A scenario generation-based lower bounding approach for stochastic scheduling problems

L Liao, S C Sarin and H D Sherali
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L Liao: Virginia Polytechnic Institute and State University, Virginia, USA
S C Sarin: Virginia Polytechnic Institute and State University, Virginia, USA
H D Sherali: Virginia Polytechnic Institute and State University, Virginia, USA

Journal of the Operational Research Society, 2012, vol. 63, issue 10, 1410-1420

Abstract: In this paper, we investigate scenario generation methods to establish lower bounds on the optimal objective value for stochastic scheduling problems that contain random parameters with continuous distributions. In contrast to the Sample Average Approximation (SAA) approach, which yields probabilistic bound values, we use an alternative bounding method that relies on the ideas of discrete bounding and recursive stratified sampling. Theoretical support is provided for deriving exact lower bounds for both expectation and conditional value-at-risk objectives. We illustrate the use of our method on the single machine total weighted tardiness problem. The results of our numerical investigation demonstrate good properties of our bounding method, compared with the SAA method and an earlier discrete bounding method.

Date: 2012
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