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El. knyga: Chemical Production Scheduling: Mixed-Integer Programming Models and Methods

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(Princeton University, New Jersey)
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Understand common scheduling as well as other advanced operational problems with this valuable reference from a recognized leader in the field. Addressing a wide range of problems arising in diverse industrial sectors, this is a perfect resource for students and seasoned researchers and practitioners alike.

Understand common scheduling as well as other advanced operational problems with this valuable reference from a recognized leader in the field. Beginning with basic principles and an overview of linear and mixed-integer programming, this unified treatment introduces the fundamental ideas underpinning most modeling approaches, and will allow you to easily develop your own models. With more than 150 figures, the basic concepts and ideas behind the development of different approaches are clearly illustrated. Addresses a wide range of problems arising in diverse industrial sectors, from oil and gas to fine chemicals, and from commodity chemicals to food manufacturing. A perfect resource for engineering and computer science students, researchers working in the area, and industrial practitioners.

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Understand common scheduling and other advanced operational problems with this valuable reference from a recognized leader in the field.
Preface xvii
Part I Background
1 Introduction
3(29)
1.1 Preliminaries
3(7)
1.1.1 Scheduling: Applications and Definition
3(1)
1.1.2 Some Simple Problems
4(1)
1.1.3 Scheduling in the Supply Chain
5(1)
1.1.4 Interactions with Other Planning Functions
6(2)
1.1.5 Scheduling in the Process Industries
8(1)
1.1.6 General Problem Statement
9(1)
1.2 Chemical Production Environments
10(12)
1.2.1 Discrete Manufacturing Machine Environments
10(3)
1.2.2 Critical Insights
13(4)
1.2.3 Sequential Environments
17(3)
1.2.4 Network. Environments
20(1)
1.2.5 General Environments
21(1)
1.3 Classes of Problems
22(4)
1.3.1 Production Environments (α)
22(1)
1.3.2 Processing Restrictions and Features (β)
23(1)
1.3.3 Objective Functions (γ)
24(1)
1.3.4 Problem Classification
25(1)
1.4 Approaches to Scheduling
26(1)
1.4.1 Problem-Specific Algorithms
26(1)
1.4.2 Metaheuristics
26(1)
1.4.3 Integrated Modeling/Solution Approaches
26(1)
1.4.4 Mathematical Programming
26(1)
1.4.5 Hybrid Methods
27(1)
1.5 Scheduling MIP Model Classification
27(2)
1.6 Book Outline
29(1)
1.7 Notes and Further Reading
30(2)
2 Mixed-Integer Programming
32(35)
2.1 Preliminaries
32(4)
2.1.1 General Optimization Problem
32(1)
2.1.2 General Mixed-Integer Programming Problem
33(1)
2.1.3 Graphs and Networks
34(2)
2.2 Modeling with Binary Variables
36(4)
2.2.1 Logic Conditions
36(2)
2.2.2 Nonlinear Functions
38(1)
2.2.3 Disjunctions
39(1)
2.3 Basic Integer Programming Problems
40(7)
2.3.1 Knapsack
40(1)
2.3.2 Assignment
41(1)
