Revenue management under general discrete choice model of consumer behavior

Customer choice behavior, such as 'buy-up' and 'buy-down', is an importantphe-nomenon in a wide range of industries. Yet there are few models ormethodologies available to exploit this phenomenon within yield managementsystems. We make some progress on filling this void. Specifically, wedevelop a model of yield management in which the buyers' behavior ismodeled explicitly using a multi-nomial logit model of demand. Thecontrol problem is to decide which subset of fare classes to offer ateach point in time. The set of open fare classes then affects the purchaseprobabilities for each class. We formulate a dynamic program todetermine the optimal control policy and show that it reduces to a dynamicnested allocation policy. Thus, the optimal choice-based policy caneasily be implemented in reservation systems that use nested allocationcontrols. We also develop an estimation procedure for our model based onthe expectation-maximization (EM) method that jointly estimates arrivalrates and choice model parameters when no-purchase outcomes areunobservable. Numerical results show that this combined optimization-estimation approach may significantly improve revenue performancerelative to traditional leg-based models that do not account for choicebehavior.

Keeping up with the Joneses: An international asset pricing model

We derive an international asset pricing model that assumes local investorshave preferences of the type "keeping up with the Joneses." In aninternational setting investors compare their current wealth with that oftheir peers who live in the same country. In the process of inferring thecountry's average wealth, investors incorporate information from the domesticmarket portfolio. In equilibrium, this gives rise to a multifactor CAPMwhere, together with the world market price of risk, there existscountry-speciffic prices of risk associated with deviations from thecountry's average wealth level. The model performs signifficantly better, interms of explaining cross-section of returns, than the international CAPM.Moreover, the results are robust, both for conditional and unconditionaltests, to the inclusion of currency risk, macroeconomic sources of risk andthe Fama and French HML factor.

A finite-population revenue management model and a risk-ratio procedure for the joint estimation of population size and parameters

Many dynamic revenue management models divide the sale period into a finite number of periods T and assume, invoking a fine-enough grid of time, that each period sees at most one booking request. These Poisson-type assumptions restrict the variability of the demand in the model, but researchers and practitioners were willing to overlook this for the benefit of tractability of the models. In this paper, we criticize this model from another angle. Estimating the discrete finite-period model poses problems of indeterminacy and non-robustness: Arbitrarily fixing T leads to arbitrary control values and on the other hand estimating T from data adds an additional layer of indeterminacy. To counter this, we first propose an alternate finite-population model that avoids this problem of fixing T and allows a wider range of demand distributions, while retaining the useful marginal-value properties of the finite-period model. The finite-population model still requires jointly estimating market size and the parameters of the customer purchase model without observing no-purchases. Estimation of market-size when no-purchases are unobservable has rarely been attempted in the marketing or revenue management literature. Indeed, we point out that it is akin to the classical statistical problem of estimating the parameters of a binomial distribution with unknown population size and success probability, and hence likely to be challenging. However, when the purchase probabilities are given by a functional form such as a multinomial-logit model, we propose an estimation heuristic that exploits the specification of the functional form, the variety of the offer sets in a typical RM setting, and qualitative knowledge of arrival rates. Finally we perform simulations to show that the estimator is very promising in obtaining unbiased estimates of population size and the model parameters.

Microscopic and macroscopic polarization within a combined quantum mechanics and molecular mechanics model

A polarizable quantum mechanics and molecular mechanics model has been extended to account for the difference between the macroscopic electric field and the actual electric field felt by the solute molecule. This enables the calculation of effective microscopic properties which can be related to macroscopic susceptibilities directly comparable with experimental results. By seperating the discrete local field into two distinct contribution we define two different microscopic properties, the so-called solute and effective properties. The solute properties account for the pure solvent effects, i.e., effects even when the macroscopic electric field is zero, and the effective properties account for both the pure solvent effects and the effect from the induced dipoles in the solvent due to the macroscopic electric field. We present results for the linear and nonlinear polarizabilities of water and acetonitrile both in the gas phase and in the liquid phase. For all the properties we find that the pure solvent effect increases the properties whereas the induced electric field decreases the properties. Furthermore, we present results for the refractive index, third-harmonic generation (THG), and electric field induced second-harmonic generation (EFISH) for liquid water and acetonitrile. We find in general good agreement between the calculated and experimental results for the refractive index and the THG susceptibility. For the EFISH susceptibility, however, the difference between experiment and theory is larger since the orientational effect arising from the static electric field is not accurately described

Stationary states and phase diagram for a model of the Gunn effect under realistic boundary conditions

A general formulation of boundary conditions for semiconductor-metal contacts follows from a phenomenological procedure sketched here. The resulting boundary conditions, which incorporate only physically well-defined parameters, are used to study the classical unipolar drift-diffusion model for the Gunn effect. The analysis of its stationary solutions reveals the presence of bistability and hysteresis for a certain range of contact parameters. Several types of Gunn effect are predicted to occur in the model, when no stable stationary solution exists, depending on the value of the parameters of the injecting contact appearing in the boundary condition. In this way, the critical role played by contacts in the Gunn effect is clearly established.

