The Disassembly Line: Balancing and Modeling by Seamus M. McGovern and Surendra M. Gupta (McGraw-Hill Professional)1CHAPTERIntroductionThis chapter provides an introduction to the book. Section 1.1 presents an overview of current disassembly issues. Section 1.2 describes the motivation of the text. The scope and objectives of the book are then given in Sec. 1.3 while the notations used throughout the text are detailed in Sec. 1.4. Finally, Sec. 1.5 presents an outline of the book.1.1Overview Manufacturers are increasingly recycling and remanufacturing their postconsumer products due to new, more rigid environmental legis-lation, increased public awareness, and extended manufacturer responsibility. In addition, the economic attractiveness of reusing products, subassemblies, or parts instead of disposing of them has helped to further energize this effort. Recycling is a process performed to retrieve the material content of used and nonfunctioning products. Remanufacturing on the other hand, is an industrial process in which worn-out products are restored to like-new conditions. Thus, reman-ufacturing provides the quality standards of new products with used parts.Product recovery seeks to obtain materials and parts from old or outdated products through recycling and remanufacturing in order to minimize the amount of waste sent to landfills. This includes the reuse of parts and products. There are many attributes of a product that enhance product recovery; examples include ease of disassem-bly, modularity, type and compatibility of materials used, material identification markings, and efficient cross-industrial reuse of com-mon parts/materials. The first crucial step of product recovery is disassembly.Disassembly is defined as the methodical extraction of valuable parts/subassemblies and materials from discarded products through a series of operations. After disassembly, reusable parts/subassemblies are cleaned, refurbished, tested, and directed to the part/subassembly inventory for use in remanufacturing operations. The recyclable materials can be sold to raw-material suppliers, while the residu-als are sent to landfills. Disassembly is a process that interacts with all phases of product recovery including before life (the period of design and life cycle analysis), the useful period (the time when the 3The Disassembly Line: Balancing and Modeling by Seamus M. McGovern and Surendra M. Gupta (McGraw-Hill Professional)4D i s a s s e m b l y B a c k g r o u n dproduct is actually being manufactured or is in use), and end-of-life(the period in which a product completes its useful life and is ready for further processing, recovery, or disposal).Disassembly has gained a great deal of attention in the literature due to its role in product recovery. A disassembly system faces many unique challenges; for example, it has significant inventory problems because of the disparity between the demands for certain parts or subassemblies and their yield from disassembly. The flow process is also different. As opposed to the normal “convergent” flow in regular assembly environment, in disassembly the flow process is “divergent” (a single product is broken down into many subassemblies and parts). There is also a high degree of uncertainty in the structure and the quality of the returned products. The condition of the products received is usually unknown and the reliability of the components is suspect. In addition, some parts of the product may cause pollution or may be hazardous. These parts may require special handling that can also influence the utilization of the disassembly workstations. For example, an automobile slated for disassembly contains a variety of parts that are dangerous to remove and/or present a hazard to the environment, such as the battery, airbags, fuel, and oil. Various demand sources may also lead to complications in disassembly-line balancing. The reusability of parts creates a demand for them; how-ever, the demands and availability of the reusable parts are signifi-cantly less predicable than what is found in the assembly process. Most products contain parts that are installed (and must be removed) in different attitudes, from different areas of the main structure, or in different directions. Since any required directional change increases the setup time for the disassembly process, it is desirable to minimize the number of directional changes in the chosen disassembly sequence. Finally, disassembly-line balancing is critical in minimiz-ing the use of valuable resources (such as time and money) invested in disassembly and maximizing the