On prediction of individual sequences

Sequential randomized prediction of an arbitrary binary sequence isinvestigated. No assumption is made on the mechanism of generating the bit sequence. The goal of the predictor is to minimize its relative loss, i.e., to make (almost) as few mistakes as the best ``expert'' in a fixed, possibly infinite, set of experts. We point out a surprising connection between this prediction problem and empirical process theory. First, in the special case of static (memoryless) experts, we completely characterize the minimax relative loss in terms of the maximum of an associated Rademacher process. Then we show general upper and lower bounds on the minimaxrelative loss in terms of the geometry of the class of experts. As main examples, we determine the exact order of magnitude of the minimax relative loss for the class of autoregressive linear predictors and for the class of Markov experts.

A tractable consideration set structure for network revenue management

Models incorporating more realistic models of customer behavior, as customers choosing from an offerset, have recently become popular in assortment optimization and revenue management. The dynamicprogram for these models is intractable and approximated by a deterministic linear program called theCDLP which has an exponential number of columns. When there are products that are being consideredfor purchase by more than one customer segment, CDLP is difficult to solve since column generationis known to be NP-hard. However, recent research indicates that a formulation based on segments withcuts imposing consistency (SDCP+) is tractable and approximates the CDLP value very closely. In thispaper we investigate the structure of the consideration sets that make the two formulations exactly equal.We show that if the segment consideration sets follow a tree structure, CDLP = SDCP+. We give acounterexample to show that cycles can induce a gap between the CDLP and the SDCP+ relaxation.We derive two classes of valid inequalities called flow and synchronization inequalities to further improve(SDCP+), based on cycles in the consideration set structure. We give a numeric study showing theperformance of these cycle-based cuts.

Solving two production scheduling problems with sequence-dependent set-up times

In today’s competitive markets, the importance of goodscheduling strategies in manufacturing companies lead to theneed of developing efficient methods to solve complexscheduling problems.In this paper, we studied two production scheduling problemswith sequence-dependent setups times. The setup times areone of the most common complications in scheduling problems,and are usually associated with cleaning operations andchanging tools and shapes in machines.The first problem considered is a single-machine schedulingwith release dates, sequence-dependent setup times anddelivery times. The performance measure is the maximumlateness.The second problem is a job-shop scheduling problem withsequence-dependent setup times where the objective is tominimize the makespan.We present several priority dispatching rules for bothproblems, followed by a study of their performance. Finally,conclusions and directions of future research are presented.

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.

Implementation, elimination of weakly dominated strategies and evolutionary dynamics

This paper is concerned with the realism of mechanisms that implementsocial choice functions in the traditional sense. Will agents actually playthe equilibrium assumed by the analysis? As an example, we study theconvergence and stability properties of Sj\"ostr\"om's (1994) mechanism, onthe assumption that boundedly rational players find their way to equilibriumusing monotonic learning dynamics and also with fictitious play. Thismechanism implements most social choice functions in economic environmentsusing as a solution concept the iterated elimination of weakly dominatedstrategies (only one round of deletion of weakly dominated strategies isneeded). There are, however, many sets of Nash equilibria whose payoffs maybe very different from those desired by the social choice function. Withmonotonic dynamics we show that many equilibria in all the sets ofequilibria we describe are the limit points of trajectories that havecompletely mixed initial conditions. The initial conditions that lead tothese equilibria need not be very close to the limiting point. Furthermore,even if the dynamics converge to the ``right'' set of equilibria, it stillcan converge to quite a poor outcome in welfare terms. With fictitious play,if the agents have completely mixed prior beliefs, beliefs and play convergeto the outcome the planner wants to implement.

Measuring and explaining farm inefficiency in a panel data set of mixed farms

This paper aims to estimate a translog stochastic frontier production function in the analysis of a panel of 150 mixed Catalan farms in the period 1989-1993, in order to attempt to measure and explain variation in technical inefficiency scores with a one-stage approach. The model uses gross value added as the output aggregate measure. Total employment, fixed capital, current assets, specific costs and overhead costs are introduced into the model as inputs. Stochasticfrontier estimates are compared with those obtained using a linear programming method using a two-stage approach. The specification of the translog stochastic frontier model appears as an appropriate representation of the data, technical change was rejected and the technical inefficiency effects were statistically significant. The mean technical efficiency in the period analyzed was estimated to be 64.0%. Farm inefficiency levels were found significantly at 5%level and positively correlated with the number of economic size units.

Interbank comptetition with costly screening

We analyse credit market equilibrium when banks screen loan applicants. When banks have a convex cost function of screening, a pure strategy equilibrium exists where banks optimally set interest rates at the same level as their competitors. This result complements Broecker s (1990) analysis, where he demonstrates that no pure strategy equilibrium exists when banks have zero screening costs. In our set up we show that interest rate on loansare largely independent of marginal costs, a feature consistent with the extant empirical evidence. In equilibrium, banks make positive profits in our model in spite of the threat of entry by inactive banks. Moreover, an increase in the number of active banks increases credit risk and so does not improve credit market effciency: this point has important regulatory implications. Finally, we extend our analysis to the case where banks havediffering screening abilities.

Principal curves and principal oriented points

Principal curves have been defined Hastie and Stuetzle (JASA, 1989) assmooth curves passing through the middle of a multidimensional dataset. They are nonlinear generalizations of the first principalcomponent, a characterization of which is the basis for the principalcurves definition.In this paper we propose an alternative approach based on a differentproperty of principal components. Consider a point in the space wherea multivariate normal is defined and, for each hyperplane containingthat point, compute the total variance of the normal distributionconditioned to belong to that hyperplane. Choose now the hyperplaneminimizing this conditional total variance and look for thecorresponding conditional mean. The first principal component of theoriginal distribution passes by this conditional mean and it isorthogonal to that hyperplane. This property is easily generalized todata sets with nonlinear structure. Repeating the search from differentstarting points, many points analogous to conditional means are found.We call them principal oriented points. When a one-dimensional curveruns the set of these special points it is called principal curve oforiented points. Successive principal curves are recursively definedfrom a generalization of the total variance.

