Disassembly levelling is to determine disassembly structures that specify components to be obtained from end-of-use/life products, and disassembly lot-sizing is to determine the timing and quantity of disassembling end-of-use/life products to satisfy the demands of their components. As an extension of the previous studies that consider them separately, this study integrates the two problems, especially in the form of multi-period model. Particularly, this study considers a generalized integrated problem in which disassembly levels may be different for the products of the same type. To describe the problem mathematically, we develop an integer programming model that minimizes the sum of setup, operation and inventory holding costs. Then, due to the problem complexity, a heuristic algorithm is proposed that consists of two phases: (a) constructing an initial solution using a priority-based greedy heuristic and (b) improving it by removing unnecessary disassembly operations after characterizing the properties of the problem. To show the performance of the heuristic algorithm, computational experiments were performed on various test instances and the results are reported.