Variations in parameters such as processing times, yields, and availability of materials and utilities can have a detrimental effect in the optimality and/or feasibility of an otherwise "optimal" production schedule. In this paper, we propose a multi-stage adjustable robust optimization approach to alleviate the risk from such operational uncertainties during scheduling decisions. We derive a novel robust counterpart of a deterministic scheduling model, and we show how to obey the observability and non-anticipativity restrictions that are necessary for the resulting solution policy to be implementable in practice. We also develop decision-dependent uncertainty sets in order to model the endogenous uncertainty that is inherently present in process scheduling applications. A computational study reveals that, given a chosen level of robustness, adjusting decisions to past parameter realizations leads to significant improvements, both in terms of worst-case objective as well as objective in expectation, compared to the traditional robust scheduling approaches.
Coping with uncertainty in system parameters is a prominent hurdle when scheduling multi-purpose batch plants. In this context, our previously introduced multi-stage adjustable robust optimization (ARO) framework has been shown to obtain more profitable solutions, while maintaining the same level of immunity against risk, as compared to traditional robust optimization approaches. This paper investigates the amenability of existing deterministic continuous-time scheduling models to serve as the basis of this ARO framework. A comprehensive computational study is conducted that compares the numerical tractability of various models across a suite of literature benchmark instances and a wide range of uncertainty sets. This study also provides, for the first time in the open literature, robust optimal solutions to process scheduling instances that involve uncertainty in production yields. slot-based models always require N -1 slots (where N represents the optimal number of event points for a global model) to achieve the optimal solution. To avoid confusion, we will adhere to the terminology of event points, that is, when we report that an instance was solved with N event points, the SK05 model specifically was solved with N -1 slots.
We
study the multi-mode resource constrained project scheduling
problem (MRCPSP), which we generalize to account for the case of alternative
prerequisite activities (MRCPSP-AP). The MRCPSP-AP arises in many
real-world applications when two or more activities can serve as the
required precursor to some subsequent activity, and it aims to determine
not only the optimal schedule
but also the optimal activity network. We propose a total of seven
discrete-time models and compare their numerical tractability through
comprehensive computational studies on literature benchmarks. We also
extend the well-known critical path method to handle
the existence of alternative prerequisites, allowing us to precalculate
tight time windows for each activity. Our computational study reveals
that a formulation implementing the generalized precedence relationships
in a time-aggregated fashion dominates the rest, in terms of solution
quality and runtime.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.