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Batching and Scheduling

Models and Methods for Several Problem Classes

Lecture Notes in Economics and Mathematical Systems Band 437

Carsten Jordan

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In some manufacturing systems significant setups are required to change production from one type of products to another. The setups render the manufacturing system inflexible as for reacting to changes in demand patterns, hence inventories must be maintained to guarantee an acceptable customer service. In this environment, production scheduling faces a number of problems, and this work deals with mathematical models to support the scheduling decisions. Some more background and motivation is given in the following sections, as well as in a case description in Section 1. 3. The synopsis in Section 1. 4 outlines the topics of the work. 1. 1 Motivation of the Planning Problem Consider the production of metal sheets in a rolling mill. If the width of the next type of sheets is greater than the width of the preceding type, then the roll needs a setup: during the rolling process the edges of a sheet cause grooves on the rolls' surface, thus, the surface must be polished if a greater width is run next. Sheets with a smaller width can be run directly, without a setup. Another example in which setups are sequence dependent is a line where cars are sprayed: if the color of the paint changes, the cleaning of the tools requires a setup depending on the sequence of the colors. Only a small setup may be needed for changing from a light to a dark color, but a thorough cleaning of the tools is 2 CHAPTER 1.


Einband Taschenbuch
Seitenzahl 178
Erscheinungsdatum 18.06.1996
Sprache Englisch
ISBN 978-3-540-61114-1
Verlag Springer Berlin
Maße (L/B/H) 23.5/15.5/1 cm
Gewicht 300 g
Auflage Softcover reprint of the original 1st ed. 1996

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  • 1 Introduction.- 1.1 Motivation of the Planning Problem.- 1.2 Background and Related Work.- 1.3 Case Description.- 1.4 Chapter Synopsis.- 2 Description of the Problems.- 2.1 Batching Types and Literature Review.- 2.2 Notation, Basic Definitions and [?/?/?] Descriptor.- 2.3 Single-Machine Case.- 2.4 Multi-Level Product Structures and Parallel Machines.- 2.5 Complexity Analysis.- 2.6 Structural Properties.- 2.7 Instance Generator.- 3 Single-Machine Case.- 3.1 Basic Enumeration Scheme.- 3.2 Item Availability — Preemptive Batching.- 3.2.1 Branch&Bound.- 3.2.2 Dynamic Programming.- 3.2.3 Construction and Improvement.- 3.2.4 Computational Results.- 3.3 Item Availability — Nonpreemptive Batching.- 3.3.1 Branch&Bound.- Minimum Cost Schedule of a Sequence.- Dominance Rules.- 3.3.2 Genetic Algorithm for Sequence Independent Setups.- 3.3.3 Computational Results.- 3.4 Batch Availability.- 3.4.1 Branch&Bound.- Late Schedule of a Sequence.- Dominance Rule.- 3.4.2 Genetic Algorithm for Sequence Independent Setups.- 3.4.3 Computational Results.- 3.4.4 Genetic Algorithm for the Flow-Shop Case.- 4 Discrete Lotsizing and Scheduling.- 4.1 Discrete Lotsizing and Scheduling Problem.- 4.2 Equivalence of DLSP and BSP.- 4.3 Comparison with Variants of the DLSP.- 4.3.1 Sequence Independent Setup Times and Costs (SISTSC).- 4.3.2 Sequence Dependent Setup Costs (SDSC).- 4.3.3 Sequence Dependent Setup Times and Costs (SDSTSC).- 4.3.4 Single-Level Batch Availability (BA).- 4.3.5 Two-Level Batch Availability (BA2LV).- 4.4 Conclusions.- 5 Multi-Level and Parallel Machine Case.- 5.1 Multi-Level Case.- 5.1.1 Single-Machine.- 5.1.2 Multi-Machine.- 5.1.3 Preliminary Computational Results.- 5.2 Parallel Machines.- 6 Artificial Intelligence Approaches.- 6.1 Introduction.- 6.2 Model Formulations.- 6.3 Performance Comparison.- 6.4 Conclusions.- 7 Summary and Future Work.- Appendix A Setup Matrices for the Instance Generator.- List of Notation.- List of Abbreviations.- List of Figures.- List of Tables.