A note on “minimizing a weighted quadratic function of job lateness in the single machine system”

A set of jobs is to be scheduled on a single machine where an idle time is allowed to be inserted before the processing of the first job begins. The objective is to find an optimal sequence that minimizes the weighted sum of a quadratic function of job lateness. Sen et al. [Sen, T., Dileepan, P., Lind, M.R., 1995. Minimizing a weighted quadratic function of job lateness in the single machine system. International Journal of Production Economics 42(3), 237–243] presented a branch-and-bound algorithm for the problem; however, as shown in this note, their algorithm does not work because the branching rule for adjacent jobs is not applicable to non-adjacent jobs.     

Adjoint-based Monte Carlo calibration of financial market models

Adjoint methods have recently gained considerable importance in the finance sector, because they allow to quickly compute option sensitivities with respect to a large number of model parameters. In this paper we investigate how the efficiency of adjoint methods can be exploited to speed up the Monte Carlo-based calibration of financial market models. After analyzing the calibration problem both theoretically and numerically, we derive the associated adjoint equation and propose its application in combination with a multi-layer method, for which we prove convergence to a stationary point of the underlying optimization problem. Detailed numerical examples illustrate the performance of the method. In particular, the proposed algorithm reduces the calibration time for a typical equity market model with time-dependent model parameters from over three hours to less than ten minutes on a usual desktop PC.