Skip to main content Accessibility help
×
Hostname: page-component-848d4c4894-8bljj Total loading time: 0 Render date: 2024-07-04T15:46:25.011Z Has data issue: false hasContentIssue false

4 - Single-Stage Environment

from Part II - Basic Methods

Published online by Cambridge University Press:  01 May 2021

Christos T. Maravelias
Affiliation:
Princeton University, New Jersey
Get access

Summary

In this chapter, we discuss problems in the single-stage or parallel-units environment. The problem statement is presented in Section 4.1. Three types of models are presented in Section 4.2 (sequence-based), Section 4.3 (continuous time grid-based), and Section 4.4 (discrete time grid-based). In Section 4.5, we present how batching decisions can be handled, and in Section 4.6 we discuss how the three types of models can be extended to handle a new feature, namely, general shared resources. Finally, in Section 4.7 we present extensions on the modeling of general resource constraints using discrete modeling of time. Building upon the material in Chapter 3, we illustrate how some of the modeling techniques introduced for single-unit problems can be extended to account for multiple units. Our goal is to outline some general ideas that the reader can apply to a wider range of problems.We focus on (1) problem features that are new, compared to the ones in single-unit problems (i.e., batching decisions and general shared resources); and (2) new modeling techniques that are necessary to account for these features.

Type
Chapter
Information
Chemical Production Scheduling
Mixed-Integer Programming Models and Methods
, pp. 98 - 127
Publisher: Cambridge University Press
Print publication year: 2021

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Blazewicz, J, Dror, M, Weglarz, J. Mathematical-Programming Formulations for Machine Scheduling – a Survey. Eur J Oper Res. 1991;51(3):283300.Google Scholar
Pinto, JM, Grossmann, IE. A Continuous-Time Mixed-Integer Linear-Programming Model for Short-Term Scheduling of Multistage Batch Plants. Ind Eng Chem Res. 1995;34(9):30373051.Google Scholar
Cerda, J, Henning, GP, Grossmann, IE. A Mixed-Integer Linear Programming Model for Short-Term Scheduling of Single-Stage Multiproduct Batch Plants with Parallel Lines. Ind Eng Chem Res. 1997;36(5):16951707.Google Scholar
Mendez, CA, Henning, GP, Cerda, J. Optimal Scheduling of Batch Plants Satisfying Multiple Product Orders with Different Due-Dates. Comput Chem Eng. 2000;24(9-10):22232245.Google Scholar
Lim, M-F, Karimi, IA. A Slot-Based Formulation for Single-Stage Multiproduct Batch Plants with Multiple Orders per Product. Ind Eng Chem Res. 2003;42(9):19141924.Google Scholar
Castro, PA, Grossmann, IE. An Efficient MILP Model for the Short-Term Scheduling of Single Stage Batch Plants. Comput Chem Eng. 2006;30(6–7):10031018.Google Scholar
Marchetti, PA, Mendez, CA, Cerda, J. Mixed-Integer Linear Programming Monolithic Formulations for Lot-Sizing and Scheduling of Single-Stage Batch Facilities. Ind Eng Chem Res. 2010;49(14):64826498.Google Scholar
Velez, S, Dong, YC, Maravelias, CT. Changeover Formulations for Discrete-Time Mixed-Integer Programming Scheduling Models. Eur J Oper Res. 2017;260(3):949963.Google Scholar
Castro, PM, Grossmann, IE. Generalized Disjunctive Programming as a Systematic Modeling Framework to Derive Scheduling Formulations. Ind Eng Chem Res. 2012;51(16):57815792.Google Scholar
Maravelias, CT, Grossmann, IE. New General Continuous-Time State-Task Network Formulation for Short-Term Scheduling of Multipurpose Batch Plants. Ind Eng Chem Res. 2003;42(13):30563074.Google Scholar
Kondili, E, Pantelides, CC, Sargent, RWH. A General Algorithm for Short-Term Scheduling of Batch-Operations .1. MILP Formulation. Comput Chem Eng. 1993;17(2):211227.Google Scholar
Pantelides, CC, editor, Unified Frameworks for Optimal Process Planning and Scheduling. 2nd Conference on Foundations of Computer Aided Process Operations; 1994 1994; Snowmass, CO: CACHE Publications.Google Scholar

Save book to Kindle

To save this book to your Kindle, first ensure coreplatform@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

Available formats
×

Save book to Dropbox

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Dropbox.

Available formats
×

Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

Available formats
×