Forecasting and turning point predictions in a Bayesian panel VAR model

We provide methods for forecasting variables and predicting turning points in panel Bayesian VARs. We specify a flexible model which accounts for both interdependencies in the cross section and time variations in the parameters. Posterior distributions for the parameters are obtained for a particular type of diffuse, for Minnesota-type and for hierarchical priors. Formulas for multistep, multiunit point and average forecasts are provided. An application to the problem of forecasting the growth rate of output and of predicting turning points in the G-7 illustrates the approach. A comparison with alternative forecasting methods is also provided.

Endogenous bargaining power

We present a novel approach to N-person bargaining, based on the idea thatthe agreement reached in a negotiation is determined by how the directconflict resulting from disagreement would be resolved. Our basic buildingblock is the disagreement function, which maps each set of feasible outcomesinto a disagreement point. Using this function and a weak axiom basedon individual rationality we reach a unique solution: the agreement inthe shadow of conflict, ASC. This agreement may be construed as the limitof a sequence of partial agreements, each of which is reached as a functionof the parties relative power. We examine the connection between ASC andasymmetric Nash solutions. We show the connection between the power ofthe parties embodied in the ASC solution and the bias in the SWF thatwould select ASC as an asymmetric Nash solution.

Proving the performance of a new revenue management system

Revenue management (RM) is a complicated business process that can best be described ascontrol of sales (using prices, restrictions, or capacity), usually using software as a tool to aiddecisions. RM software can play a mere informative role, supplying analysts with formatted andsummarized data who use it to make control decisions (setting a price or allocating capacity fora price point), or, play a deeper role, automating the decisions process completely, at the otherextreme. The RM models and algorithms in the academic literature by and large concentrateon the latter, completely automated, level of functionality.A firm considering using a new RM model or RM system needs to evaluate its performance.Academic papers justify the performance of their models using simulations, where customerbooking requests are simulated according to some process and model, and the revenue perfor-mance of the algorithm compared to an alternate set of algorithms. Such simulations, whilean accepted part of the academic literature, and indeed providing research insight, often lackcredibility with management. Even methodologically, they are usually awed, as the simula-tions only test \within-model" performance, and say nothing as to the appropriateness of themodel in the first place. Even simulations that test against alternate models or competition arelimited by their inherent necessity on fixing some model as the universe for their testing. Theseproblems are exacerbated with RM models that attempt to model customer purchase behav-ior or competition, as the right models for competitive actions or customer purchases remainsomewhat of a mystery, or at least with no consensus on their validity.How then to validate a model? Putting it another way, we want to show that a particularmodel or algorithm is the cause of a certain improvement to the RM process compared to theexisting process. We take care to emphasize that we want to prove the said model as the causeof performance, and to compare against a (incumbent) process rather than against an alternatemodel.In this paper we describe a \live" testing experiment that we conducted at Iberia Airlineson a set of flights. A set of competing algorithms control a set of flights during adjacentweeks, and their behavior and results are observed over a relatively long period of time (9months). In parallel, a group of control flights were managed using the traditional mix of manualand algorithmic control (incumbent system). Such \sandbox" testing, while common at manylarge internet search and e-commerce companies is relatively rare in the revenue managementarea. Sandbox testing has an undisputable model of customer behavior but the experimentaldesign and analysis of results is less clear. In this paper we describe the philosophy behind theexperiment, the organizational challenges, the design and setup of the experiment, and outlinethe analysis of the results. This paper is a complement to a (more technical) related paper thatdescribes the econometrics and statistical analysis of the results.

Exploiting fitness distance correlation of set covering problems

The set covering problem is an NP-hard combinatorial optimization problemthat arises in applications ranging from crew scheduling in airlines todriver scheduling in public mass transport. In this paper we analyze searchspace characteristics of a widely used set of benchmark instances throughan analysis of the fitness-distance correlation. This analysis shows thatthere exist several classes of set covering instances that have a largelydifferent behavior. For instances with high fitness distance correlation,we propose new ways of generating core problems and analyze the performanceof algorithms exploiting these core problems.

Subset correspondence analysis: Visualizing relationships among a selected set of response categories from a questionnaire survey

It is shown how correspondence analysis may be applied to a subset of response categories from a questionnaire survey, for example the subset of undecided responses or the subset of responses for a particular category. The idea is to maintain the original relative frequencies of the categories and not re-express them relative to totals within the subset, as would normally be done in a regular correspondence analysis of the subset. Furthermore, the masses and chi-square metric assigned to the data subset are the same as those in the correspondence analysis of the whole data set. This variant of the method, called Subset Correspondence Analysis, is illustrated on data from the ISSP survey on Family and Changing Gender Roles.

Insurance with frequent trading

This paper looks at the dynamic management of risk in an economy with discrete time consumption and endowments and continuous trading. I study how agents in such an economy deal with all the risk in the economy and attain their Pareto optimal allocations by trading in a few natural securities: private insurance contracts and a common set of derivatives on the aggregate endowment. The parsimonious nature ofthe implied securities needed for Pareto optimality suggests that insuch contexts complete markets is a very reasonable assumption.

Restoration of a lost geological reference point: the loggingstone of Pedralta (Girona, Spain)

The Pedralta is a loggingstone formed of monzonitic leucogranites, which has a volume of about 38 m3 and weighs 101 tons. After its fall in December 1996, a public subscription was opened to meet the expenses of the restoration work, which was completed in May 1999