Minimizing the maximal weighted lateness of delivering orders between two railroad stations

We consider the planning problem for freight transportation between two railroad stations. We are required to fulfill orders (transport cars by trains) that arrive at arbitrary time moments and have different value (weight). The speed of trains moving between stations may be different. We consider problem settings with both fixed and undefined departure times for the trains. For the problem with fixed train departure times we propose an algorithm for minimizing the weighted lateness of orders with time complexity $O(qn^2\log n)$ operations, where $q$ is the number of trains and $n$ is the number of orders. For the problem with undefined train departure and arrival times we construct a Pareto optimal set of schedules optimal with respect to criteria $wL_\mathrm{max}$ and $C_\mathrm{max}$ in $O(n^2\mathrm{max}\{n\log n,q\log v\})$ operations, where $v$ is the number of time windows during which the trains can depart. The proposed algorithm allows to minimize both weighted lateness $wL_\mathrm{max}$ and total time of fulfilling freight delivery orders $C_\mathrm{max}$.