Dilfuza Sunatova
This article examines the models of basic Just-In-Time (JIT) systems using point processes in reverse time. This method permits certain presumptions regarding the workings of actual systems. We thus formulate and solve a few very basic optimal control problems for a system with bounded intensity and for a multi-stage just-in-time system. For the objective functions, results are computed as expected linear or quadratic forms of the trajectories' deviations from the intended values. The statements' proofs employ the martingale method. In logistics tasks, just-in-time systems are frequently taken into consideration, and only (or mostly) deterministic methods are used to describe them. Nonetheless, it is evident that stochastic events are frequently observed in these systems and the related processes.
It is crucial to identify strategies for the best just-in-time process management in these kinds of stochastic situations. In this paper, we propose to use martingale methods for this description. Here, straightforward methods for stochastic JIT process optimization are shown.
