Static Pricing Problems under Mixed Multinomial Logit Demand

Price differentiation is a common strategy for many transport operators. In this paper, we study a static multiproduct price optimization problem with demand given by a continuous mixed multinomial logit model. To solve this new problem, we design an efficient iterative optimization algorithm that asymptotically converges to the optimal solution. To this end, a linear optimization (LO) problem is formulated, based on the trust-region approach, to find a "good" feasible solution and approximate the problem from below. Another LO problem is designed using piecewise linear relaxations to approximate the optimization problem from above. Then, we develop a new branching method to tighten the optimality gap. Numerical experiments show the effectiveness of our method on a published, non-trivial, parking choice model

Modeling Dependencies in Finance using Copulae

In this paper we provide a review of copula theory with applications to finance. We illustrate the idea on the bivariate framework and discuss the simple, elliptical and Archimedean classes of copulae. Since the cop- ulae model the dependency structure between random variables, next we explain the link between the copulae and common dependency measures, such as Kendall's tau and Spearman's rho. In the next section the copulae are generalized to the multivariate case. In this general setup we discuss and provide an intensive literature review of estimation and simulation techniques. Separate section is devoted to the goodness-of-fit tests. The importance of copulae in finance we illustrate on the example of asset allocation problems, Value-at-Risk and time series models. The paper is complemented with an extensive simulation study and an application to financial data.Distribution functions, Dimension Reduction, Risk management, Statistical models

Assortment and Pricing Optimisation under non-conventional customer choice models

Nowadays, extensive research is being done in the area of revenue management, with applications across industries. In the center of this area lays the assortment problem, which amounts to find a subset of products to offer in order to maximise revenue, provided that customers follow a certain model of choice. Most studied models satisfy the following property: whenever the offered set is enlarged, then the probability of selecting a specific product decreases. This property is called regularity in the literature. However, customer behaviour often shows violations of this condition such as the decoy effect, where adding extra options sometimes leads to a positive effect for some products, whose probabilities of being selected increase relative to other products (e.g., including a medium size popcorn slightly cheaper than the large one, with the purpose of making the latter more attractive by comparison). We study two models of customer choice where regularity violations can be accommodated (hence the non-conventionality), and show that the assortment optimisation problem can still be solved in polynomial time. First we analyse the Sequential Multinomial Logit (SML). Under the SML model, products are partitioned into two levels, to capture differences in attractiveness, brand awareness and, or visibility of the products in the market. When a consumer is presented with an assortment of products, she first considers products on the first level and, if none of them is purchased, products in the second level are considered. This model is a special case of the Perception-Adjusted Luce Model (PALM) recently proposed by Echenique et al.(2018). It can explain many behavioural phenomena such as the attraction, compromise, similarity effects and choice overload which cannot be explained by the Multinomial Logit (MNL) model or any discrete choice model based on random utility. We show that the concept of revenue-ordered assortment sets, which contain an optimal assortment under the MNL model, can be generalized to the SML model. More precisely, we show that all optimal assortments under the SML are revenue-ordered by level, a natural generalization of revenue-ordered assortments that contains, at most, a quadratic number of assortments. As a corollary, assortment optimization under the SML is polynomial-time solvable Secondly, the Two-Stage Luce model (2SLM), is a discrete choice model introduced by Echenique and Saito (2018) that generalizes the standard multinomial logit model (MNL). The 2SLM does not satisfy the Independence of Irrelevant Alternatives (IIA) property nor regularity, and to model customer behaviour, each product has an intrinsic utility, and uses a dominance relation between products. Given a proposed assortment S, consumers first discard all dominated products in S before using an MNL model on the remaining products. As a result, the model can capture behaviour that cannot be replicated by any discrete choice model based on random utilities. We show that the assortment problem under the 2SLM is polynomially-solvable. Moreover, we prove that the capacitated assortment optimization problem is NP-hard and present polynomial-time algorithms for the cases where (1) the dominance relation is attractiveness correlated and (2) its transitive reduction is a forest. The proofs exploit a strong connection between assortments under the 2SLM and independent sets in comparability graphs. The third and final contribution is an in-depth study of the pricing problem under the 2SLM. We first note that changes in prices should be reflected in the dominance relation if the differences between the resulting attractiveness are large enough. This is formalised by solving the joint assortment and pricing problem under the Threshold Luce model, where one product dominates another if the ratio between their attractiveness is greater than a fixed threshold. In this setting, we show that this problem can be solved in polynomial time

Socioeconomic Influence on the Health of Older People: Estimates Based on Two Longitudinal Surveys

There is a strong positive relationship between socioeconomic status (SES) and health, but identifying the direction of causation is difficult. This study exploits the longitudinal nature of two Canadian surveys, the Survey of Labour and Income Dynamics and the National Population Health Survey, to study the link from SES to health. For people aged 50 and older who are initially in good health we examine whether changes in health status over the next two to four years are related to prior SES, as represented by income and education. Although the two surveys were designed for quite different purposes the evidence they yield with respect to the probability of remaining in good health is strikingly similar. Both suggest that SES does play a role, that the differences across SES groups are quantitatively significant, that the differences increase with age, and that they are much same for men and women.health; socioeconomic status; SLID; NPHS

Healthy Aging at Older Ages: Are Income and Education Important?

