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E-grāmata: Capacitated Planned Maintenance: Models, Optimization Algorithms, Combinatorial and Polyhedral Properties

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Capacitated Planned Maintenance: Models, Optimization Algorithms, Combinatorial and Polyhedral PropertiesPalielināt
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This book examines the problem of maintenance planning and scheduling in industrial production systems. It presents two practically relevant, deterministic mathematical models: the capacitated planned maintenance problem (CPMP) and the weighted uncapacitated planned maintenance problem (WUPMP). It introduces specific optimization algorithms such as construction heuristics, Lagrangean and tabu search metaheuristics. A problem independent hybrid approach links and alternates between two Lagrangean relaxations. It also analyzes the solvability with respect to the computational complexity of several problem classes, polyhedral properties and lower bounds. Computational studies demonstrate the performance of the heuristics, lower bounds, subgradients obtained from heuristics and the quality of dual information. This unique book includes implementation details and an introduction to the necessary theory making it suitable for upper undergraduate students.

Introduction.- The Capacitated Planned Maintenance Problem.- Known concepts and solution techniques.- The Weighted Uncapacitated Planned Maintenance Problem.- Analyzing the solvability of the Capacitated Planned Maintenance Problem.- Algorithms for the Capacitated Planned Maintenance Problem.- Computations for the Capacitated Planned Maintenance Problem.- Final remarks and future perspectives.
1 Introduction
1(6)
References
5(2)
2 The Capacitated Planned Maintenance Problem
7(18)
2.1 Problem Definition and Motivation
7(3)
2.2 Known Maintenance Problems
10(5)
2.2.1 Periodic Maintenance
10(1)
2.2.2 Machine Scheduling with Periodic Maintenance
11(1)
2.2.3 Periodic Maintenance Inspection
12(1)
2.2.4 Aircraft Maintenance
13(1)
2.2.5 Other Maintenance Approaches
13(2)
2.3 The Mathematical Formulation
15(10)
2.3.1 Assumptions and Terminology
17(2)
2.3.2 Data Structure
19(2)
References
21(4)
3 Known Concepts and Solution Techniques
25(46)
3.1 Computational Complexity
25(2)
3.2 Linear and Integer Programming
27(8)
3.2.1 The Simplex Algorithm
34(1)
3.2.2 The Primal-Dual Simplex Algorithm
34(1)
3.3 Dual Decomposition: Lagrangean Relaxation
35(14)
3.3.1 Column Generation
41(2)
3.3.2 Subgradient Optimization
43(6)
3.4 Primal Decomposition: Benders' Reformulation
49(3)
3.5 Local Search and Tabu Search
52(3)
3.5.1 Local Search
52(1)
3.5.2 Tabu Search
53(2)
3.6 The Knapsack Problem
55(16)
3.6.1 Valid Inequalities
56(3)
3.6.2 Lower and Upper Bounds
59(3)
3.6.3 An Exact Algorithm
62(3)
References
65(6)
4 The Weighted Uncapacitated Planned Maintenance Problem
71(32)
4.1 The Mathematical Formulation
71(3)
4.2 Polyhedral Properties
74(8)
4.3 Computational Complexity
82(7)
4.4 The Single Weighted Uncapacitated Planned Maintenance Problem
89(5)
4.4.1 An Optimal Solution to the Primal Problem
89(2)
4.4.2 An Optimal Solution to the Corresponding Dual Problem of the LP Relaxation
91(3)
4.5 The Uncapacitated Planned Maintenance Problem
94(9)
References
101(2)
5 Analyzing the Solvability of the Capacitated Planned Maintenance Problem
103(62)
