Soulaymane Kachani

Fluid dynamics models and their applications in transportation and pricing

Abstract Fluid dynamics models provide a powerful deterministic technique to approximate stochasticity in a variety of application areas. In this paper, we study two classes of fluid models, investigate their relationship as well as some of their applications. This analysis allows us to provide analytical models of travel times as they arise in dynamically evolving environments, such as transportation networks as well as supply chains. In particular, using the laws of hydrodynamic theory, we first propose and examine a general second-order fluid model. We consider a first-order approximation of this model and show how it is helpful in analyzing the dynamic traffic equilibrium problem. Furthermore, we present an alternate class of fluid models that are traditionally used in the context of dynamic traffic assignment. By interpreting travel times as price/inventory–sojourn-time relationships, we are also able to connect this approach with a tractable fluid model in the context of dynamic pricing and inventory management.

A Robust Optimization Approach to Capital Rationing and Capital Budgeting

We study the pure capital rationing and the horizon capital budgeting problems using a robust optimization framework. The models and the methodology we propose take into account the uncertainty of the input data. The uncertainty of the cash flows is modeled as a range of values that is allowed for each uncertain data. Unlike stochastic models, this approach does not make assumptions on the probability distribution of uncertain data. Moreover, this approach is highly tractable, easy to implement, and provides insights into portfolio selection problems. An attractive point of the model is that the decision maker can set the value of the parameters that control the robustness of the optimal solution, in order to balance the trade-off between protection level and performance. We illustrate our models with examples that show promising results. We also provide new duality and KKT optimality conditions.

Modeling the Transient Nature of Dynamic Pricing with Demand Learning in a Competitive Environment

This paper focuses on joint dynamic pricing and demand learning in an oligopolistic market. Each firm seeks to learn the price-demand relationship for itself and its competitors, and to set optimal prices, taking into account its competitors’ likely moves. We follow a closed-loop approach to capture the transient aspect of the problem, that is, pricing decisions are updated dynamically over time, using the data acquired thus far.

An Efficiency-Based Approach to Stock Selection

This study investigates the relationship between operational efficiency and stock performance. The analysis is conducted by building an efficiency-based stock selection strategy and assessing its performance over different investment horizons in a contextual and empirical setting provided by the U.S. Information Technology sector. By means of data envelopment analysis (DEA), operational efficiency is quantified into an efficiency score representing a consolidated measure of financial ratios. Based on the rankings of the estimated efficiency scores, various portfolios are formed and their performance is evaluated relative to appropriate market indices and the strategic benchmarks. Our empirical findings demonstrate that there is a significant and positive relationship between operational efficiency and stock performance, and establish that operational efficiency has significant explanatory power in describing the cross-sectional variations of stock returns. This study further presents an economic argument that posits operational efficiency as a systematic risk factor and the most likely source of excess returns of investing in efficient firms.