Abstract

Abstract

Abstract
Forecasting future sales is one of the most important issues that is beyond all strategic and planning decisions in effective operations of retail supply chains. For profitable retail businesses, accurate sales forecasting is crucial in organizing and planning purchasing, production, transportation and labor force. Retail sales series belong to a special type of time series that typically contain strong trend and seasonal patterns, presenting challenges in developing effective forecasting models. This paper compares the forecasting performance of state space models and ARIMA models. The forecasting performance is demonstrated through a case study of retail sales of five different categories of women footwear: Boots, Booties, Flats, Sandals and Shoes. An approach based on cross-validation is used to identify automatically appropriate state space and ARIMA models. The forecasting performance of these models is also compared by examining the out-of-sample forecasts. The results indicate that the overall out-of-sample forecasting performance of ARIMA models evaluated via RMSE, MAE and MAPE is better than state space models. The performance of both forecasting methodologies in producing forecast intervals was also evaluated and the results indicate that ARIMA produces slightly better coverage probabilities than state space models for the nominal 95% forecast intervals. For the nominal 80% forecast intervals the performance of state space models is slightly better.

Abstract
Personnel scheduling problems are widely studied both by the scientific community and by the human resource managers of the companies. The financial impact of the decisions, the welfare of the employees, or more subjective concepts like "fairness" and "balance", turn this case into much more than just a routine problem. When it comes to medical personnel scheduling, additional difficulties can be found, such as uninterrupted work (24 hours per day, 7 days per week), or the quality of service that has to be ensured. The work presented in this paper was based on the rules defined in INRCII - Second International Nurse Rostering Competition - but always with the vision of creating the necessary basis for the future development of an automatic and optimized generic personnel scheduling software.

Abstract
At a time when the need to reduce costs has become part of the day-to-day reality of all educational institutions, it is unthinkable to continue to manually perform those tasks (i.e., the creation of timetables) that can be automated and optimized. The automatic creation of timetables for educational institutions is one of the most studied problems by the scientific community. However, almost all studies have been based on very simplified models of reality that have no practical application. A realistic model of the problem, robust algorithms that are able to find valid solutions in highly restricted environments, and optimization methods that are able to quickly provide quality results are key factors to consider when attempting to solve this (real) problem faced by educational institutions. This paper presents a summary of the work performed by Bullet Solutions over the last few years, from the first stage of understanding and modelling the problem to the final analysis of the results obtained using the developed software under real conditions.

Abstract
In this work, a cross-validation procedure is used to identify an appropriate Autoregressive Integrated Moving Average model and an appropriate state space model for a time series. A minimum size for the training set is specified. The procedure is based on one-step forecasts and uses different training sets, each containing one more observation than the previous one. All possible state space models and all ARIMA models where the orders are allowed to range reasonably are fitted considering raw data and log-transformed data with regular differencing (up to second order differences) and, if the time series is seasonal, seasonal differencing (up to first order differences). The value of root mean squared error for each model is calculated averaging the one-step forecasts obtained. The model which has the lowest root mean squared error value and passes the Ljung-Box test using all of the available data with a reasonable significance level is selected among all the ARIMA and state space models considered. The procedure is exemplified in this paper with a case study of retail sales of different categories of women's footwear from a Portuguese retailer, and its accuracy is compared with three reliable forecasting approaches. The results show that our procedure consistently forecasts more accurately than the other approaches and the improvements in the accuracy are significant.