5.1 Valid Inequalities and Polyhedral Properties
103(9)
5.2 Computational Complexity
112(15)
5.3 Lower Bounds
127(38)
5.3.1 Considered Lower Bounds
127(6)
5.3.2 Relative Strengths and Computational Complexity
133(11)
5.3.3 Transformations of the Lower Bounds
144(1)
5.3.3.1 Network Flow Problems
145(2)
5.3.3.2 Facility Location Problems
147(3)
5.3.4 Mathematical Formulations of the Lagrangean Duals
150(1)
5.3.4.1 Lagrangean Duals Z+(Q) and Z+(Q)
150(4)
5.3.4.2 Lagrangean Dual Z(P)
154(2)
5.3.4.3 Lagrangean Dual Z(C)
156(1)
5.3.4.4 Lagrangean Dual Z(P)/(C)
157(4)
5.3.4.5 Lagrangean Dual Z(V)
161(1)
References
162(3)
6 Algorithms for the Capacitated Planned Maintenance Problem
165(58)
6.1 Three Construction Heuristics
165(5)
6.1.1 The First Fit Heuristic
166(1)
6.1.2 The Overlap Heuristic
167(3)
6.1.3 The Iterated Best-of-Three Heuristic
170(1)
6.2 Two Lagrangean Heuristics
170(25)
6.2.1 The Lagrangean Relaxation of the Capacity Constraint
171(1)
6.2.1.1 The LP Lower Bound
172(2)
6.2.1.2 The Dual Priority Rule Lower Bound
174(2)
6.2.1.3 The Combined Lower Bound
176(1)
6.2.1.4 The Primal-Dual Lower Bound
176(7)
6.2.1.5 The Shortest Path Lower Bound
183(1)
6.2.1.6 The Upper Bound Heuristic
183(3)
6.2.2 The Lagrangean Relaxation of the Period Covering Constraint
186(1)
6.2.3 The Lagrangean Heuristic for Both Relaxations
187(2)
6.2.3.1 Initial Lagrangean Multiplier
189(2)
6.2.3.2 A Lagrangean Heuristic
191(4)
6.3 A More Sophisticated Lagrangean Hybrid Heuristic
195(16)
6.3.1 A General Approach to Link Two Lagrangean Relaxations
195(6)
6.3.2 The Lagrangean Hybrid Heuristic
201(1)
6.3.2.1 Initial Extended Cover Inequalities
202(1)
6.3.2.2 A Hybrid Heuristic
202(5)
6.3.3 Mathematical Formulations of the Auxiliary LPs
207(1)
6.3.3.1 The Auxiliary LP DL(C)
207(2)
6.3.3.2 The Auxiliary LP DL(P)
209(2)
6.4 A Tabu Search Heuristic
211(12)
6.4.1 The Tabu Search Heuristic
211(7)
6.4.2 Bitshifting in the Calculation of the Tabu Search Objective Function
218(3)
References
221(2)
7 Computations for the Capacitated Planned Maintenance Problem
223(44)
7.1 Instance Generation and Test-Sets
223(2)
7.1.1 A Value for the Mean rØ
224(1)
7.1.2 Test-Sets
225(1)
7.2 Absolute Strength of the Lower Bounds
225(5)
7.3 Performance of the Heuristics
230(37)
7.3.1 Heuristics to the Lagrangean Relaxations and Pseudo-Subgradient Optimization
231(1)
7.3.1.1 The Performance of the Heuristics
231(2)
7.3.1.2 Applying Different Heuristics in the Lagrangean Heuristic
233(4)
7.3.1.3 The Approximation of the Lagrangean Duals
237(2)
7.3.2 Heuristics to the Planned Maintenance Problem
239(1)
7.3.2.1 The Construction Heuristics
239(2)
7.3.2.2 Variants of the Lagrangean Hybrid Heuristic
241(13)
7.3.2.3 The Metaheuristics
254(11)
Reference
265(2)
8 Final Remarks and Future Perspectives
267(6)
A Additional Material for the Capacitated Planned Maintenance Problem
273(10)
A.1 Problem Extensions
273(5)
A.1.1 Capacitated Weighted Planned Maintenance Problems
273(1)
A.1.2 Multiple Machines
274(1)
A.1.3 Multiple Repairmen
274(1)
A.1.4 Maintenance Precedence Constraints
275(1)
A.1.5 Minimal Time Between Maintenance Activities
275(1)
A.1.6 Integration with Lot-Sizing
276(2)
A.2 Mathematical Formulations
278(5)
References
282(1)
Index 283
Torben Kuschel's academic passion is Operations Research and Operations Management since 2004. He is a researcher at the University of Wuppertal, Germany. 
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