Classification of Chemical Production Scheduling Problems and Approaches, and a General Solution Framework

Classification of Chemical Production Scheduling
Problems and Approaches, and a General Solution Framework

Sara Zenner, Christos T. Maravelias

The present talk consists of three parts:

(1) A classification of chemical production scheduling problems

(2) A critical review of the types of modeling approaches proposed in the literature

(3) A general representation and solution method for chemical production scheduling

Problem Classification

Scheduling problems appear in a number of sectors and applications, ranging from the oil industry to the pharmaceutical and specialty chemical sectors, and from consumer goods and the food industry to metal manufacturing. In addition, there is a large number of different processing characteristics and restrictions (e.g., batch vs. continuous processing, transportation vs. conversion processes, mixing rules, storage constraints, etc) which lead to a wide range of scheduling problems. In this paper we present a general classification of scheduling problems based on a series of attributes, including: (i) the industrial/market environment within which a company operates, (ii) the interaction of the scheduling problem with the other planning functions of the enterprise, (iii) the characteristics of the production environment, (iv) the structure of the facility, (v) the production recipe, and (vi) the detailed processing restrictions. We then discuss how three specific aspects (bill-of-materials requirements, mixing/splitting rules, batch integrity restrictions) can lead to problem classes that existing modeling approaches cannot address and we critically review the shortcomings of existing representations and modeling approaches.

Review Modeling Approaches

Based on the insights provided by our problem classification we review existing scheduling approaches in terms of a broad spectrum of attributes. Most existing method classifications are based on a subset of these attributes (e.g., facility structure and time representation). In this talk we attempt to synthesize all previous approaches and propose a roadmap that includes all known modeling approaches. Specifically, we propose a multi-dimensional view where the “universe” of scheduling approaches is treated as a multi-dimensional space where each dimension corresponds to a key modeling feature. The primary dimensions are:

a)      Major entity(ies) modeled: these typically include orders (or batches) and materials/resources.

b)      Optimization decisions: the major decisions are batching (or lot-sizing), assignment, and sequencing and timing; all approaches involve a subset of these three.

c)      Time representation: this includes the selection of the type of time grid (discrete vs. continuous), as well as more subtle choices (e.g., unit-specific vs. common time grid, local vs. global precedence variables, etc.). 

General Modeling and Solution Framework

Based on our representation of modeling approaches, we revisit the classes of problems that cannot be addressed using existing methods. We explain why this is the case and highlight the “holes” in terms of problem representation. We then present a general framework, which is a generalization of the approach of Sundaramoorthy and Maravelias (2011), to address some of these shortcomings. Finally, we show how our approach can be used to represent problems that have been addressed using different modeling approaches, and how other modeling approaches can be “reduced” to ours. We close with some computational results. 

Sundaramoorthy, A.; Maravelias, C. T. A General Framework for Process Scheduling. AIChE J., 57(3), 695-710, 2011.             (DOI: 10.1002/aic.12300).