level of automation of the disas-sembly process and the quality of the parts (or materials) recovered.This part of the book (Part I) provides a background to many of the issues and much of the current research, as well as an introduc-tion to the problems and possible solutions. Included in this is a review of assembly lines, an introduction to disassembly lines, a sur-vey of current research, graphical representations of products, an overview of computational complexity, and a description of combi-natorial optimization searches.In Part II of this book, the DISASSEMBLY LINE BALANCING PROBLEM (DLBP) is addressed using combinatorial optimization methodologies. While exhaustive search consistently provides the optimal solution, its exponential time complexity quickly reduces its practicality. Combinatorial optimization techniques are instrumental in obtaining optimal or near-optimal solutions to problems with The Disassembly Line: Balancing and Modeling by Seamus M. McGovern and Surendra M. Gupta (McGraw-Hill Professional)I n t r o d u c t i o n5intractably large solution spaces. Combinatorial optimization is an emerging field that combines techniques from applied mathematics, operations research, and computer science to solve optimization problems over discrete structures. Some of these techniques include greedy algorithms, integer and linear programming, branch-and-bound, divide-and-conquer, dynamic programming, local optimiza-tion, simulated annealing, genetic algorithms, and approximation algorithms.The seven techniques selected for application in this text seek to provide a feasible disassembly sequence (i.e., one in which no prece-dence constraints are violated since some tasks cannot be performed until their predecessor tasks have been completed), minimize the number of workstations, minimize the total idle time, and minimize the variation in idle times between workstations, while attempting to remove hazardous and high-demand product components as early as possible and remove parts with similar part removal direc-tions together. Four data sets are used as case studies. These instances are used with all of the solution techniques to illustrate implementation of the methodologies, measure performance, and enable comparisons.In Part III of this book, other problems related to the disassembly line are explored. This part visits the bulk of the remaining disassembly-related areas. A background—much of it from traditional assembly line and production theory—is provided and then disassembly-specific issues and research are detailed. These research areas include product plan-ning, facility and line layout, sequencing and scheduling, inventory, just-in-time, revenue, and unbalanced lines.1.2MotivationEnd-of-life processing for products is becoming increasingly desir-able due to consumer preference, government regulation, and corpo-rate financial interests. Obtaining components and materials that have some value while minimizing the amount of waste sent to land-fills and reducing the amount of processed toxins introduced into the environment are all compelling reasons that disassembly is of such importance and has garnered so much global interest.Disassembly has unique characteristics. While possessing similarities to assembly, it is not the reverse of the assembly process (Brennan et al., 1994); therefore, new and efficient approaches and methodologies are needed to effectively perform disassembly-line operations. The difficulty in obtaining efficient disassembly-line sequence solutions stems from the fact that a solution sequence consists of a permutation of num-bers. This permutation would contain as many elements as there are parts in the product. As such, the observation can be made that the DISASSEMBLY LINE BALANCING PROBLEM would appear to be The Disassembly Line: Balancing and Modeling by Seamus M. McGovern and Surendra M. Gupta (McGraw-Hill Professional)6D i s a s s e m b l y B a c k g r o u n dNP-hard and the decision version would appear to be NP-complete. Also of interest, the DISASSEMBLY LINE BALANCING PROBLEM is a recent problem, first formally described in this century (Güngör and Gupta, 2002).The importance of the disassembly line’s role in end-of-life pro-cessing, the contemporary nature of the problem, and its NP-complete characteristics makes the DISASSEMBLY LINE BALANCING PROBLEM—and the disassembly line in general—interesting and relevant.1.3Scope and ObjectivesThis book introduces the disassembly line (Part I) and details its primary focus—disassembly-line balancing (Part II)—and then considers other disassembly-line problems