Customer Order Scheduling Problem (COSP) is an NP-Hard problem that has important practical applications e.g., in the paper industry and the pharmaceutical industry. The existing algorithms to solve COSP still either find low quality solutions or scramble with large-sized problems. In this paper, we propose a new constructive heuristic called repair-based mechanism (RBM) that outperforms the best-known heuristics in the literature. We also propose a mixed neighbourhood local search (MNLS) algorithm. MNLS embeds a number of move operators to diversify the local exploitation making different areas around the current solution accessible. Moreover, we also propose a greedy diversification method to keep the search focussed even when it is in a plateau. Our experimental results on 960 well-known problem instances indicate statistically significant improvement obtained by the proposed MNLS over existing state-of-the-art algorithms. MNLS has found new best solutions for 721 out of the 960 problem instances.