Absolute semi-deviation risk measure for ordering problem with transportation cost in Supply Chain

TL;DR

This paper introduces a decomposition algorithm for stochastic supply chain models using the absolute semi-deviation risk measure, improving computational efficiency and decision-making under uncertainty.

Contribution

It proposes a novel decomposition method leveraging expected excess to efficiently solve ASD risk-measure models with 0-1 variables.

Findings

The method provides tighter bounds for ASD models.

Computational results show improved performance over direct solvers.

ASD risk measure enhances decision-making in supply chain problems.

Abstract

We present a decomposition method for stochastic programs with 0-1 variables in the second-stage with absolute semi-deviation (ASD) risk measure. Traditional stochastic programming models are risk-neutral where expected costs are considered for the second-stage. A common approach to address risk is to include a dispersion statistic in addition with expected costs and weighted appropriately. Due to the lack of block angular structure, stochastic programs with ASD risk-measure possess computational challenges. The proposed decomposition algorithm uses another risk-measure `expected excess', and provides tighter bounds for ASD stochastic models. We perform computational study on a supply chain replenishment problem and standard knapsack instances. The computational results using supply chain instances demonstrate the usefulness of ASD risk-measure in decision making under uncertainty, and knapsack instances indicate that the proposed methodology outperforms a direct solver.