that do not directly address balancing. Various techniques are explored that involve multiple objectives to address disassembly-line balancing. Since the decision version of the DISASSEMBLY LINE BALANCING PROBLEM is NP-complete, this book considers a rigorous combinatorial optimization treatment of the problem. As part of this, the problem is mathematically defined and proven to be NP-complete (as well as unary NP-complete and NP-hard), quantitative and qualitative evaluation criteria are developed, and four problem instances are introduced. Next, seven different techniques from the realm of combinatorial optimization are employed to solve the four instances. The seven methodologies are then compared to each other.The first methodology used is exhaustive search, which here employs a depth-first search using a recursive backtracking proce-dure to visit all permutations of an instance’s n parts to consistently obtain the optimal solution sequence. The exhaustive search algo-rithm is presented for obtaining the optimal solution to small instances of the DLBP. While always optimal, it is limited in the size of the instance it can solve since the time to solve an instance grows expo-nentially with the size of the instance. The second technique used is a genetic algorithm (GA), a metaheuristic that recombines and mutates the best solutions over many generations. The genetic algorithm considered here involves either a randomly generated or a hot-started initial population with crossover, mutation, and fitness competition performed over many generations. The third technique used is ant colony optimization (ACO), another metaheuristic. The ant colony optimization metaheuristic applied here is an ant system algorithm known as the ant-cycle model that is enhanced for the DLBP. Ant colony optimization uses software agents referred to as ants that grow a solution from first to last part under greedy decision-making rules. Successful ants add pheromone (in proportion to the quality of their solution) to their paths, all paths slowly evaporate, and the pro-cess repeats for a given number of cycles. The fourth technique used The Disassembly Line: Balancing and Modeling by Seamus M. McGovern and Surendra M. Gupta (McGraw-Hill Professional)I n t r o d u c t i o n7is a deterministic first-fit-decreasing greedy algorithm, similar to that developed for the BIN-PACKING problem. Two 2-phase hybrids are considered next. The first hybrid process consists of the greedy sorting algorithm followed by a hill-climbing local search. The problem-specific hill-climbing algorithm only considers swapping parts that are in adjacent workstations. A second deterministic hybrid process is then shown. It consists of the same greedy sorting algorithm followed by a 2-optimal (2-opt) local search. The 2-opt search is modified for the DLBP by exchanging parts instead of the arcs connecting them. The final technique used is an uninformed, modified British Muse-um–type search that moves through the search space similarly to exhaustive search but only samples the space, methodically visiting equally spaced solutions in a deterministic manner. Influenced by the hunter-killer search tactics of military helicopters, this general-purpose heuristic algorithm easily lends itself to the DLBP. All of the techniques deliver optimal or near-optimal solutions while preserving the prece-dence relationships among the components. Next (Part III), other wide-ranging disassembly-line problems are introduced. These problems encompass the areas of product design, facility location and line layout, sequencing and scheduling, removed-part inventory, just-in-time, revenue, and intentionally or uninten-tionally unbalanced lines.1.4Format and NotationThe following general guidelines are used throughout the book. Using the format of Garey and Johnson (1979), names of problems, including NP-complete problems, are capitalized when referring to the problem but not when referring to a methodology (e.g., “the LIN-EAR PROGRAMMING problem” is a different use than “modeling a problem using linear programming”) or when the formal name of the problem is not appropriate. Since the search methodologies in this book are used for problems other than the DLBP, the versions used in this book make use of a title case format and are often prefaced by “DLBP,” while generic references to the methodologies are made in lowercase (e.g., “DLBP Exhaustive Search” and “Exhaustive Search” refer to the problem-specific methodologies developed for use in this book while “exhaustive search” refers to any type or implementation of exhaustive