This study reintroduces the famous discriminant functions from Edward Altman and Begley, Ming and Watts (BMW) that were used to predict bankrupts. We will formulate three new discriminant functions which differ from Altman's and BMW's re-estimated Altman model. Altman's models as well as Begley, Ming and Watts's re-estimated Altman model apply to publicly traded industries, whereas the new models formulated in this study are based on retail companies. The three new functions will provide better predictions on retail bankruptcy and they will minimize the chance of misclassifications.

In this note, we will consider the problem of recovering an unknown input function when the output function is observed in its entirety, blurred with functional error. An estimator is constructed whose risk converges at an optimal rate. In this functional model, convergence rates of order 1/n (n is the sample size) are possible, provided that the error distribution is sufficiently concentrated so as to compensate for the ill‐posedness of the inverse of the model operator.

Singapore Mass Rapid Transit (SMRT) operates two train lines with 83 kilometers of track and 48 stations. A total of 77 trains are in operation during peak hours and 41 during off-peak hours. In this article we report on an optimization based approach to develop a computerized train-operator scheduling system that has been implemented at SMRT. The approach involves a bipartite matching algorithm for the generation of night duties and a tabu search algorithm for the generation of day duties. The system automates the train-operator scheduling process at SMRT and produces favorable schedules in comparison with the manual process. It is also able to handle the multiple objectives inherent in the crew scheduling system. While trying to minimize the system wide crew-related costs, the system is also able to address concern with respect to the number of split duties.

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