Our two major concerns, which should be taken into consideration as soon as we start the selecting the machining parameters, are the minimization of the machining time and the maintaining of the high-speed machining machine in good state. The manufacturing strategy is one of the parameters which practically influences the time of the different geometrical forms manufacturing, as well as the machine itself. In this article, we propose an optimization methodology of the machining strategy for pockets of complex forms. For doing this, we have developed analytic models expressing the feed rate of the cutting tools trajectory. Then, we have elaborated an optimization method based on the analysis of the different critical parameters so as to distinguish the most suitable strategies to calculate the cutting time and define the machine dynamics. To validate our results, we have compared them to the experimental ones and also to those found in literature.

The minimum variance portfolio weights, the ERC (Equally-weighted Risk Contribution) portfolio, the MDP (Most Diversified Portfolio), the IVP (Inverse Volatility Portfolio), and the MDECP (Maximum Decorrelation Portfolio) are all direct functions of the estimated covariance matrix. We conduct a study of two econometric models, the EWMA historical simulation model and the DCC-GARCH model, to first assess the impact of a specification error in the covariance matrix on these risk-based portfolios over daily, weekly forecast horizons, and to study the performance of these portfolio allocation strategies during the Covid-19 health crisis. In this article We will try to evaluate to what extent the application of portfolio optimization models based on the sole risk criterion would make it possible to develop portfolios capable of remedying the failure of the mean-variance model, particularly in times of the Covid-19 health crisis while addressing the sensitivity of portfolio weightings based on the risk of covariance forecasting. The empirical study is based on four risky assets: two stock indices, namely: S&P 500 and IEF (Exchange Traded Fund), and two commodities, namely: XAU (the PHLX Gold/Silver Sector Index) and USO (the United States Oil Fund), over a four-year period (2018-2022). Our results show that using dynamic conditional correlation (DCC) or exponentially weighted moving average (EWMA) provides similar covariance forecasts. Indeed, risk-based indexing strategies allow for the minimization of specific risk rather than market risk because these aforementioned portfolio optimization models seek to eliminate diversifiable risk and do not offer protection against systematic risk. The best results are obtained with rebalancing every five trading days but with small magnitude deviations.