Aiming at the problems of poor global search ability, low search accuracy and weak adaptive ability of mayfly algorithm (MA), a multi-strategy mayfly algorithm was proposed. Firstly, an adaptive and dynamically adjusted gravity coefficient was constructed and an attractive enhancement factor was introduced to balance the search and exploitation capabilities. Secondly, the median position was proposed as a part of the population position to strengthen population communication and avoid falling into the locally optimal solution. Finally, the sines and cosines strategy was introduced to enhance the global search ability, improve the convergence precision and enhance the stability. The simulation results of 8 typical functions show that the convergence ability and convergence accuracy of the improved algorithm are improved. When the modified mayflies algorithm is applied to engineering, the cost of adjusting the proportion-integration-differentiation (PID) parameter in the supply chain inventory system is reduced by 9.5% compared with other algorithms, which proves that the algorithm is applicable in engineering.