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3 - Single-Unit Environment

from Part II - Basic Methods

Published online by Cambridge University Press:  01 May 2021

Christos T. Maravelias
Christos T. Maravelias
Affiliation:
Princeton University, New Jersey
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Summary

This chapter introduces scheduling in the simplest production environment, the single-unit environment. The statements of different problems are presented in Section 3.1. Two different types of MIP sequence-based models are presented in Section 3.2. Section 3.3 discusses models based on a continuous time grid, while Section 3.4 presents models based on a discrete time grid. A number of extensions are discussed in Section 3.5, and we close in Section 3.6 with some general remarks.

Keywords

Single-unit problemsequencingtimingprize collection problemproduct families
Type
Chapter
Information
Chemical Production Scheduling
Mixed-Integer Programming Models and Methods
 , pp. 67 - 97
Publisher: Cambridge University Press
Print publication year: 2021

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References

Sousa, JP, Wolsey, LA. A Time Indexed Formulation of Nonpreemptive Single-Machine Scheduling Problems. Math Program. 1992;54(3):353–367.Google Scholar
Wolsey, LA. Valid Inequalities for 0-1 Knapsacks and MIPs with Generalized Upper Bound Constraints. Discrete Applied Mathematics. 1990;29(2–3):251–261.CrossRefGoogle Scholar
van den Akker, JM, Hurkens, CAJ, Savelsbergh, MWP. Time-Indexed Formulations for Machine Scheduling Problems: Column Generation. INFORMS J Comput. 2000;12(2):111–124.Google Scholar
Sadykov, R, Wolsey, LA. Integer Programming and Constraint Programming in Solving a Multimachine Assignment Scheduling Problem with Deadlines and Release Dates. INFORMS J Comput. 2006;18(2):209–217.Google Scholar
van den Akker, JM, van Hoesel, CPM, Savelsbergh, MWP. A Polyhedral Approach to Single-Machine Scheduling Problems. Math Program. 1999;85(3):541–572.CrossRefGoogle Scholar
Pekny, JF, Miller, DL, Mcrae, GJ. An Exact Parallel Algorithm for Scheduling When Production Costs Depend on Consecutive System States. Comput Chem Eng. 1990;14(9):1009–1023.CrossRefGoogle 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):211–227.CrossRefGoogle Scholar
Shah, N, Pantelides, CC, Sargent, RWH. A General Algorithm for Short-Term Scheduling of Batch-Operations .2. Computational Issues. Comput Chem Eng. 1993;17(2):229–244.CrossRefGoogle Scholar
Karmarkar, US, Schrage, L. The Deterministic Dynamic Product Cycling Problem. Oper Res. 1985;33(2):326–345.CrossRefGoogle Scholar
Kelly, JD, Zyngier, D. An Improved MILP Modeling of Sequence-Dependent Switchovers for Discrete-Time Scheduling Problems. Ind Eng Chem Res. 2007;46(14):4964–4973.Google Scholar
Velez, S, Dong, Y, Maravelias, CT. Changeover Formulations for Discrete-Time Mixed-Integer Programming Scheduling Models. Eur J Oper Res. 2017;260(3):949–963.CrossRefGoogle Scholar
Wolsey, LA. MIP modelling of changeovers in production planning and scheduling problems. Eur J Oper Res. 1997;99(1):154-65.CrossRefGoogle Scholar
Lasserre, JB, Queyranne, M, editors. Generic Scheduling Polyhedra and a New Mixed-Integer Formulation for Single-Machine Scheduling. Paper from the conference IPCO: Integer Programming and Combinatorial Optimization. 1992.Google Scholar
Kopanos, GM, Puigjaner, L, Maravelias, CT. Production Planning and Scheduling of Parallel Continuous Processes with Product Families. Ind Eng Chem Res. 2011;50(3):1369–1378.CrossRefGoogle Scholar
Lima, RM, Grossmann, IE, Jiao, Y. Long-Term Scheduling of a Single-Unit Multi-Product Continuous Process to Manufacture High Performance Glass. Comput Chem Eng. 2011;35(3):554–574.CrossRefGoogle Scholar

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