Capacity trilemma: robust capacity planning for demand, productive scale size and sustainability

Capacity planning is a critical issue for business, particularly when addressing demand volatility, production scale, and pollutant emissions in a highly uncertain and environmentally sustainable context. Considering the harmful effects of byproducts while meeting market demands and maintaining optimal productivity is crucial yet challenging for manufacturing plants. This study proposes a mathematical model that incorporates data envelopment analysis constraints to formulate an efficient target that represents the trade-off between productivity, sustainability, and demand fulfilment. This study also applies a robust optimisation approach to address demand uncertainty. The results demonstrate how the decision-making units should allocate resources based on a given set of inputs, outputs, and undesirable outputs. The computational study and empirical study are conducted to validate the proposed framework, and the results show that it can significantly reduce the expected value of perfect information compared to a baseline benchmark. Sensitivity analysis also shows that the proposed framework is suitable for high demand fluctuation scenarios.