The increasing recognition of environmental concerns and the adoption of Extended Producer Responsibility (EPR) have contributed significantly to the development of sustainable industries. Reverse logistics (RL) and closed-loop supply chain (CLSC) are two concepts that involve effective management of product returns to minimise consumer waste. In this paper, the authors develop a mathematical model for inventory management in CLSC systems with multiple recovery options, including product, material and energy recoveries. The model was developed based on a supply chain structure that includes a supplier, a manufacturer, a retailer, and a material recovery facility (MRF). The proposed model helps to maximise the profit of the supply chain. A hybrid method of analytical and numerical approaches is used to determine the optimal inventory decisions, including order cycle time and number of shipments between parties. Solution procedures are proposed for decentralised (DDMS) and centralised decision-making structures (CDMS). Furthermore, a profit-sharing mechanism is also analysed in the model. A sensitivity analysis is carried out to investigate the model's behaviour concerning variations in crucial parameters, including demand, product returns, recycling cost, post-consumer recycled content, and energy recoverable item rate. The results of this study show that the CDMS, without profit-sharing, generates the highest profits for the system. On the other hand, implementing a profit-sharing mechanism provides a fairer profit enhancement to the parties involved. Applying the energy recovery at the supplier results in financial benefits for the system. Additional discussion is carried out to understand the impact of energy recovery on the model's optimal solution.