search). The first time a proper mathematical or scien-tific term is defined (or if it is not defined, the first time it is used in the chapter that primarily references it, or lacking this, the first time it is used in the book) it is italicized. This is primarily the case when mathematical terms have a specific meaning but make use of a word common to the English language, an example being use of the word “language” in Chap. 6. Italics are also used to highlight some proper names. Most of the mathematical conventions are as found in Cormen The Disassembly Line: Balancing and Modeling by Seamus M. McGovern and Surendra M. Gupta (McGraw-Hill Professional)8D i s a s s e m b l y B a c k g r o u n det al. (2001), Rosen (1999), or Garey and Johnson (1979). Finally, part removal times may also refer to virtual parts (also referred to as virtualcomponents; Lambert and Gupta, 2005); that is, a task performed that is required (or desired or possible) and takes a finite amount of time but does not result in the immediate removal of any part. Therefore, the terms “task time” and “part removal time” are both used here with the understanding that the two are potentially distinct. Unless otherwise specified, work element, job, part, component, subassem-bly, and task may be used interchangeably throughout this text.1.4.1General and Disassembly-Line Balancing NotationThe following notation is used in the remainder of the book:1, 2, …, nordered n-tuple{1, 2, …, n} set (using the formal definition, i.e., list of n distinct items)(1, 2, …, n)list of n items(p, q)arc (i.e., direct edge) pq[p, q]edge pqA-Bsubassembly made up of part A and part Bpolynomial time reduction or polynomial transfor-Pmation; read as: “can be converted to,” “is easier than,” “is a subset of,” or “is a smaller problem than”partial ordering, that is, x precedes y is written xyXcardinality of the set Xxceiling function of x; assigns the smallest integer x,for example, 1.3 = 2max(x, y)maximum of x and ymin(x, y)minimum of x and y“for all,” “for every”“an element of,” “is in”“there exists,” “there exists at least one,” “for some”“in proportion to”intersectionunionsubsetconjunction (logical AND)disjunction (logical OR)!factorial:“such that,” used primarily to avoid confusion with the vertical bars used to define cardinalityThe Disassembly Line: Balancing and Modeling by Seamus M. McGovern and Surendra M. Gupta (McGraw-Hill Professional)I n t r o d u c t i o n9|“such that,” used primarily to avoid confusion with the pseudo-code equal sign “:=” also used as a triplet separator in scheduling theory and to represent absolute value in the efficacy index“maps to”“if and only if”weight of existing pheromone (trail) in path selec-tion; also refers to the machine environment in scheduling theoryweight of the edges in path selection; also refers to the processing characteristics and constraints in scheduling theoryempty stringobjective to be minimized in scheduling theory(t) visibility value of edge (arc for the DLBP) pq at time tp, qvariable such that 1 represents the pheromone evaporation rate(NC) amount of trail on edge pq (arc for the DLBP) p, qduring cycle NCkth element’s skip measure (i.e., for the solution’s kthird element, visit every second possible task for = 2)3kth element’s delta skip measure; difference kbetween problem size n and skip size (i.e., for k = 10 and n = 80, = 70)“big-oh,” g(x) is (h(x)) whenever y : g(x)yh(x)xzproduct; also refers to a decision problem (consisting of a set D of decision instances and a subset YD of yes-instances) in complexity theory“big-theta,” g(x) is (h(x)) whenever g(x) is (h(x))and g(x) is (h(x))summation; also refers to an alphabet (a finite set of symbols, e.g., = {0, 1}) in complexity theoryset containing all possible strings from “big-omega,” g(x) is (h(x)) whenever y : g(x)yh(x)xzaMULTIPROCESSOR SCHEDULING problem task variable; also refers to a function variable in com-plexity theoryAMULTIPROCESSOR SCHEDULING problem task setbfunction variable in complexity theoryThe Disassembly Line: Balancing and Modeling by Seamus M. McGovern and Surendra M. Gupta (McGraw-Hill Professional)10D i s a s s e m b l y B a c k g r o u n dBMULTIPROCESSOR SCHEDULING problem deadline boundBSTidentification of kth part in temporary best solution ksequence during adjacent element hill-climbing (AEHC) and 2-Optcinitial amount of pheromone on all of the paths at time t = 0; also refers to a cost function that maps feasible points to the real numbers in complexity theoryCcompletion time of task k in a flow shop in schedul-king theoryCcompletion time of the last task to be