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

Abstract

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.

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Correspondence to Sophie Weiss.

Appendix: Detailed results for Erlang-k and Cox-2 distributed instances

Appendix: Detailed results for Erlang-k and Cox-2 distributed instances

See Tables 10, 11, and 12.

Table 10 Detailed results (Cox-2 distribution, \(S\) = 5)
Table 11 Detailed results (Erlang-k distribution, \(S\) = 7)
Table 12 Detailed results (Cox-2 distribution, \(S\) = 7)

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Weiss, S., Stolletz, R. Buffer allocation in stochastic flow lines via sample-based optimization with initial bounds. OR Spectrum 37, 869–902 (2015). https://doi.org/10.1007/s00291-015-0393-z

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Keywords

  • Buffer allocation
  • Stochastic flow lines
  • Benders Decomposition
  • Sampling
  • Bounds