Decomposition techniques for the solution of large‐scale scheduling problems

Bassett, Matthew H.; Pekny, Joseph F.; Reklaitis, Gintaras V.

doi:10.1002/aic.690421209

Cited by 147 publications

(82 citation statements)

References 12 publications

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“…To tackle the computational challenge of MILP scheduling models, several solution methods have been proposed: (1) tightening methods based on preprocessing algorithms and valid inequalities [32][33][34][35][36][37][38]; (2) reformulations [5,37,[39][40][41]; (3) decomposition methods [42][43][44][45][46][47]; (4) heuristics [19,[48][49][50]; and (5) hybrid methods [51][52][53][54][55]. Finally, parallel computing has been utilized to obtain faster solutions [56][57][58].…”

Section: Solution Methodsmentioning

confidence: 99%

A General State-Space Formulation for Online Scheduling

Gupta

Maravelias

2017

Processes

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Abstract:We present a generalized state-space model formulation particularly motivated by an online scheduling perspective, which allows modeling (1) task-delays and unit breakdowns; (2) fractional delays and unit downtimes, when using discrete-time grid; (3) variable batch-sizes; (4) robust scheduling through the use of conservative yield estimates and processing times; (5) feedback on task-yield estimates before the task finishes; (6) task termination during its execution; (7) post-production storage of material in unit; and (8) unit capacity degradation and maintenance. Through these proposed generalizations, we enable a natural way to handle routinely encountered disturbances and a rich set of corresponding counter-decisions. Thereby, greatly simplifying and extending the possible application of mathematical programming based online scheduling solutions to diverse application settings. Finally, we demonstrate the effectiveness of this model on a case study from the field of bio-manufacturing.

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Section: Solution Methodsmentioning

confidence: 99%

A General State-Space Formulation for Online Scheduling

Gupta

Maravelias

2017

Processes

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“…This leads to permanently updated demand data and to a decreasing problem size (depending on the time horizon chosen). Technically, this way of optimizing Postprint of the article "An efficient two-stage algorithm for decentralized scheduling of micro-CHP units" In European Journal of Operational Research, Volume 245, Issue 3, Pages 862-874, https://doi.org/10.1016/j.ejor.2015 16 corresponds to a time-based decomposition of the global optimization into several static sub-problems (Bassett et al, 1996). Other decomposition techniques, e.g.…”

Section: Implementation As Rolling Window Optimisationmentioning

confidence: 99%

“…However, in Chu (1995) some other cases are discussed, in which a myopic approach does lead to global optimality or at least to the socalled near-optimality. Another problem of the myopic approach is that a small time window might cause infeasibilities although the global problem actually has feasible solutions (Bassett et al, 1996). Alternative (2) describes the principle of a rolling window optimization (also called receding horizon optimization).…”

Section: Implementation As Rolling Window Optimisationmentioning

confidence: 99%

An efficient two-stage algorithm for decentralized scheduling of micro-CHP units

Jochem

Schönfelder

Fïchtner

2015

European Journal of Operational Research

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In this paper we present an efficient two-stage hierarchical decomposition algorithm aiming at determining economically improved operation schedules for residential proton exchange membrane fuel cell microcombined heat and power (PEMFC micro-CHP) units and optimizing local charging of electric vehicles (EV) in the same household. Based on an individual short-term load forecasting (STLF) approach (imperfect forecast) for households implemented as an adaptive network-based fuzzy inference system (ANFIS), a mixed-integer linear program (MILP) and a two-stage greedy algorithm are used for determining optimized schedules based on a rolling-window approach. The results of the case study performed for eight variants in exemplary German households reveal that with both the MILP and the algorithmic approach, significant economic savings can be achieved compared to the standard heat-led strategy. Compared to the MILP, however, the two-stage algorithm has the additional advantage of a reduced computing time of only about 151 . Deviations from the MILP solutions are mostly smaller than 3 percent regarding the annual supply costs. Moreover, the comparison between the use of perfect and imperfect demand forecasts quantifies additional average losses due to forecasting errors of 2 percent and 3.3 percent at the maximum. Altogether, the algorithmic approach Postprint of the article "An efficient two-stage algorithm for decentralized scheduling of micro-CHP units" In European Journal of Operational Research, Volume 245, Issue 3, Pages 862-874, https://doi.org/10.1016/j.ejor.2015 3 seems to be convincing for real applications in households due to its good results, high reliability, easy implementation, and short computing times. The combination of a micro-CHP unit and an EV is highly synergetic.

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“…Similar bi-level decomposition schemes have been developed by Bok et al (2000) for supply chain optimization problem, and by Erdirik-Dogan and for the simultaneous planning and scheduling of single-stage continuous multiproduct plants. Finally, another major decomposition approach relies on a rolling horizon strategy in which multiperiod problems are solved by recursively applying a more detailed model in the first time period and a simpler aggregate problem in the remaining time periods (Bassett et al, 1996;Dimitriadis et al, 1997). After each stage, the decisions in the first time period are fixed and the horizon time is effectively shrunk as seen in Fig.…”

Section: Decomposition Techniquesmentioning

confidence: 99%

Advances in mathematical programming models for enterprise-wide optimization

Grossmann

2012

Computers & Chemical Engineering

187

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Enterprise-wide optimization (EWO) is an area that lies at the interface of chemical engineering and operations research, and has become a major goal in the process industries due to the increasing pressures for remaining competitive in the global marketplace. EWO involves optimizing the operations of supply, manufacturing and distribution activities of a company to reduce costs, inventories and environmental impact, and to maximize profits and responsiveness. A major focus in EWO is the optimal operation of manufacturing facilities that often require the use of nonlinear process models. Major operational items include planning, scheduling, real-time optimization and control. We provide an overview of EWO in terms of a mathematical programming framework. We first provide a brief overview of mathematical programming techniques (mixed-integer linear and nonlinear optimization methods), as well as decomposition methods, stochastic programming and modeling systems. We then address some of the major issues involved in the modeling and solution of these problems. Finally, based on the EWO program at the Center of Advanced Process Decision-making at Carnegie Mellon, we describe several applications to show the potential of this area. Keywords

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Decomposition techniques for the solution of large‐scale scheduling problems

Abstract: With increased product specialization within the chemical-processing industries

Cited by 147 publications

References 12 publications

A General State-Space Formulation for Online Scheduling

A General State-Space Formulation for Online Scheduling

An efficient two-stage algorithm for decentralized scheduling of micro-CHP units

Advances in mathematical programming models for enterprise-wide optimization

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