**2. Problem Formulation**

This section formulates the concerned scheduling scheme as a combinatorial optimization problem, which is focused on how to use unmanned dump trucks and excavators to deliver mine materials efficiently in open-pit mining. The purpose of the combinatorial optimization problem is to minimize the consumed energies, maximize the mineral transport capacity, and minimize the operation time.

In this work, unmanned dump trucks and excavators are the two types of machinery operated in the concerned mining transport scheme. Given that the terrain of the open-pit mine is not even, some parts of the terrain occupied by obstacles are not drivable; thus, the uneven parts of the terrain are regarded as obstacles. Suppose that the number of deployed unmanned dump trucks is Ntruck. This work assumes that each excavator is fixed at a loading spot, a designated location where loading operations occur. The gross number of loading spots is denoted as Nloading\_spots. Similarly, we assume that the number of unloading spots is Nunloading\_spots. Before its battery is completely depleted, an unmanned dump truck should visit a charging spot for battery recharging. The basic working states of an unmanned dump truck include moving to the loading spot, loading, moving to the unloading spot, unloading, and moving to the charging spot. Given that the excavators are fixed, operating the devices in this open-pit mine means manipulating the Ntruck unmanned dump trucks. Thus, the concerned scheduling task is about deciding the working states and targets of each unmanned dump truck in a sequence for the next Nstep steps.