Diffusionless first-order phase transitions in systems with frozen configurational degrees of freedom

We consider systems that can be described in terms of two kinds of degree of freedom. The corresponding ordering modes may, under certain conditions, be coupled to each other. We may thus assume that the primary ordering mode gives rise to a diffusionless first-order phase transition. The change of its thermodynamic properties as a function of the secondary-ordering-mode state is then analyzed. Two specific examples are discussed. First, we study a three-state Potts model in a binary system. Using mean-field techniques, we obtain the phase diagram and different properties of the system as a function of the distribution of atoms on the different lattice sites. In the second case, the properties of a displacive structural phase transition of martensitic type in a binary alloy are studied as a function of atomic order. Because of the directional character of the martensitic-transition mechanism, we find only a very weak dependence of the entropy on atomic order. Experimental results are found to be in quite good agreement with theoretical predictions.

Avalanches in a fluctuationless first-order phase transition in a random-bond Ising model

We study the behavior of the random-bond Ising model at zero temperature by numerical simulations for a variable amount of disorder. The model is an example of systems exhibiting a fluctuationless first-order phase transition similar to some field-induced phase transitions in ferromagnetic systems and the martensitic phase transition appearing in a number of metallic alloys. We focus on the study of the hysteresis cycles appearing when the external field is swept from positive to negative values. By using a finite-size scaling hypothesis, we analyze the disorder-induced phase transition between the phase exhibiting a discontinuity in the hysteresis cycle and the phase with the continuous hysteresis cycle. Critical exponents characterizing the transition are obtained. We also analyze the size and duration distributions of the magnetization jumps (avalanches).

1/c expansion of a separable model of direct-interaction type

The properties of a proposed model of N point particles in direct interaction are considered in the limit of small velocities. It is shown that, in this limit, time correlations cancel out and that Newtonian dynamics is recovered for the system in a natural way.

Studying Avalanches in the ground-state of the two-dimensional random field Ising model driven by an external field

We study the exact ground state of the two-dimensional random-field Ising model as a function of both the external applied field B and the standard deviation ¿ of the Gaussian random-field distribution. The equilibrium evolution of the magnetization consists in a sequence of discrete jumps. These are very similar to the avalanche behavior found in the out-of-equilibrium version of the same model with local relaxation dynamics. We compare the statistical distributions of magnetization jumps and find that both exhibit power-law behavior for the same value of ¿. The corresponding exponents are compared.

1/c expansion of a separable model of direct-interaction type

The properties of a proposed model of N point particles in direct interaction are considered in the limit of small velocities. It is shown that, in this limit, time correlations cancel out and that Newtonian dynamics is recovered for the system in a natural way.

Continuous phase transition in a spin-glass model without time-reversal symmetry

We investigate the phase transition in a strongly disordered short-range three-spin interaction model characterized by the absence of time-reversal symmetry in the Hamiltonian. In the mean-field limit the model is well described by the Adam-Gibbs-DiMarzio scenario for the glass transition; however, in the short-range case this picture turns out to be modified. The model presents a finite temperature continuous phase transition characterized by a divergent spin-glass susceptibility and a negative specific-heat exponent. We expect the nature of the transition in this three-spin model to be the same as the transition in the Edwards-Anderson model in a magnetic field, with the advantage that the strong crossover effects present in the latter case are absent.

Stationary states and phase diagram for a model of the Gunn effect under realistic boundary conditions

A general formulation of boundary conditions for semiconductor-metal contacts follows from a phenomenological procedure sketched here. The resulting boundary conditions, which incorporate only physically well-defined parameters, are used to study the classical unipolar drift-diffusion model for the Gunn effect. The analysis of its stationary solutions reveals the presence of bistability and hysteresis for a certain range of contact parameters. Several types of Gunn effect are predicted to occur in the model, when no stable stationary solution exists, depending on the value of the parameters of the injecting contact appearing in the boundary condition. In this way, the critical role played by contacts in the Gunn effect is clearly established.

Anisotropic fluid with SU(2) type structure in general relativity: A model of localized matter

A model of anisotropic fluid with three perfect fluid components in interaction is studied. Each fluid component obeys the stiff matter equation of state and is irrotational. The interaction is chosen to reproduce an integrable system of equations similar to the one associated to self-dual SU(2) gauge fields. An extension of the BelinskyZakharov version of the inverse scattering transform is presented and used to find soliton solutions to the coupled Einstein equations. A particular class of solutions that can be interpreted as lumps of matter propagating in empty space-time is examined.