Integrated job shop and transportation scheduling under time-of-use electricity pricing and human-robot interactions

The transition toward Industry 5.0 challenges manufacturers to balance profitability and sustainability. While prior studies address energy-aware scheduling, transportation, or humancentric manufacturing separately, their combined effects remain underexplored. This paper proposes a bi-objective job shop scheduling framework with integrated transportation under stochastic human–robot interactions (HRIs) and time-of-use (ToU) electricity pricing. A simulation–optimization framework is developed, combining system-level modeling with an ϵ-constraint approach to minimize total energy cost (TEC) under makespan constraints. Tasks are scheduled following several high-pricing-period avoidance rules, while the scheduling horizon is progressively reduced to generate a representative set of non-dominated solutions. Computational results indicate that allowing up to 33% of production during high-pricing periods yields the best trade-offs, whatever the scheduling approach (static or dynamic) used. HRIs exhibit a limited overall impact but become significant under prolonged interactions, whereas flow-shop-like job sets tend to produce infeasible schedules under stricter avoidance rules.