MIP-based decomposition strategies for large-scale scheduling problems in multiproduct multistage batch plants: A benchmark scheduling problem of the pharmaceutical industry

Kopanos, Georgios M.; Méndez, Carlos A.; Puigjaner, Luís

doi:10.1016/j.ejor.2010.06.002

Cited by 95 publications

(70 citation statements)

References 23 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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“…For the construction phase of the heuristic, we set a CPU time limit of 5 seconds per iteration for the Gurobi Optimizer; for the improvement phase, no CPU time limit was set. Similar to Kopanos et al (2010), who conclude that larger group sizes do not guarantee better schedules but require more CPU time, we chose for both phases a group size of one make batch. Moreover, we applied the preprocessing methodology described in Baumann and Trautmann (2013) in both phases to exclude certain matchings between make batches and pack batches without loss of generality.…”

Section: Computational Resultsmentioning

confidence: 99%

“…For the scheduling of the individual groups, both a batch-based and a network-based MILP model are proposed, but the computational cost of the latter turns out to be significantly higher. Kopanos et al (2010) consider the same type of production process, but additionally account for sequence-dependent changeover times. In an experimental analysis of the effect of group sizes, the best results were obtained when only a single batch was scheduled per iteration.…”

Section: Hybrid Iterative Scheduling Methodsmentioning

confidence: 99%

“…In an experimental analysis of the effect of group sizes, the best results were obtained when only a single batch was scheduled per iteration. The method of Kopanos et al (2010) comprises a constructive step and an improvement step. In the constructive step, the batches are ordered according to the number of suitable processing units; for the scheduling of the batches, two alternative batch-based MILP formulations are proposed.…”

Section: Hybrid Iterative Scheduling Methodsmentioning

confidence: 99%

“…Similar to the related papers mentioned in Subsection 3.4, we apply a batch-based MILP formulation to the solution of the scheduling problem in each iteration. However, in contrast to the methods of and Kopanos et al (2010), we eliminate a large number of the variables and constraints that have become redundant due to the decisions taken in previous iterations. For large-scale instances, this elimination technique reduces the overall computational cost considerably.…”

Section: Solution Strategy Of the Hybrid Methodsmentioning

confidence: 99%

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A hybrid method for large-scale short-term scheduling of make-and-pack production processes

Baumann

Trautmann

2014

European Journal of Operational Research

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Due to the ongoing trend towards increased product variety, fast-moving consumer goods such as food and beverages, pharmaceuticals, and chemicals are typically manufactured through so-called make-and-pack processes. These processes consist of a make stage, a pack stage, and intermediate storage facilities that decouple these two stages. In operations scheduling, complex technological constraints must be considered, e.g., non-identical parallel processing units, sequence-dependent changeovers, batch splitting, no-wait restrictions, material transfer times, minimum storage times, and finite storage capacity. The shortterm scheduling problem is to compute a production schedule such that a given demand for products is fulfilled, all technological constraints are met, and the production makespan is minimised. A production schedule typically comprises 500-1500 operations. Due to the problem size and complexity of the technological constraints, the performance of known mixed-integer linear programming (MILP) formulations and heuristic approaches is often insufficient.We present a hybrid method consisting of three phases. First, the set of operations is divided into several subsets. Second, these subsets are iteratively scheduled using a generic and flexible MILP formulation. Third, a novel critical path-based improvement procedure is applied to the resulting schedule. We develop several strategies for the integration of the MILP model into this heuristic framework. Using these strategies, high-quality feasible solutions to large-scale instances can be obtained within reasonable CPU times using standard optimisation software. We have applied the proposed hybrid method to a set of industrial problem instances and found that the method outperforms state-of-the-art methods.

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