First results on A Benders Decomposition approach for the optimization of flow lines with stochastic processing times

The allocation of buffers in flow lines with stochastic processing times is an important decision in the design of production systems. The aim is to minimize the overall number of buffer capacities obtaining at least a goal production rate. We derive a mixed integer program by sampling the effective processing times. The computation time with standard solvers becomes very long. To reduce the computation time, a Benders Decomposition approach is developed. The master problem contains the binary variables of the original MIP and the subproblem contains the real-valued decision variables only. Cuts are iteratively derived from the subproblem and added to the master problem such that optimality is proven at the termination. This paper discusses different cuts that influence the performance of the algorithm. Numerical experiments are carried out in order to evaluate these influences.