A general framework for process scheduling

Sundaramoorthy, Arul; Maravelias, Christos T.

doi:10.1002/aic.12300

Cited by 51 publications

(56 citation statements)

References 29 publications

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“…Also, material‐based models have been extended to address problems in sequential production environments as well as facilities that combine sequential and network environments . Thus, our methods, which are applicable to all aforementioned models, have the potential to benefit a wide range of tools and models.…”

Section: Constraint Propagation Algorithmmentioning

confidence: 99%

“…These lower bounds, which are calculated from instance data within seconds, are then used to write four classes of strong valid inequalities; that is, constraints that reduce the feasible space of the linear programming (LP) relaxation of mixed‐integer programming (MIP) scheduling models, and therefore speedup their solution, without cutting off any feasible integer solution. Although our methods can be applied to a wide range of MIP models, we choose to apply them to discrete‐time models because a recent study suggests that they are computationally more effective than their continuous‐time counterparts, they can be easily extended to account for different processing characteristics and constraints, and they are used as the backbone in a wide range of chemical production scheduling tools as well as in in‐house tools developed by chemical companies …”

Section: Introductionmentioning

confidence: 99%

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Valid Inequalities Based on Demand Propagation for Chemical Production Scheduling MIP Models

2013

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Although several mixed-integer programming (MIP) models have been proposed for the scheduling of chemical manufacturing facilities, the development of solution methods for these formulations has received limited attention. In this article, we develop a constraint propagation algorithm for the calculation of lower bounds on the number and size of tasks necessary to satisfy given demand. These bounds are then used to express four types of valid inequalities which greatly enhance the computational performance of the MIP scheduling model. Specifically, the addition of these inequalities leads to reductions in the computational requirements of more than three orders of magnitude, thereby allowing us to address medium-sized problems of industrial relevance. Importantly, the proposed methods are applicable to a wide range of problem classes and time-indexed MIP models for chemical production scheduling. V C 2013 American Institute of Chemical Engineers AIChE J, 59: 872-887, 2013 Keywords: chemical production scheduling, mathematical programming IntroductionChemical production involves the conversion of raw materials (feedstocks) into final products, both of which are most often fluids (gases or liquids). Each production task converts a set of input materials into a set of output materials and is carried out in equipment units that are capable of processing different amounts of materials. Although there are chemical facilities with a wide range of processing characteristics and constraints, there are two major types of chemical production environments, sequential and network.1,2 In sequential environments, it is assumed that production tasks have a single input and a single output material; the input material of a task is produced by a single upstream task; and the output of a task is consumed by a single downstream task. Thus, materials from different tasks are not mixed, and the output of a task cannot be split to be consumed by multiple tasks. Also, it is implicitly assumed that each material is produced and consumed by at most one task. In the process systems engineering (PSE) literature, these facilities are termed either as multistage, if the routing through the stages is the same for all batches/products, or multipurpose, if there are batch/product-specific routings. In network environments, tasks may consume or produce multiple materials, and a material can be produced and consumed by different types of tasks. Also, material coming from different tasks can be mixed in a storage vessel, the output of a task can be consumed by multiple downstream tasks, and material can also be recycled.Interestingly, the methods that have been developed to address chemical production scheduling problems follow for the most part the aforementioned classification. Early work focused on sequential facilities where a batch of raw material has to go through multiple production stages to be converted to the final product. In other words, the processing of fluids is represented as the processing of a discrete batch that goes through diff...

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Section: Constraint Propagation Algorithmmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Valid Inequalities Based on Demand Propagation for Chemical Production Scheduling MIP Models

2013

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“…[15][16][17][18][19] Nevertheless, significantly less attention has been directed to solution methods for general MIP scheduling models.…”

Section: Significancementioning

confidence: 99%

Tightening methods for continuous‐time mixed‐integer programming models for chemical production scheduling

2013

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SignificanceImportant advances in modeling chemical production scheduling problems have been made in recent years, yet effective solution methods are still required. We use an algorithm that uses process network and customer demand information to formulate powerful valid inequalities that substantially improve the solution process. In particular, we extend the ideas recently developed for discrete-time formulations to continuous-time models and show that these tightening methods lead to a significant decrease in computational time, up to more than three orders of magnitude for some instances. Keywords: Mixed-integer programming, demand propagation, valid inequalities Introduction R esearch efforts in the area of chemical production scheduling have been primarily focused on the development of alternative formulations to ensure both generality and computational efficiency.1,2 Starting from the work of Pantelides and coworkers, 3-5 several general mixed-integer programming (MIP) models, relying on material balances and time grids, have been proposed to (1) reduce computational requirements, 6-14 and (2) account for constraints on storage, utilities, changeovers, connectivity, material transfers, material-handling restrictions, and combined production environments. [15][16][17][18][19] Nevertheless, significantly less attention has been directed to solution methods for general MIP scheduling models.To address the computational challenge, various researchers have studied the structure of MIP chemical production scheduling models, 20,21 used decomposition-based algorithms, 22-27 exploited parallel computing tools, 28,29 developed reformulations, 30-32 and developed tightening methods based on valid inequalities. 31,[33][34][35] An example of the latter is the work of Maravelias and coworkers 35,36 where process network information (recipes and unit capacities) and customer demand are used to calculate a set of parameters (the minimum amount of each material and the minimum production goal for each task that are required to meet the given demand), which are then used to generate strong valid inequalities. This strategy was implemented in discrete-time models leading to dramatic computational time reductions, up to four orders of magnitude for many instances. Discrete-time models have a number of advantages, including (1) the linear modeling of inventory and utility costs, (2) the treatment of intermediate raw material deliveries and final product orders at no additional computational cost, (3) the straightforward modeling of events during the execution of tasks, and (4) the modeling of time-varying utility availability and pricing using no new variables or constraints. Furthermore, a recent study showed that discrete-time models are in general faster than their continuous-time counterparts. 37 Nevertheless, continuous-time models are likely to be preferred in some specific problems (e.g., in problems with sequence-dependent changeovers), so it is important to develop methods that enhance the solution of this type of mod...

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“…However, these studies focus on the unit level of the equipment hierarchy rather than the area/site level that is relevant for the current study. General frameworks for chemical production scheduling are suggested by Sundaramoorthy and Maravelias (2011) and Maravelias (2012), but these frameworks focus on batch processes and are not as intuitive for sites with continuous production.…”

Section: Introductionmentioning

confidence: 99%