(761e) An Improved Robust Optimization Approach for Scheduling Under Uncertainty

Production scheduling is a decision-making process to determine what to produce, when to produce and how much to produce. Traditionally, these operations were carried out by trained individuals without mathematical optimization [1]. The increase in production volumes, product portfolios, alternative production recipes and energy cost has raised the complexity of manual scheduling. The increased complexity coupled with demand and price uncertainty has made it essential to deploy effective optimization tools to provide feasible and flexible solutions. The uncertainty in processing parameters can not only lead to delays in schedules but also lead to infeasibility of otherwise “optimal” solution [2] leading to decrease in operators’ confidence in the optimal schedule. Typically, scenario-based stochastic methods with heuristic recourse mechanisms or deterministic robust scheduling has been proposed in the literature to handle uncertainty in scheduling [3]. Alternatively, reactive scheduling has been proposed to adjust the a apriori obtained deterministic scheduling on realization of uncertain parameter [4] [5]. Owing to “on-line” nature of reactive schedules, timely update of schedule is done using heuristics approaches.

In this work, we propose a multi-stage robust optimization approach with corrective action to ensure feasibility of the worst case solution while reducing the conservatism arising from traditional robust optimization approaches. We generate a deterministic robust counterpart of unit-specific event-based continuous time scheduling models [6] [7] for box, ellipsoidal and polyhedral uncertainty sets [8] and arrive at a robust solution. Using the information from these robust solution, we create proactive-reactive corrective measure to alleviate the problem of conservatism. We quantify the probability of constraint satisfaction by using apriori and aposteriori probabilistic bounds for known and unknown uncertainty distributions [9], consequently, improving the objective value for a given risk scenario. Computational experiments were carried out on example problems [10] [11] to measure the effectiveness of the proposed method. For a given constraint satisfaction probability, the proposed method improves the objective value compared to the traditional robust optimization approaches.

References
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