Equivalence of piecewise-linear approximation and Lagrangian relaxation for network revenue management

The network revenue management (RM) problem arises in airline, hotel, media,and other industries where the sale products use multiple resources. It can be formulatedas a stochastic dynamic program but the dynamic program is computationallyintractable because of an exponentially large state space, and a number of heuristicshave been proposed to approximate it. Notable amongst these -both for their revenueperformance, as well as their theoretically sound basis- are approximate dynamic programmingmethods that approximate the value function by basis functions (both affinefunctions as well as piecewise-linear functions have been proposed for network RM)and decomposition methods that relax the constraints of the dynamic program to solvesimpler dynamic programs (such as the Lagrangian relaxation methods). In this paperwe show that these two seemingly distinct approaches coincide for the network RMdynamic program, i.e., the piecewise-linear approximation method and the Lagrangianrelaxation method are one and the same.

The network origins of aggregate fluctuations

This paper argues that in the presence of intersectoral input-output linkages, microeconomicidiosyncratic shocks may lead to aggregate fluctuations. In particular, itshows that, as the economy becomes more disaggregated, the rate at which aggregatevolatility decays is determined by the structure of the network capturing such linkages.Our main results provide a characterization of this relationship in terms of the importanceof different sectors as suppliers to their immediate customers as well as theirrole as indirect suppliers to chains of downstream sectors. Such higher-order interconnectionscapture the possibility of "cascade effects" whereby productivity shocks to asector propagate not only to its immediate downstream customers, but also indirectlyto the rest of the economy. Our results highlight that sizable aggregate volatility isobtained from sectoral idiosyncratic shocks only if there exists significant asymmetryin the roles that sectors play as suppliers to others, and that the "sparseness" of theinput-output matrix is unrelated to the nature of aggregate fluctuations.

A new compact linear programming formulation for choice network revenue management

The choice network revenue management model incorporates customer purchase behavioras a function of the offered products, and is the appropriate model for airline and hotel networkrevenue management, dynamic sales of bundles, and dynamic assortment optimization.The optimization problem is a stochastic dynamic program and is intractable. A certainty-equivalencerelaxation of the dynamic program, called the choice deterministic linear program(CDLP) is usually used to generate dyamic controls. Recently, a compact linear programmingformulation of this linear program was given for the multi-segment multinomial-logit (MNL)model of customer choice with non-overlapping consideration sets. Our objective is to obtaina tighter bound than this formulation while retaining the appealing properties of a compactlinear programming representation. To this end, it is natural to consider the affine relaxationof the dynamic program. We first show that the affine relaxation is NP-complete even for asingle-segment MNL model. Nevertheless, by analyzing the affine relaxation we derive a newcompact linear program that approximates the dynamic programming value function betterthan CDLP, provably between the CDLP value and the affine relaxation, and often comingclose to the latter in our numerical experiments. When the segment consideration sets overlap,we show that some strong equalities called product cuts developed for the CDLP remain validfor our new formulation. Finally we perform extensive numerical comparisons on the variousbounds to evaluate their performance.

Aggregate fluctuations and the network structure of intersectoral trade

This paper analyzes the flow of intermediate inputs across sectors by adopting a network perspective on sectoral interactions. I apply these tools to show how fluctuationsin aggregate economic activity can be obtained from independent shocks to individualsectors. First, I characterize the network structure of input trade in the U.S. On thedemand side, a typical sector relies on a small number of key inputs and sectors arehomogeneous in this respect. However, in their role as input-suppliers sectors do differ:many specialized input suppliers coexist alongside general purpose sectors functioningas hubs to the economy. I then develop a model of intersectoral linkages that can reproduce these connectivity features. In a standard multisector setup, I use this modelto provide analytical expressions linking aggregate volatility to the network structureof input trade. I show that the presence of sectoral hubs - by coupling productiondecisions across sectors - leads to fluctuations in aggregates.

An analysis of the accounting principles applied by the European Farm Accountancy Data Network

In spite of its relative importance in the economy of many countriesand its growing interrelationships with other sectors, agriculture has traditionally been excluded from accounting standards. Nevertheless, to support its Common Agricultural Policy, for years the European Commission has been making an effort to obtain standardized information on the financial performance and condition of farms. Through the Farm Accountancy Data Network (FADN), every year data are gathered from a rotating sample of 60.000 professional farms across all member states. FADN data collection is not structured as an accounting cycle but as an extensive questionnaire. This questionnaire refers to assets, liabilities, revenues and expenses, and seems to try to obtain a "true and fair view" of the financial performance and condition of the farms it surveys. However, the definitions used in the questionnaire and the way data is aggregated often appear flawed from an accounting perspective. The objective of this paper is to contrast the accounting principles implicit in the FADN questionnaire with generally accepted accounting principles, particularly those found in the IVth Directive of the European Union, on the one hand, and those recently proposed by the International Accounting Standards Committee’s Steering Committeeon Agriculture in its Draft Statement of Principles, on the other hand. There are two reasons why this is useful. First, it allows to make suggestions how the information provided by FADN could be more in accordance with the accepted accounting framework, and become a more valuable tool for policy makers, farmers, and other stakeholders. Second, it helps assessing the suitability of FADN to become the starting point for a European accounting standard on agriculture.