Nanda Piersma

Mathematical Programming for Network Revenue Management Revisited

Mathematical programming models for airline seat inventory control provide booking limits and bid-prices for all itineraries and fare classes. E.L. Williamson [Airline network seat inventory control: methodologies and revenue impacts, Ph.D. thesis, Massachusetts Institute of Technology, Cambridge, MA, 1992] finds that simple deterministic approximation methods based on average demand often outperform more advanced probabilistic heuristics. We argue that this phenomenon is due to a booking process that includes nesting of the fare classes, which is ignored in the modeling phase. The differences in the performance between these approximations are studied using a stochastic programming model that includes the deterministic model as a special case. Our study carefully examines the trade-off between computation time and the aggregation level of demand uncertainty with examples of a multi-leg flight and a single-hub network.

A framework for Response Surface Methodology for simulation optimization

We develop a framework for automated optimization of stochastic simulation models using Response Surface Methodology. The framework is especially intended for simulation models where the calculation of the corresponding stochastic response function is very expensive or time-consuming. Response Surface Methodology is frequently used for the optimization of stochastic simulation models in a non-automated fashion. In scientific applications there is a clear need for a standardized algorithm based on Response Surface Methodology. In addition, an automated algorithm is less time-consuming, since there is no need to interfere in the optimization process. In our framework for automated optimization we describe the many choices that have to be made in constructing such an algorithm.

Determining the optimal direct mailing frequency

This paper studies the mailing frequency problem that addresses the issue of how often to send a mailing to an individual customer in order to establish a profitable long-term relation rather than targeting profitable groups of customers at every new mailing instance. The mailing frequency is optimized using long-term objectives but restricts the decisions to the number of mailings to send to the individual over consecutive finite planning periods. A stochastic dynamic programming model is formulated for this problem that can easily be applied to various direct marketing frameworks such as catalog sales or charity organizations. The model is calibrated for a large Dutch non-profit organization and shows that substantial improvements can be achieved by approaching the mailing strategy with the mailing frequency problem, both in the number of mailings to send and in the profits resulting from the responses.

overview of OR techniques for airline revenue management

With the increasing interest in decision support systems and the continuous advance of computer science, revenue management is a discipline which has received a great deal of interest in recent years. Although revenue management has seen many new applications throughout the years, the main focus of research continues to be the airline industry. Ever since LITTLEWOOD (1972) first proposed a solution method for the airline revenue management problem, a variety of solution methods have been introduced. In this paper we give an overview of the solution methods presented throughout the literature.

Automated response surface methodology for stochastic optimization models with unknown variance

Response surface methodology (RSM) is an optimization tool that was introduced in the early 50s by Box and Wilson (1951). In this paper we are interested in finding the best settings for an automated RSM procedure when there is very little information about the objective function. We present a framework of the RSM procedures that is founded in recognizing local optima in the presence of noise. We emphasize both stopping rules and restart procedures. The results show that considerable improvement is possible over the proposed settings in the existing literature.

A Probabilistic Feasibility and Value Analysis of the Generalized Assignment Problem

We study the generalized assignment problem, under a probabilistic model for its cost and requirement parameters. First we address the issue of feasibility by deriving a tight condition on the probabilistic model that ensures that the corresponding problem instances are feasible with probability one as the number of jobs goes to infinity. Then, under an additional condition on the parameters, we show that the optimal solution value, normalized by dividing by the number of jobs, converges with probability one to a constant, again as the number of jobs goes to infinity. Finally, we discuss various examples.

Estimating Parameters of a Microsimulation Model for Breast Cancer Screening Using the Score Function Method

In developing decision-making models for the evaluation of medical procedures, the model parameters can be estimated by fitting the model to data observed in (randomized) trials. For complex models that are implemented by discrete event simulation (microsimulation) of individual life histories, the Score Function (SF) method can potentially be an appropriate approach for such estimation exercises. We test this approach for a microsimulation model for breast cancer screening that is fitted to data from the HIP randomized trial for early detection of breast cancer. Comparison of the parameter values estimated using the SF method and the analytical solution shows that method performs well on this simple model. The precision of the estimated parameter values depends (as expected) on the size of the sample of simulated life histories, and on the number of parameters estimated. Using analytical representations for parts of the microsimulation model can increase the precision of the estimated parameter values. Compared to the Nelder and Mead Simplex method which is often used in stochastic simulation because of its ease of implementation, the SF method is clearly more efficient (ratio computer time: precision of estimates). The additional analytical investment needed to implement the SF method in an (existing) simulation model may well be worth the effort.

A Probabilistic Analysis of the Capacitated Facility Location Problem

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A local search heuristic for unrelated parallel machine scheduling with efficient neighborhood search

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