Multistage stochastic programming approach for joint optimization of job scheduling and material ordering under endogenous uncertainties

Abstract Job scheduling incorporated with material ordering can better meet practical needs and lead to overall cost reduction. In this paper, we present a stochastic approach for this joint optimization problem, considering uncertainties in job processing times and resource consumptions. We formulate this integrated problem as a multistage stochastic mixed-integer program involving endogenous uncertainties. Several theoretical properties that can reduce the model size are studied. Based on this, a branch-and-bound exact algorithm and a sampling-based approximate method are designed as solution algorithms. The effectiveness of the integrated scheduling approaches and the efficiency of the proposed solution algorithms are evaluated via numerical experiments. It is shown that our approach can greatly reduce the overall cost compared with the traditional separate production planning approach, especially when production resources are not very restricted.