Augmented progressive hedging algorithm for a capacitated firm subject to demand and supply uncertainties considering discount

¹ Department of Industrial Engineering, Amirkabir University of Technology, Tehran, Iran
² Department of Industrial Engineering, College of Engineering, University of Tehran, Tehran, Iran

^* Corresponding author: fatemi@aut.ac.ir

Received: 22 January 2024
Accepted: 30 August 2025

Abstract

Decision-makers face different uncertainties, and ignoring them leads to negative consequences and significant losses. In the business environment, sourcing is one of the most critical decisions for capacitated firms. So, this article develops a multi-period model to formulate the uncertainties in demand, production line capacity and disruption time. Considering the cited uncertainty helps the decision-makers make the best decisions about production planning, supplier selection, and order amount. It provides a more accurate analysis of the final cost of fulfilling each demand unit. Another contribution of this model is introducing discounts in order, which makes it so complicated to solve. The augmented progressive hedging algorithm is introduced as the solution approach. The original progressive hedging algorithm is augmented by an updating method for the penalty coefficient and clustering the scenarios instead of solving each problem one by one. This contribution leads to reducing the running time with acceptable accuracy.