable is small per solution‐estimation iteration, the number of effective grid points increases with the number of estimation iterations. This is how we help ease the “curse of dimensionality.” We simulate and estimate several versions of a simple model of entry and exit to illustrate our methodology. We also prove that under standard conditions, the parameters converge in probability to the true posterior distribution, regardless of the starting values.  相似文献   

15.
    
We consider a discrete‐time infinite‐horizon inventory system with non‐stationary demand, full backlogging, and deterministic replenishment lead time. Demand arrives according to a probability distribution conditional on the state of the world that undergoes Markovian transitions over time. But the actual state of the world can only be imperfectly estimated based on past demand data. We model the inventory replenishment problem for this system as a Markov decision process (MDP) with an uncountable state space consisting of both the inventory position and the most recent belief, a conditional probability mass function, about the actual state of the world. Assuming that the state of the world evolves as an ergodic Markov chain, using the vanishing discount method along with a coupling argument, we prove the existence of an optimal average cost that is independent of the initial system state. For our linear cost structure, we also establish the average‐cost optimality of a belief‐dependent base‐stock policy. We then discretize the uncountable belief space into a regular grid and observe that the average cost under our discretization converges to the optimal average cost as the number of grid points grows large. Finally, we conduct numerical experiments to evaluate the use of a myopic belief‐dependent base‐stock policy as a heuristic for our MDP with the uncountable state space. On a test bed of 108 instances, the average cost obtained from the myopic policy deviates by no more than a few percent from the best lower bound on the optimal average cost obtained from our discretization.  相似文献   

16.
    
This paper develops a method for inference in dynamic discrete choice models with serially correlated unobserved state variables. Estimation of these models involves computing high‐dimensional integrals that are present in the solution to the dynamic program and in the likelihood function. First, the paper proposes a Bayesian Markov chain Monte Carlo estimation procedure that can handle the problem of multidimensional integration in the likelihood function. Second, the paper presents an efficient algorithm for solving the dynamic program suitable for use in conjunction with the proposed estimation procedure.  相似文献   

17.
    
In dynamic discrete choice analysis, controlling for unobserved heterogeneity is an important issue, and finite mixture models provide flexible ways to account for it. This paper studies nonparametric identifiability of type probabilities and type‐specific component distributions in finite mixture models of dynamic discrete choices. We derive sufficient conditions for nonparametric identification for various finite mixture models of dynamic discrete choices used in applied work under different assumptions on the Markov property, stationarity, and type‐invariance in the transition process. Three elements emerge as the important determinants of identification: the time‐dimension of panel data, the number of values the covariates can take, and the heterogeneity of the response of different types to changes in the covariates. For example, in a simple case where the transition function is type‐invariant, a time‐dimension of T = 3 is sufficient for identification, provided that the number of values the covariates can take is no smaller than the number of types and that the changes in the covariates induce sufficiently heterogeneous variations in the choice probabilities across types. Identification is achieved even when state dependence is present if a model is stationary first‐order Markovian and the panel has a moderate time‐dimension (T 6).  相似文献   

18.
    
It is common for suppliers operating in batch‐production mode to deal with patient and impatient customers. This paper considers inventory models in which a supplier provides alternative lead times to its customers: a short or a long lead time. Orders from patient customers can be taken by the supplier and included in the next production cycle, while orders from impatient customers have to be satisfied from the on‐hand inventory. We denote the action to commit one unit of on‐hand inventory to patient or impatient customers as the inventory‐commitment decision, and the initial inventory stocking as the inventory‐replenishment decision. We first characterize the optimal inventory‐commitment policy as a threshold type, and then prove that the optimal inventory‐replenishment policy is a base‐stock type. Then, we extend our analysis to models to consider cases of a multi‐cycle setting, a supply‐capacity constraint, and the on‐line charged inventory‐holding cost. We also evaluate and compare the performances of the optimal inventory‐commitment policy and the inventory‐rationing policy. Finally, to further investigate the benefits and pitfalls of introducing an alternative lead‐time choice, we use the customer‐choice model to study the demand gains and losses, known as demand‐induction and demand‐cannibalization effects, respectively.  相似文献   

19.
    
Many production processes not only produce desired quality products (high‐end products), but also generate yield loss or Not‐Quite‐Perfect Products (NQPPs) that do not fully meet the quality standards. In practice, a manufacturer may choose to (1) scrap all NQPPs at a cost and carry the high‐end products only, or (2) sell some or all NQPPs to a value‐conscious low‐end market and carry both high‐end products and low‐end products (NQPPs). This research studies the optimal decision on production yield loss (scrap or sell) and the corresponding pricing and operational strategies under different practical situations. Building upon a standard marketing model for two separated markets, that is, the high‐end and the low‐end markets, we model the manufacturer’s profit maximization problem as a nonlinear programming problem. We characterize the optimal yield–loss decision and the corresponding optimal pricing for each market and production quantity. We also consider the situation that the NQPPs may face competition in the low‐end market with products designed and produced specifically for that market. In contrast to the common belief that selling NQPPs to a low‐end market can recover some of the cost and hence lead to a higher profit, we show that when the yield rate is small or large enough, selling NQPPs may hurt the manufacturer due to the loss of full control over both markets. This is especially true when competition exists in the low‐end market. This research provides practitioners with detailed guidelines on when and how a specific yield loss (product line or marketing) strategy should be adopted. Managerial insights are generated for the optimal yield loss strategies; numerical tests further demonstrate our results.  相似文献   

20.
We experimentally investigate the sensitivity of bidders demanding multiple units of a homogeneous commodity to the demand reduction incentives inherent in uniform price auctions. There is substantial demand reduction in both sealed bid and ascending price clock auctions with feedback regarding rivals' drop‐out prices. Although both auctions have the same normal form representation, bidding is much closer to equilibrium in the ascending price auctions. We explore the behavioral process underlying these differences along with dynamic Vickrey auctions designed to eliminate the inefficiencies resulting from demand reduction in the uniform price auctions.  相似文献   

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