Discontinuous reception (DRX) is a key technology for reducing the energy consumption of industrial Internet of Things (IIoT) devices. Specifically, DRX allows the devices to operate in a low-power mode when no data reception is scheduled, and its effectiveness depends on the proper configuration of the DRX parameters. In this paper, we characterize the DRX process departing from a semi-Markov chain modeling and detail two ways to set DRX parameters to minimize the device power consumption while meeting a mean delay constraint. The first method exhaustively searches for the optimal configuration, while the second method uses a low-complexity metaheuristic to find a sub-optimal configuration, thus considering ideal and practical DRX configurations. Notably, within the DRX parameters, the inactivity timer (IT) is a caution time that specifies how long a device remains active after the last information exchange as a precedent to a low-power mode. Traditionally, the IT is restarted whenever new data is received, which might sometimes needlessly extend the active time. Herein, we propose a more efficient method in which the transmit base station (BS) explicitly indicates restarting the timer through the control channel only when appropriate. The decision is based on the BS's knowledge about its buffer status. We consider Poisson and bursty traffic models, which are typical in IIoT setups, and verify our proposal's suitability for reducing the devices' energy consumption without significantly compromising the communication latency. Specifically, energy saving gains up to 30% can be obtained regardless of the arrivals rate and delay constraints.