Modeling and solving production planning in a two-factories symbiotic network with uncertain demands

Abstract

Industrial Symbiosis (IS) refers to an eco-collaboration between factories, where the waste (i.e., byproduct) generated by one factory is repurposed as an alternative raw material for another. This study investigates the integrated production planning problem within a symbiotic network of two factories operating under uncertain demand in an IS setting. The problem is modeled as an integrated capacitated lot-sizing problem, for which two mathematical formulations are proposed: a natural formulation and a plant-location reformulation. To address uncertain demand with known probability distributions, a two-stage stochastic programming model is developed based on the plant-location reformulation and solved using the Sample Average Approximation (SAA) method. Subsequently, a distributionally robust optimization (DRO) model–with a polynomial number of constraints–is developed to handle demand characterized by unknown distributions with infinite support. Computational experiments demonstrate that, in terms of robustness and cost variability, DRO solutions consistently outperform those obtained via the SAA method. Although DRO yields more conservative plans than SAA, it offers enhanced robustness and reduced variability, with superior worst-case performance–particularly in complex scenarios arising from multi-modal distributions. From a practical perspective, cost segmentation reveals that DRO-based solutions significantly reduce cost variability by minimizing reliance on expensive outsourcing in extreme scenarios. Overall, the results show that symbiotic collaboration reduces network costs by eliminating disposal charges and lowering expenses for purchased raw materials. These findings highlight the potential of robust planning to enhance cost efficiency for industrial organizations engaged in IS and operating in volatile markets.