Determining a rational planned lead time (PLT) is a critical and difficult problem in production planning, especially for a remanufacturing system. This paper considers an optimisation problem of the PLT in a make-to-order remanufacturing system to coordinate disassembly–remanufacturing–reassembly and to improve performance. This optimisation model is designed to determine the PLT that minimises the inventory holding and shortage costs. Given the unknown distribution of remanufacturing time but with known first and second moments, this model is solved by a min–max approach, which can capture distributions with the same first and second moments. How the PLT and total cost are affected by yield rate with different first and second moments, unit holding cost, unit shortage cost and purchasing lead time are also investigated through numerical examples in this paper. The results of this study are shown to be consistent with practice and can be a support to decision-making in production planning and scheduling for remanufacturing.