The Internet of Things (IoT) has become ubiquitous due to its flexibility, ease-of-use, and reduced cost. As a consequence, the industry is adopting these systems in its transformation into Industry 4.0. However, the strict Quality of Service (QoS) requirements of the industry are not met with the default best-effort provisions of the IoT. Most industrial applications require strict guarantees in terms of end-to-end network reliability and latency. For instance, consecutive packet losses can lead to communication disruptions in supply chain systems. Therefore, adaptations are being made to fulfill these requirements with the IEEE Std 802.15.4-2015 Time slotted Channel Hopping (TSCH) link-layer standard and the IPv6 Routing Protocol for Low-Power and Lossy Networks (RPL) standard at the Internet Engineering Task Force (IETF). However, even by employing such industrial protocols, it is still difficult to achieve the expected QoS levels. Considering that RPL constructs and maintains a single-path from a source to a destination if there are potential issues on this path (e.g., queue overflow, variable wireless link quality) packets may suffer unexpected delays and even drops. If we consider a multi-path implementation where each node can replicate a packet into several paths, the transmission reliability improves since each packet copy is used to forward the packet information. However, uncontrolled replication can lead to network flooding, resulting in excessive power consumption. In this article, we present On-Demand Selection (ODeSe), a novel multi-path routing algorithm, which improves our previous work, the Common Ancestor (CA) algorithms, by selecting the most suitable upward forwarders. Moreover, we use the Packet Automatic Repeat reQuest, Replication and Elimination, and Overhearing (PAREO) functions in order to improve network reliability and availability. In order to control the number of relay nodes during a transmission, ODeSe forces each node of the same relay level to select the same Preferred Parent (PP) and the same Alternative Parent (AP). Thus, we address the trade-off between the total number of traversed nodes in the network and high reliability. Using the Cooja network simulator running the Contiki OS, we compare ODeSe against single-path RPL and multi-path RPL with different alternative parent selection algorithms. The results demonstrate that ODeSe outperforms single-path RPL in terms of reliability, and multi-path RPL in terms of energy consumption while maintaining a 99.14% packet delivery ratio.