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During retail stage of food supply chain (FSC), food waste and stock-outs occur mainly due to inaccurate sales forecasting which leads to inappropriate ordering of products. The daily demand for a fresh food product is affected by external factors, such as seasonality, price reductions and holidays. In order to overcome this complexity and inaccuracy, the sales forecasting should try to consider all the possible demand influencing factors. The objective of this study is to develop a Seasonal Autoregressive Integrated Moving Average with external variables (SARIMAX) model which tries to account all the effects due to the demand influencing factors, to forecast the daily sales of perishable foods in a retail store. With respect to performance measures, it is found that the proposed SARIMAX model improves the traditional Seasonal Autoregressive Integrated Moving Average (SARIMA) model.

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Four-band color imaging of the Martian surface using the Color and Stereo Surface Imaging System (CaSSIS) onboard the European Space Agency’s ExoMars Trace Gas Orbiter exhibits a high color diversity in specific regions. Not only is the correlation of color diversity maps with local morphological properties desirable, but mineralogical interpretation of the observations is also of great interest. The relatively high spatial resolution of CaSSIS data mitigates its low spectral resolution. In this paper, we combine the broad-band imaging of the surface of Mars, acquired by CaSSIS with hyperspectral data from the Compact Reconnaissance Imaging Spectrometer (CRISM) onboard NASA’s Mars Reconnaissance Orbiter to achieve a fusion of both datasets. We achieve this using dimensionality reduction and data clustering of the high dimensional datasets from CRISM. In the presented research, CRISM data from the Coprates Chasma region of Mars are tested with different machine learning methods and compared for robustness. With the help of a suitable metric, the best method is selected and, in a further step, an optimal cluster number is determined. To validate the methods, the so-called “summary products” derived from the hyperspectral data are used to correlate each cluster with its mineralogical properties. We restrict the analysis to the visible range in order to match the generated clusters to the CaSSIS band information in the range of 436–1100 nm. In the machine learning community, the so-called UMAP method for dimensionality reduction has recently gained attention because of its speed compared to the already established t-SNE. The results of this analysis also show that this method in combination with the simple K-Means outperforms comparable methods in its efficiency and speed. The cluster size obtained is between three and six clusters. Correlating the spectral cluster maps with the given summary products from CRISM shows that four bands, and especially the NIR bands and VIS albedo, are sufficient to discriminate most of these clusters. This demonstrates that features in the four-band CaSSIS images can provide robust mineralogical information, despite the limited spectral information using semi-automatic processing.