completed in maxthe flow shop in scheduling theoryCTcycle time; maximum time available at each work-stationddemand; quantity of part k requestedkDdemand rating for a given solution sequence; also demand bound for the decision version of DLBP; also refers to the set of all instances of a decision problem in complexity theoryDoptimal demand rating for a given instance; also used to refer to the set of solutions optimal in DDlower demand bound for a given instancelowerDupper demand bound for a given instanceupperDPset of demanded partseencoding function in complexity theoryE[x]expected value of xEI efficacy index of measure x; generates values xbetween 0 and 100 percentfa feasible solution in complexity theoryFmeasure of balance for a given solution sequence; also refers to the finite set of feasible points in com-plexity theoryFoptimal measure of balance for a given instance; also used to refer to the set of solutions optimal in FFlower measure of balance bound for a given instancelowerFupper measure of balance bound for a given instanceupperFmeasure of balance of ant r’s sequence at time tt, rFmflow shop with m machinesFSfeasible sequence binary value; FS = 1 if feasible, 0 otherwiseg(x)function in complexity theoryThe Disassembly Line: Balancing and Modeling by Seamus M. McGovern and Surendra M. Gupta (McGraw-Hill Professional)I n t r o d u c t i o n11hbinary value; 1 if part k is hazardous, else 0kh(x)function in complexity theoryHhazard rating for a solution; also hazard bound for the decision version of DLBPHoptimal hazard rating for a given instance; also used to refer to the set of solutions optimal in HHlower hazard bound for a given instancelowerHupper hazard bound for a given instanceupperHPset of hazardous partsicounter variableItotal idle time for a given solution sequence; also refers to an instance of a problem in complexity theoryIoptimum idle time for a given instanceItotal idle time of workstation jjIlower idle time bound for a given instancelowerIupper idle time bound for a given instanceupperISSbinary value; 1 if part k is in the solution sequence, kelse 0jworkstation count (1, …, NWS)kcounter variable (typically k {1, 2, …, n} and iden-tifies a part or refers to a sequence position)l(a)MULTIPROCESSOR SCHEDULING problem task lengthLLanguage in complexity theory, that is, any set of strings over (e.g., L = {1, 10, 100, 010, 1001, …})LACO delta-trail divisor value; set equal to F for rn, rthe DLBPmnumber of processors in the MULTIPROCESSOR SCHEDULING problem; also number of ants; also number of machinesnnumber of parts for removalNnumber of chromosomes (population)Nset of natural numbers, that is, {0, 1, 2, …}NCmaximum number of cycles for ACOmaxNPWnumber of parts in workstation jjNWS number of workstations required for a given solu-tion sequenceNWSoptimal (minimum) number of workstations for n partsNWSlower bound on the minimum possible number of lower workstations for n partsDocument Outline
- Contents
- Untitled
- Preface
- Acknowledgments
- Part I: Disassembly Background
- 1 Introduction
- 1.1 Overview
- 1.2 Motivation
- 1.3 Scope and Objectives
- 1.4 Format and Notation
- 1.5 Outline
- 2 Assembly Lines
- 2.1 Introduction
- 2.2 Production Background
- 2.3 History of the Assembly Line
- 2.4 Assembly-Line Balancing
- 2.5 Line Modeling
- 2.6 Summary
- 3 Disassembly Lines
- 3.1 Introduction
- 3.2 Overview
- 3.3 History of the Disassembly Line
- 3.4 Disassembly-Specific Considerations
- 4 Related Research
- 4.1 Introduction
- 4.2 Environmentally Conscious Manufacturing and Product Recovery
- 4.3 Assembly-Line Balancing and Manufacturing Systems
- 4.4 Disassembly and Remanufacturing
- 4.5 Optimization and Algorithms
- 5 Graphical Representations of Products to Be Disassembled
- 5.1 Introduction
- 5.2 General Product Disassembly Representations
- 5.3 Task-Based Precedence Diagrams
- 5.4 Disassembly Constraint Graphs
- 5.5 Schematic/Flowchart-Style Vertex and Arc Disassembly Representation
- 5.6 Other Representations
- 6 Computational Complexity of Combinatorial Problems
- 6.1 Introduction
- 6.2 Complexity Theory Background
- 6.3 NP-Completeness
- 6.4 NP-Completeness in the Strong Sense
- 6.5 NP-Hardness
- 6.6 Overview of NP-Complete Problems
- 6.7 Solving NP-Complete Problems
- 6.8 Other Classes of Problems
- 6.9 Heuristic Performance Analysis
- 6.10 Hardware and Software Considerations
- Part II: Disassembly-Line Balancing
- 7 Disassembly-Line Balancing Overview
- 7.1 Introduction
- 7.2 The Disassembly-Line Balancing Problem
- 7.3 Model Considerations
- 7.4 Balancing Objectives
- 8 Description of the Disassembly Line and the Mathematical Model