2.3.3 Traveling Salesman
41(2)
2.3.4 Set Covering
43(1)
2.3.5 Production Planning
43(2)
2.3.6 Facility Location
45(1)
2.3.7 Network Problems
46(1)
2.4 Solution Methods
47(10)
2.4.1 Branch-and-Bound Algorithm
48(2)
2.4.2 Cutting Planes
50(3)
2.4.3 Reformulations
53(2)
2.4.4 Decomposition Methods
55(2)
2.5 Software Tools
57(2)
2.5.1 Modeling Languages
58(1)
2.5.2 Solvers
59(1)
2.6 Notes and Further Reading
59(1)
2.7 Exercises
60(7)
Part II Basic Methods
3 Single-Unit Environment
67(31)
3.1 Problem Statement
67(1)
3.2 Sequence-Based Models
68(3)
3.2.1 Global Sequence Models
68(2)
3.2.2 Immediate Sequence Models
70(1)
3.3 Models Based on a Continuous Time Grid
71(4)
3.4 Models Based on a Discrete Time Grid
75(8)
3.5 Extensions
83(3)
3.5.1 Prize Collection Problem
83(2)
3.5.2 Product Families
85(1)
3.6 Remarks
86(6)
3.6.1 Assumptions
87(1)
3.6.2 Variable Fixing
87(1)
3.6.3 Alternative Models
88(1)
3.6.4 Model Size
89(1)
3.6.5 Problem-Specific versus General Models
90(1)
3.6.6 Recommendations
91(1)
3.7 Notes and Further Reading
92(2)
3.8 Exercises
94(4)
4 Single-Stage Environment
98(30)
4.1 Problem Statement
98(1)
4.2 Sequence-Based Models
99(2)
4.3 Models Based on a Continuous Time Grid
101(4)
4.4 Models Based on a Discrete Time Grid
105(2)
4.5 Batching Decisions
107(4)
4.5.1 Sequence-Based Models
108(2)
4.5.2 Model Based on a Continuous Time Grid
110(1)
4.5.3 Model Based in a Discrete Time Grid
110(1)
4.6 General Shared Resources
111(9)
4.6.1 Preliminaries
111(3)
4.6.2 Sequence-Based Models
114(1)
4.6.3 Models Based on a Common Continuous Time Grid
115(3)
4.6.4 Models Based on a Discrete Time Grid
118(2)
4.7 General Shared Resources: Extensions
120(2)
4.7.1 Time-Varying Resource Capacity and Cost
120(1)
4.7.2 Varying Resource Consumption during Batch Execution
121(1)
4.8 Notes and Further Reading
122(1)
4.9 Exercises
123(5)
5 Multistage Environment
128(19)
5.1 Problem Statement
128(1)
5.2 Sequence-Based Models
129(2)
5.3 Models Based on a Continuous Time Grid
131(2)
5.4 Models Based on a Discrete Time Grid
133(2)
5.5 Storage Constraints
135(7)
5.5.1 Preliminaries
135(2)
5.5.2 Problem Statement
137(1)
5.5.3 Basic Sequence-Based Model
138(3)
5.5.4 Modifications and Extensions
141(1)
5.6 Notes and Further Reading
142(1)
5.7 Exercises
143(4)
6 Multipurpose Environment
147(10)
6.1 Problem Statement
147(3)
6.2 Sequence-Based Model
150(1)
6.3 Model Based on a Continuous Time Grid
151(2)
6.4 Models Based on a Discrete Time Grid
153(1)
6.5 Notes and Further Reading
154(1)
6.6 Exercises
155(2)
7 Network Environment Basics
157(36)
7.1 Problem Representation
157(6)
7.1.1 State-Task Network
159(2)
7.1.2 Resource-Task Network
161(2)
7.2 Models Based on Discrete Time Grids
163(9)
7.2.1 Intermediate Shipments and Time-Varying Utility Capacity and Pricing
164(2)
7.2.2 STN-Based Models
166(3)
7.2.3 RTN-Based Models
169(2)
7.2.4 Interpretation of Backlogs and Lost Sales
171(1)
7.3 Models Based on a Common Continuous Time Grid
172(11)
7.3.1 Basic Model
172(5)
7.3.2 Extensions
177(2)
7.3.3 Remarks
179(4)
7.4 Notes and Further Reading
183(1)
7.5 Exercises
