Robustness measures for operation schedules subject to disruptions

Abstract

Operation schedules are frequently subject to disruptions or uncertainties that render them suboptimal or even infeasible to implement. Among the approaches that address stochastics in schedules, preventive methods incorporate uncertainty in the scheduling model to develop an a priori robust solution, while reactive techniques seek to repair the schedule after a disruption has occurred. In this work, an alternate perspective to schedules subject to disruptions is propounded. We seek to quantify robustness of a given schedule. Given a schedule and information about the possible disruptions, we evaluate its robustness in terms of the outcome for each possible disruption scenario. The consequent action(s) required on the part of the planner/scheduler, such as complete rescheduling, schedule repair, or none, is then identified and serves as the basis to classify the scenario into tiers. Robustness metrics are proposed based on the distribution of the tiers. Malleability is an indicator of a schedule's ability to provide the performance as in the nominal case. Brittleness is a measure of the schedule's feasibility and reschedulability under disruptions. These metrics are independent of economic indicators such as profit that are typically objectives in scheduling algorithms and can therefore be used as additional criteria to compare schedules. The proposed framework is illustrated using a refinery crude oil scheduling problem. Further, sensitivity studies are conducted to identify critical resources and disruption classes. Such studies can directly help a planner/scheduler to choose the best schedule overall for implementation and take preventive measures to safeguard critical elements. © 2009 American Chemical Society.