Energy- and labour-aware scheduling under uncertainty: a decomposition framework for stochastic batch-processing systems

Motivated by the energy-intensive heat-treatment operations of a European lead-acid battery manufacturer, this study addresses energy- and labour-aware scheduling for a stochastic batch-processing system with waiting-time constraints and programme-compatibility requirements. We formalise the problem as a two-level optimisation decomposed into five sub-decisions and design a generic scheduling framework spanning from simple Rule-Based Heuristics (RH) to rules automatically synthesised by Genetic Programming (GP) for a single sub-decision. All approaches are evaluated in an agent-based discrete-event simulation mirroring the company's production. Optimising all five sub-decisions using handcrafted rules (Best RH) significantly reduces costs by 40.8% at low and 85.4% at high utilisation over Current Practice, with substantially improved solution robustness. Substituting a single sub-decision with GP-evolved rules reveals both what evolved rules achieve alone and what potential handcrafted rules leave. At high utilisation, it yields a significant 41.9% cost reduction over Current Practice, whereas on the already optimised Best RH the cost gain is marginal and non-significant – but robustness still improves markedly, a critical advantage in stochastic environments. The central contribution is methodological: partitioning the problem by decision structure rather than machine structure reduces complexity enough for handcrafted rules to remain competitive with evolved ones.