A model for the optimal design of a supply chain network driven by stochastic fluctuations

TL;DR

This paper develops a supply chain model incorporating stochastic fluctuations in costs, demonstrating that selecting producers with Pareto-distributed costs can optimize profits, with results validated through model simulations.

Contribution

It introduces a novel approach to supply chain optimization by including stochastic cost fluctuations and identifies Pareto distribution as optimal for cost reduction.

Findings

Pareto distribution with lower exponent improves cost predictions

Normal and lognormal distributions lead to higher costs

Model predictions align well with simulation results

Abstract

Supply chain optimization schemes have more often than not underplayed the role of inherent stochastic fluctuations in the associated variables. The present article focuses on the associated reengagement and correlated renormalization of supply chain predictions now with the inclusion of stochasticity induced fluctuations in the structure. With a processing production plant in mind that involves stochastically varying production and transportation costs both from the site to the plant as well as from the plant to the customer base, this article proves that the producer may benefit through better outlay in the form of higher sale prices with lowered optimized production costs only through a suitable selective choice of producers whose production cost probability density function abides a Pareto distribution. Lower the Pareto exponent, better is the supply chain prediction for cost optimization. On the other hand, other symmetric (normal) and asymmetric (lognormal) distributions lead to upscaled costs both in terms of inlays and outlays. While this is an averaged out statistics over large time regimes, transient features may still affect such probabilistic predictions and offset results. The predictions are shown to be in good harmony with model results shown.