184(9)
Part III Advanced Methods
8 Network Environment: Extensions
193(23)
8.1 Material Consumption and Production during Task Execution
193(2)
8.2 Material Storage and Transfer
195(10)
8.2.1 Storage in Shared Vessels
196(1)
8.2.2 Storage in Processing Units and Material Flows
196(3)
8.2.3 Material Storage Extensions
199(2)
8.2.4 Material Transfer Tasks
201(4)
8.3 Setups and Task Families
205(5)
8.3.1 Unit Setups
205(1)
8.3.2 Task Setups
206(1)
8.3.3 Task Families
207(3)
8.4 Unit Deterioration and Maintenance
210(4)
8.4.1 No Effect on Capacity and Conversion
211(1)
8.4.2 Unit Capacity Reduction
212(1)
8.4.3 Conversion Reduction
213(1)
8.5 Notes and Further Reading
214(2)
9 Continuous Processes
216(17)
9.1 Preliminaries
216(4)
9.1.1 Background
216(1)
9.1.2 Batch versus Continuous Processing
217(3)
9.2 Basic Model
220(3)
9.3 Extensions
223(8)
9.3.1 Startups and Shutdowns
223(2)
9.3.2 Transitions between Steady States
225(1)
9.3.3 Time Delays
226(2)
9.3.4 General Startups and Shutdowns with Time Delays
228(2)
9.3.5 General Transitions
230(1)
9.4 Notes and Further Reading
231(1)
9.5 Exercises
231(2)
10 Periodic Scheduling
233(28)
10.1 Single-Unit Environment
233(12)
10.1.1 Problem Statement
234(1)
10.1.2 Preliminaries and Motivation
234(5)
10.1.3 Notation
239(1)
10.1.4 Basic Discrete Time Model
240(2)
10.1.5 Advanced Discrete Time Model
242(2)
10.1.6 Remarks
244(1)
10.2 Single-Stage Environment
245(9)
10.2.1 Problem Statement
245(1)
10.2.2 Basic Model
246(1)
10.2.3 Shipments at Specified Times
247(2)
10.2.4 Simplifying Assumptions and Solution Features
249(2)
10.2.5 Unit-Specific Solutions
251(1)
10.2.6 Continuous Time Models: Basics
252(1)
10.2.7 Continuous Processing: Basics
253(1)
10.3 Network Environment
254(4)
10.3.1 Problem Statement
255(1)
10.3.2 Model
256(2)
10.4 Notes and Further Reading
258(1)
10.5 Exercises
258(3)
11 Multiperiod Blending
261(28)
11.1 Preliminaries
262(3)
11.1.1 Pooling
262(1)
11.1.2 Pooling Formulations
263(1)
11.1.3 Product Blending
264(1)
11.2 Product Blending: Nonlinear Models
265(4)
11.2.1 Concentration-Based Model
265(2)
11.2.2 Source-Based Model
267(2)
11.2.3 Remarks and Extensions
269(1)
11.3 Product Blending: Linear Approximate Models
269(6)
11.3.1 Discretization-Based Model
270(2)
11.3.2 Discretization-Relaxation-Based Model
272(3)
11.4 Process Blending
275(6)
11.4.1 Problem Statement
275(1)
11.4.2 Basic Model
276(2)
11.4.3 Illustrative Example
278(2)
11.4.4 Extensions
280(1)
11.5 Notes and Further Reading
281(1)
11.6 Exercises
282(7)
Part IV Special Topics
12 Solution Methods: Sequential Environments
289(29)
12.1 Decomposition Methods
289(11)
12.1.1 Preliminaries
289(2)
12.1.2 Single-Stage Environment: Cost Minimization
291(2)
12.1.3 Multistage Environment: Cost Minimization
293(2)
12.1.4 Makespan Minimization
295(2)
12.1.5 Remarks and Extensions
297(3)
12.2 Tightening and Preprocessing
300(7)
12.2.1 Tightening Based on Batch-Unit Assignments: Single-Stage
300(5)
12.2.2 Tightening Based on Batch-Unit Assignments: Multistage
305(1)
12.2.3 Fixing Sequencing Binary Variables: Multistage