- 8.1 Introduction
- 8.2 Problem Overview
- 8.3 Balance Measure and Theoretical Bounds Formulation
- 8.4 Hazard Measure and Theoretical Bounds Formulation
- 8.5 Demand Measure and Theoretical Bounds Formulation
- 8.6 Direction Measure and Theoretical Bounds Formulation
- 8.7 Models and Measures as Prototypes
- 8.8 Matrices for Precedence Representation
- 9 Computational Complexity of DLBP
- 9.1 Introduction
- 9.2 DLBP NP-Completeness
- 9.3 DLBP NP-Completeness in the Strong Sense
- 9.4 DLBP NP-Hardness
- 10 Combinatorial Optimization Searches
- 10.1 Introduction
- 10.2 Combinatorial Optimization Methodologies
- 10.3 Exhaustive Search
- 10.4 Genetic Algorithm
- 10.5 Ant Colony Optimization
- 10.6 Greedy Algorithm
- 10.7 Adjacent Element Hill-Climbing Heuristic
- 10.8 k-Opt Heuristic
- 10.9 H-K General-Purpose Heuristic
- 11 Experimental Instances
- 11.1 Introduction
- 11.2 Personal Computer Instance
- 11.3 The 10-Part Instance
- 11.4 Cellular Telephone Instance
- 11.5 DLBP A Priori Optimal Solution Benchmark Instances
- 12 Analytical Methodologies
- 12.1 Introduction
- 12.2 Graphical Analysis Tools
- 12.3 Multiple-Criteria Decision-Making Considerations
- 12.4 Normalization and Efficacy Index Equations
- 12.5 Simulation
- 13 Exhaustive Search
- 13.1 Introduction
- 13.2 Model Description
- 13.3 Numerical Results
- 13.4 Conclusions
- 14 Genetic Algorithm
- 14.1 Introduction
- 14.2 Model Description
- 14.3 DLBP-Specific Genetic Algorithm Architecture
- 14.4 DLBP-Specific Qualitative Modifications
- 14.5 DLBP-Specific Quantitative Modifications
- 14.6 Numerical Results
- 14.7 Conclusions
- 15 Ant Colony Optimization
- 15.1 Introduction
- 15.2 Model Description
- 15.3 DLBP-Specific Qualitative Modifications and the Metaheuristic
- 15.4 Quantitative Assignments
- 15.5 Numerical Results
- 15.6 Conclusions
- 16 Greedy Algorithm
- 16.1 Introduction
- 16.2 Model Description
- 16.3 Numerical Results
- 16.4 Conclusions
- 17 Greedy/Adjacent Element Hill-Climbing Hybrid
- 17.1 Introduction
- 17.2 Model Description
- 17.3 Numerical Results
- 17.4 Conclusions
- 18 Greedy/2-Opt Hybrid
- 18.1 Introduction
- 18.2 Model Description
- 18.3 Numerical Results
- 18.4 Conclusions
- 19 H-K Heuristic
- 19.1 Introduction
- 19.2 DLBP Application
- 19.3 DLBP A Priori Numerical Analysis for Varying Skip Size
- 19.4 Numerical Results
- 19.5 Conclusions
- 20 Quantitative and Qualitative Comparative Analysis
- 20.1 Introduction
- 20.2 Experimental Results
- 20.3 Conclusions
- 21 Other Disassembly-Line Balancing Research
- 21.1 Overview
- 21.2 Problem Extensions
- 21.3 Additional Solution Methodologies
- 21.4 Probabilistic Disassembly-Line Balancing
- 21.5 Probabilistic Disassembly-Line Data
- 21.6 Future Research Directions
- Part III: Further Disassembly-Line Considerations
- 22 Overview of Additional Disassembly-Line Related Problems
- 22.1 Introduction
- 22.2 Mathematical Models
- 22.3 Computational Complexity
- 22.4 Case Studies
- 22.5 Analytical and Solution Methodologies
- 23 Disassembly-Line Product Planning
- 23.1 Introduction
- 23.2 Sustainable Product Design Overview
- 23.3 New-Product Design Metrics for Demanufacturing
- 23.4 Additional Design-for-Disassembly Studies
- 23.5 Summary
- 24 Disassembly-Line Design
- 24.1 Introduction
- 24.2 Background
- 24.3 Facility Location and Layout Overview
- 24.4 Mixed-Model Disassembly-Line Design
- 24.5 Disassembly-Line Design Metrics
- 25 Disassembly-Line Sequencing and Scheduling
- 25.1 Introduction
- 25.2 Machine Sequencing and Scheduling Overview
- 25.3 Disassembly Sequencing and Scheduling
- 25.4 Stochastic Sequencing and Scheduling
- 25.5 Additional Disassembly-Sequencing Studies
- 25.6 Additional Disassembly-Scheduling Studies
- 26 Disassembly-Line Inventory
- 26.1 Introduction
- 26.2 Inventory Theory Background
- 26.3 Disassembly to Order
- 26.4 Additional Disassembly-Inventory Studies
- 27 Disassembly-Line Just-in-Time
- 27.1 Introduction
- 27.2 Just-in-Time Background
- 27.3 Just-in-Time Research
- 27.4 Multikanban System for End-of-Life Products
- 28 Disassembly-Line Revenue
- 28.1 Introduction
- 28.2 Disassembly-Line Revenue Background
- 28.3 Disassembly-Line Revenue Modeling
- 28.4 Additional Disassembly-Line Revenue Studies
- 29 Unbalanced Disassembly Lines
- 29.1 Introduction
- 29.2 Background
- 29.3 Stochastic Line Modeling and Unbalanced Lines
- 29.4 Queueing Theory Background
- 29.5 Benchmark Data for Measuring Unbalance
- References
- Appendix: Acronyms
- Author Index
- A
- B
- C
- D
- E
- F
- G
- H
- I
- J
- K
- L
- M
- N
- O
- P
- R
- S
- T
- U
- V
- W
- X
- Y
- Z
- Subject Index
Add New Comment