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Medical assistance is offered by walk-in clinics (WC). These clinics must keep track of patients' turn in line. Some private companies offer an extra follow-up service to WC patients, which notifies them when their consultation approaches, so patients can use their free time elsewhere than in the waiting room. This paper aims to develop an applied forecasting approach for consultation service time estimation and waiting-time estimation. A model based on particle filters and mixture models helps to estimate the waiting time for each consultation, using historical and new incoming data from patient consultations. The system considers two types of patients, namely, regular and follow-up. Our method gives an estimate of the waiting time for consultation better than simple statistics.

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The agro-food industry wastes tons of oil and grease not suitable for immediate consumption. Their collection mostly relies on the experience of managers and this results in inaccurate visits by truck drivers and operations teams. Indeed, the measurement of by-products waste is complex and thus information is imprecise, making the collecting operations inefficient. In this paper, we propose a model that forecasts the daily input of thousands of industrial and commercial sites of the agrofood industry based on historical data. The algorithm rejects errors and mistakes in the routing-collection-measuring process. In our model, the site container capacity is known and remains constant. The main contribution of this study is to propose a model based on the Theil-Sen constrained regression (Theil-Sen CR) that rejects errors and outliers to simplify the forecast of future collections. We apply this method to a real case study and compare its performance at different collecting sites. The forecasting error is significant compared to Linear Regression (LR). We have calculated, for our industrial partner, based on 12.2 km between sites and a fleet of 200 trucks, a potential reduction of 940 tCO 2 equivalent per year.

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