Product mix optimisation is one of the most important strategic decisions determining the product type and the corresponding quantity to maximise the system throughput. This paper proposes a new heuristic named shifting bottleneck-driven TOC heuristic (STOCh) for solving product mix problems with multiple bottleneck resources. STOCh is comprised of master product schedule (MPS) generation and its local adjustment. The major improvement is that STOCh dynamically identifies and utilises shifting bottlenecks, rather than fixed bottlenecks commonly used in the existing literature, to avoid being caught in a local optimum. Besides, local adjustment strategy can refine neighbourhood space and limit the search in a high-quality solution space to gain better solutions. Numerical studies show that STOCh outperforms three most famous TOC heuristics in the existing literature, i.e. RTOCh, TOC_AK and TOC_SN. The average relative deviation of the solutions by STOCh from the optimal solutions by CPLEX is only around 3%. Further results show that STOCh performs particularly well when facing multiple bottleneck scenarios, especially when the capacity of bottleneck resource is very scarce. A case study based on real data from a SME in China demonstrates the effectiveness of the proposed STOCh.