Buffer allocation in stochastic flow lines via sample-based optimization with initial bounds

The allocation of buffer space in flow lines with stochastic processing times is an important decision, as buffer capacities influence the performance of these lines. The objective of this problem is to minimize the overall number of buffer spaces achieving at least one given goal production rate. We optimally solve this problem with a mixed-integer programming approach by sampling the effective processing times. To obtain robust results, large sample sizes are required. These incur large models and long computation times using standard solvers. This paper presents a Benders Decomposition approach in combination with initial bounds and different feasibility cuts for the Buffer Allocation Problem, which provides exact solutions while reducing the computation times substantially. Numerical experiments are carried out to demonstrate the performance and the flexibility of the proposed approaches. The numerical study reveals that the algorithm is capable to solve long lines with reliable and unreliable machines, including arbitrary distributions as well as correlations of processing times.