306(1)
12.3 A Reformulation and Tightening Based on Variable Time Windows
307(4)
12.4 Discrete-Continuous Algorithm
311(2)
12.5 Notes and Further Reading
313(1)
12.6 Exercises
314(4)
13 Solution Methods: Network Environments
318(43)
13.1 Background and Motivation
318(6)
13.1.1 Problem Statement
318(1)
13.1.2 Basic STN-Based Model
319(1)
13.1.3 Motivating Examples
320(4)
13.2 Preprocessing and Tightening
324(10)
13.2.1 General Networks
325(3)
13.2.2 Networks with Loops
328(1)
13.2.3 Preprocessing Algorithm
329(2)
13.2.4 Valid Inequalities
331(2)
13.2.5 Extensions
333(1)
13.3 Reformulations
334(3)
13.3.1 New Variables and Branching Strategies
335(1)
13.3.2 Remarks
336(1)
13.4 Models Based on Multiple Discrete Time Grids
337(11)
13.4.1 Time Windows
337(2)
13.4.2 Exact Task and Unit Time Discretization
339(3)
13.4.3 Approximate Task and Unit Time Discretization
342(2)
13.4.4 Material Grids
344(1)
13.4.5 Model
344(3)
13.4.6 Types of Time Grids
347(1)
13.5 Discrete-Continuous Algorithm
348(7)
13.5.1 Preliminaries and Outline
349(2)
13.5.2 Mapping
351(1)
13.5.3 Third-Stage Linear Programming Model
352(1)
13.5.4 Extensions
353(2)
13.6 Notes and Further Reading
355(3)
13.7 Exercises
358(3)
14 Real-Time Scheduling
361(40)
14.1 Motivation and Background
362(5)
14.1.1 Uncertainty versus New Information
362(1)
14.1.2 Event Triggered versus Periodic Rescheduling
363(2)
14.1.3 Notation
365(2)
14.1.4 Approach Classification
367(1)
14.2 State-Space Scheduling Model
367(9)
14.2.1 Preliminaries
368(1)
14.2.2 Basic Model
369(2)
14.2.3 Modeling of Disturbances
371(3)
14.2.4 Extensions
374(2)
14.3 Design of Real-Time Scheduling Algorithm
376(10)
14.3.1 Algorithmic Parameters
376(1)
14.3.2 System Characteristics
377(2)
14.3.3 Design through Simulation: Deterministic Case
379(2)
14.3.4 Model Modifications
381(1)
14.3.5 Design through Simulation: Stochastic Case
382(2)
14.3.6 Integrated Framework
384(2)
14.4 Feedback through Integration with Other Functions
386(6)
14.4.1 Integration with Automation Logic
386(3)
14.4.2 Integration with Process Control
389(3)
14.5 Notes and Further Reading
392(3)
14.6 Exercises
395(6)
15 Integration of Production Planning and Scheduling
401(34)
15.1 Preliminaries
401(6)
15.1.1 Production Planning
401(3)
15.1.2 Motivation
404(2)
15.1.3 Lot Sizing
406(1)
15.2 Generalized Capacitated Lot Sizing
407(9)
15.2.1 Motivation
408(1)
15.2.2 Basic Concepts
409(3)
15.2.3 Solution Properties
412(1)
15.2.4 Basic Model
413(2)
15.2.5 Model for Short and Long Setups
415(1)
15.3 Multiple Units Production Planning-Scheduling
416(6)
15.3.1 Preliminaries
417(1)
15.3.2 Basic Model
418(3)
15.3.3 Extensions
421(1)
15.4 Projection-Based Surrogate Methods
422(9)
15.4.1 Feasible Region Projection
422(2)
15.4.2 Method Outline
424(3)
15.4.3 Remarks and Extensions
427(4)
15.5 Notes and Further Reading
431(1)
15.6 Exercises
432(3)
Index 435
Christos Maravelias is the Anderson Family Professor in Energy and the Environment and Professor of Chemical and Biological Engineering at Princeton University.
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