Being higher on the socioeconomic scale is correlated with being in better health, but is there is a causal relationship? Using three years of longitudinal data for individuals aged 50 and older from the Canadian Survey of Labour and Income Dynamics, we study the health transitions for those who were in good health in the first year, focussing especially on income and education. The initial good health restriction removes from the sample those whose incomes may have been affected by a previous history of poor health, thus avoiding a well known problem of econometric endogeneity. We then ask, for those in good health, whether later transitions in health status are related to socioeconomic status. We find that they are -- that changes in health status over the subsequent two years are related in particular to income and education.aging, health, income, education

Stochastic equilibrium models for generation capacity expansion

Capacity expansion models in the power sector were among the first applications of operations research to the industry. The models lost some of their appeal at the inception of restructuring even though they still offer a lot of possibilities and are in many respect irreplaceable provided they are adapted to the new environment. We introduce stochastic equilibrium versions of these models that we believe provide a relevant context for looking at the current very risky market where the power industry invests and operates. We then take up different questions raised by the new environment. Some are due to developments of the industry like demand side management: an optimization framework has difficulties accommodating them but the more general equilibrium paradigm offers additional possibilities. We then look at the insertion of risk related investment practices that developed with the new environment and may not be easy to accommodate in an optimization context. Specifically we consider the use of plant specific discount rates that we derive by including stochastic discount rates in the equilibrium model. Linear discount factors only price systematic risk. We therefore complete the discussion by inserting different risk functions (for different agents) in order to account for additional unpriced idiosyncratic risk in investments. These different models can be cast in a single mathematical representation but they do not have the same mathematical properties. We illustrate the impact of these phenomena on a small but realistic example.capacity adequacy, risk functions, stochastic equilibrium models, stochastic discount factors

Healthy Aging at Older Ages: Are Income and Education Important?

Being higher on the socioeconomic scale is correlated with being in better health, but is there is a causal relationship? Using three years of longitudinal data for individuals aged 50 and older from the Canadian Survey of Labour and Income Dynamics, we study the health transitions for those who were in good health in the first year, focussing especially on income and education. The initial good health restriction removes from the sample those whose incomes may have been affected by a previous history of poor health, thus avoiding a well known problem of econometric endogeneity. We then ask, for those in good health, whether later transitions in health status are related to socioeconomic status. We find that they are that changes in health status over the subsequent two years are related in particular to income and education.aging, health, income, education

Supply Chain Management with Demand Substitution

Demand substitution is a very common practice, but due to its inherent difficulty of mathematical modeling, little has been done on the impact of the demand substitution to the supply chain network.This dissertation studied the impact of demand substitution to a supply chain network. One of the most important measurements of supply chain network, Bullwhip effect, is studied under the demand substitution case. To help understand the influence, a new qualitative measurement of the bullwhip effect is proposed to better capture the essence of the uncertainty associated with supply chain networks. Then a mathematical model is formulated to investigate the bullwhip effect of two products substitution case. Due to the difficulty of the mathematical modeling of the demand substitution process, “Metamodel” methodology is applied to study the relationship among different aspects of the supply chain network. Finally, a network based algorithm is proposed to represented the demand substitution process. Graphical Evaluation And Review Technique (GERT) is used to solve the network model. The results demonstrated the effectiveness of the network model to approximate the demand substitution problem. In the end, the dissertation concludes with a summary of the contributions to the state of the art

Socioeconomic Influences on the Health of Older Canadians: Estimates Based on Two Longitudinal Surveys

It is well established that there is a positive statistical relationship between socioeconomic status (SES) and health but identifying the direction of causation is difficult. This study exploits the longitudinal nature of two Canadian surveys, the Survey of Labour and Income Dynamics and the National Population Health Survey, to study the link from SES to health (as distinguished from the health-to-SES link). For people aged 50 and older who are initially in good health we examine whether changes in health status over the next two to four years are related to prior SES, as represented by income and education. Although the two surveys were designed for different purposes and had different questions for income and health, the evidence they yield with respect to the probability of remaining in good health is similar. Both suggest that SES does play a role and that the differences across SES groups are quantitatively significant, increase with age, and are much the same for men and women.health transitions, income, education