After-sale service plays an essential role in the electronics retail industry, where providers must supply the required repair parts to consumers during the product warranty period. The rapid evolution of electronic products prevents part suppliers from maintaining continuous production, making it impossible to supply spare parts consistently during the warranty periods and requiring the providers to purchase all necessary spare parts on Last Time Buy (LTB). The uncertainty of customer demand in spare parts brings out difficulties to maintain optimal spare parts inventory. In this paper, we address the challenge of forecasting spare parts demand and optimizing the purchase volumes of spare parts during the regular monthly replenishment period and LTB. First, the problem is well defined and formulated based on the dynamic economic lotsize model. Second, a transfer function model is constructed between historical demand values and product sales, aiming to identify the length of warranty period and forecast the spare part demands. In addition, the linear Model Predictive Control (MPC) scheme is adopted to optimize the purchase volumes of spare part considering the inaccuracy in the demand forecasts. A real-world case considering different categories of spare parts consumption is studied. The results demonstrate that our proposed algorithm outperforms other algorithms in terms of forecasting accuracy and the inventory cost.

In autonomous driving, an unprotected left turn is a highly challenging scenario. It refers to the situation where there is no dedicated traffic signal controlling the left turns; instead, left-turning vehicles rely on the same traffic signal as the through traffic. This presents a significant challenge, as left-turning vehicles may encounter oncoming traffic with high speeds and pedestrians crossing against red lights. To address this issue, we propose a Model Predictive Control (MPC) framework to predict high-quality future trajectories. In particular, we have adopted the infinity norm to describe the obstacle avoidance for rectangular vehicles. The high degree of non-convexity due to coupling terms in our model makes its optimization challenging. Our way to solve it is to employ Sequential Convex Optimization (SCP) to approximate the original non-convex problem near certain initial solutions. Our method performs well in the comparison with the widely used sampling-based planning methods.