Buffer dimensioning and control stations positioning with a space partitioning-tabu search approach

We propose an efficient heuristic method based on Space Partitioning (SP) and Tabu Search (TS) to solve the buffer sizing problem in unreliable production lines with several inspection stations. In such problem, we have an unreliable production line consisting of a certain number of machines and fixed-size buffers. These machines produce a single part with two different quality levels: conforming and non-conforming parts. The production line may contain inspection stations whose job is to reject the non-conforming parts from the line. The production line must meet a constant rate of demand for the conforming finished parts. The objective is to minimize the average long term combined storage and shortage costs, while also specifying the optimal location of inspection stations. This design problem is a difficult mixed integer nonlinear program. Solving even a small instance of 10 machines and one inspection station using a direct dynamic programming method takes hours. If we especially increase the number of machines or the inspection stations, the dynamic programming approach becomes drastically inefficient. The method we propose divides the search space into a set of disjoint subspaces using a space partitioning technique. Tabu search is used to intensify the search in the selected subspaces. This combined method finds optimal solutions for small instances in a fraction of dynamic programming time. For the largest instances (up to 20 machines) the dynamic programming approach was unable to solve, our method finds high-quality solutions in reasonable times.