Solution of Large-Scale Supply Chain Models using Graph Sampling & Coarsening

TL;DR

This paper introduces a graph sampling and coarsening method (gSC) for efficiently solving large-scale supply chain models by providing bounds and approximate solutions with reduced computational resources.

Contribution

The paper proposes a novel gSC scheme combining sampling and coarsening to compute bounds and approximate solutions for large supply chain models, improving efficiency.

Findings

gSC yields solutions with less than 0.5% optimality gap.

Significant reductions in solution time and memory usage.

Successfully applied to a model with over 38 million variables.

Abstract

We present a graph sampling and coarsening scheme (gSC) for computing lower and upper bounds for large-scale supply chain models. An edge sampling scheme is used to build a low-complexity problem that is used to finding an approximate (but feasible) solution for the original model and to compute a lower bound (for a maximization problem). This scheme is similar in spirit to the so-called sample average approximation scheme, which is widely used for the solution of stochastic programs. A graph coarsening (aggregation) scheme is used to compute an upper bound and to estimate the optimality gap of the approximate solution. The coarsening scheme uses node sampling to select a small set of support nodes that are used to guide node/edge aggregation and we show that the coarsened model provides a relaxation of the original model and a valid upper bound. We provide numerical evidence that gSC can yield significant improvements in solution time and memory usage over state-of-the-art solvers. Specifically, we study a supply chain design model (a mixed-integer linear program) that contains over 38 million variables and show that gSC finds a solution with an optimality gap of <0.5% in less than 22 minutes.