The robust single machine scheduling problem with uncertain release and processing times

In this work, we study the single machine scheduling problem with uncertain release times and processing times of jobs. We adopt a robust scheduling approach, in which the measure of robustness to be minimized for a given sequence of jobs is the worst-case objective function value from the set of all possible realizations of release and processing times. The objective function value is the total flow time of all jobs. We discuss some important properties of robust schedules for zero and non-zero release times, and illustrate the added complexity in robust scheduling given non-zero release times. We propose heuristics based on variable neighborhood search and iterated local search to solve the problem and generate robust schedules. The algorithms are tested and their solution performance is compared with optimal solutions or lower bounds through numerical experiments based on synthetic data

Choice probability generating functions

This paper establishes that every random utility discrete choice model (RUM) has a representation that can be characterized by a choice-probability generating function (CPGF) with specific properties, and that every function with these specific properties is consistent with a RUM. The choice probabilities from the RUM are obtained from the gradient of the CPGF. Mixtures of RUM are characterized by logarithmic mixtures of their associated CPGF. The paper relates CPGF to multivariate extreme value distributions, and reviews and extends methods for constructing generating functions for applications. The choice probabilities of any ARUM may be approximated by a cross-nested logit model. The results for ARUM are extended to competing risk survival models.Discrete choice; random utility; mixture models; duration models; logit; generalised extreme value; multivariate extreme value

A theoretical analysis of the cross-nested logit model

The emergence of Intelligent Transportation Systems and the associated technologies has increased the need for complex models and algorithms. Namely, real-time information systems, directly influencing transportation demand, must be supported by detailed behavioral models capturing travel and driving decisions. Discrete choice models methodology provide an appropriate framework to capture such behavior. Recently, the Cross-Nested Logit (CNL) model has received quite a bit of attention in the literature to capture decisions such as mode choice, departure time choice and route choice. %The CNL model is an extension of the Nested Logit model, providing %more flexibility at the cost of some complexity in the model formulation. In this paper, we develop on the general formulation of the Cross Nested Logit model proposed by Ben-Akiva and Bierlaire (1999) and based on the Generalized Extreme Value (GEV) model. We show that it is equivalent to the formulations byby Papola (2004) and Wen and Koppelman (2001). We also show that the formulations by Small(1987) and Vovsha(1997) are special cases of this formulation. We formally prove that the Cross-Nested Logit model is indeed a member of the GEV models family. In doing so, we clearly distinguish between conditions that are necessary to prove consistency with the GEV theory, from normalization conditions. Finally, we propose to estimate the model with non-linear programming algorithms, instead of heuristics proposed in the literature. In order to make it operational, we provide the first derivatives of the log-likelihood function, which are necessary to such optimization procedure

Bayesian Estimation of Mixed Multinomial Logit Models: Advances and Simulation-Based Evaluations

Variational Bayes (VB) methods have emerged as a fast and computationally-efficient alternative to Markov chain Monte Carlo (MCMC) methods for scalable Bayesian estimation of mixed multinomial logit (MMNL) models. It has been established that VB is substantially faster than MCMC at practically no compromises in predictive accuracy. In this paper, we address two critical gaps concerning the usage and understanding of VB for MMNL. First, extant VB methods are limited to utility specifications involving only individual-specific taste parameters. Second, the finite-sample properties of VB estimators and the relative performance of VB, MCMC and maximum simulated likelihood estimation (MSLE) are not known. To address the former, this study extends several VB methods for MMNL to admit utility specifications including both fixed and random utility parameters. To address the latter, we conduct an extensive simulation-based evaluation to benchmark the extended VB methods against MCMC and MSLE in terms of estimation times, parameter recovery and predictive accuracy. The results suggest that all VB variants with the exception of the ones relying on an alternative variational lower bound constructed with the help of the modified Jensen's inequality perform as well as MCMC and MSLE at prediction and parameter recovery. In particular, VB with nonconjugate variational message passing and the delta-method (VB-NCVMP-Delta) is up to 16 times faster than MCMC and MSLE. Thus, VB-NCVMP-Delta can be an attractive alternative to MCMC and MSLE for fast, scalable and accurate estimation of MMNL models

Income and distance elasticities of values of travel time savings: New Swiss results

This paper presents the findings of a study looking into the valuation of travel time savings (VTTS) in Switzerland, across modes as well as across purpose groups. The study makes several departures from the usual practice in VTTS studies, with the main one being a direct representation of the income and distance elasticity of the VTTS measures. Here, important gains in model performance and significantly different results are obtained through this approach. Additionally, the analysis shows that the estimation of robust coefficients for congested car travel time is hampered by the low share of congested time in the overall travel time, and the use of an additional rate-of-congestion coefficient, in addition to a generic car travel time coefficient, is preferable. Finally, the analysis demonstrates that the population mean of the indicators calculated is quite different from the sample means and presents methods to calculate those, along with the associated variances. These variances are of great interest as they allow the generation of confidence intervals, which can be extremely useful in cost-benefit analyses

A Simulation-Based Optimization Framework for Urban Transportation Problems

This paper proposes a simulation-based optimization (SO) method that enables the efficient use of complex stochastic urban traffic simulators to address various transportation problems. It presents a metamodel that integrates information from a simulator with an analytical queueing network model. The proposed metamodel combines a general-purpose component (a quadratic polynomial), which provides a detailed local approximation, with a physical component (the analytical queueing network model), which provides tractable analytical and global information. This combination leads to an SO framework that is computationally efficient and suitable for complex problems with very tight computational budgets. We integrate this metamodel within a derivative-free trust region algorithm. We evaluate the performance of this method considering a traffic signal control problem for the Swiss city of Lausanne, different demand scenarios, and tight computational budgets. The method leads to well-performing signal plans. It leads to reduced, as well as more reliable, average travel times