An Adaptive Gradient Algorithm for Solving the Buffer Allocation Problem in Unreliable Production Lines

The optimal allocation of buffers is an important research issue in the area of manufacturing system design and optimization, as buffers can have a large impact on system performance. In this study, we consider one of the most common buffer allocation problems in unreliable production lines: maximizing the throughput of a line subject to a total buffer capacity constraint. We propose an efficient gradient algorithm to solve this problem. Compared to the existing gradient algorithms based on approximate evaluation methods, the proposed algorithm uses simulation to evaluate throughput and can be applied to a wider range of systems, such as production lines with non-exponential failures. To address the challenge posed by the time-consuming nature of simulation, the algorithm employs an adaptive search mechanism that can greatly reduce the number of simulation runs. The algorithm automatically sets the initial search step size based on the scale of buffer allocation problems and dynamically adjusts it during the search process. The algorithmic complexity is characterized as O(lnN), where N denotes the total buffer capacity to be allocated. Numerical results demonstrate that the adaptive gradient algorithm is as accurate as the fixed-step gradient algorithm, while the computational time required is significantly reduced. Therefore, the algorithm shows a substantial advantage in solving large-scale buffer allocation problems.