Lang Production and Inventory Management with Substitutions

1. Auflage 2009
ISBN: 978-3-642-04247-8
Verlag: Springer
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, Band 636, 260 Seiten

Reihe: Lecture Notes in Economics and Mathematical Systems

Quantitativeapproachesforsolvingproductionplanningandinventorymanagement problems in industry have gained growing importance in the past years. Due to the increasinguse of AdvancedPlanningSystems, a widespreadpracticalapplicationof the sophisticated optimization models and algorithms developed by the Production Management and Operations Research community now seem within reach. The possibility that productscan be replaced by certain substitute productsexists in various application areas of production planning and inventory management. Substitutions can be useful for a number of reasons, among others to circ- vent production and supply bottlenecks and disruptions, increase the service level, reduce setup costs and times, and lower inventories and thereby decrease ca- tal lockup. Considering the current trend in industry towards shorter product life cycles and greater product variety, the importance of substitutions appears likely to grow. Closely related to substitutions are ?exible bills-of-materials and recipes in multi-level production systems. However, so far, the aspect of substitutions has not attracted much attention in academic literature. Existing lot-sizing models matching complex requirements of industrial optimization problems (e.g., constrained capacities, sequence-dependent setups, multiple resources) such as the Capacitated Lot-Sizing Problem with Sequence-Dependent Setups (CLSD) and the General Lot-Sizing and Scheduling Problem for Multiple Production Stages (GLSPMS) do not feature in substitution options.

Autoren/Hrsg.

Lang, J. Christian

Inhaltsverzeichnis

1;Foreword;5
2;Preface;7
3;Contents;9
4;List of Figures;13
5;List of Tables;16
6;Acronyms;18
7;1 Introduction;20
7.1;1.1 Definitions;22
7.2;1.2 Motivation;23
7.3;1.3 Goals;24
7.4;1.4 Outline;25
8;2 Production and Operations Management:Models and Algorithms;28
8.1;2.1 Dynamic Lot-Sizing;29
8.1.1;2.1.1 Classification of Models;30
8.1.1.1;2.1.1.1 Context of Model;30
8.1.1.2;2.1.1.2 Production System Characteristics;36
8.1.1.3;2.1.1.3 Modeling Technique;45
8.1.1.4;2.1.1.4 Decision Variables;49
8.1.1.5;2.1.1.5 Objective(s);50
8.1.2;2.1.2 The Wagner–Whitin Problem;52
8.1.3;2.1.3 The Capacitated Lot-Sizing Problem;53
8.1.4;2.1.4 The Capacitated Lot-Sizing Problemwith Sequence-Dependent Setups;55
8.1.5;2.1.5 The General Lot-Sizing and Scheduling Problem;58
8.1.6;2.1.6 The Multi-Level Capacitated Lot-Sizing Problem;61
8.1.7;2.1.7 The General Lot-Sizing and Scheduling Problemfor Multiple Production Stages;63
8.1.8;2.1.8 Comparison of Models;70
8.2;2.2 Solution Techniques for Dynamic Lot-Sizing;71
8.2.1;2.2.1 Overview;71
8.2.2;2.2.2 Valid Inequalities;73
8.2.3;2.2.3 Reformulations;74
8.2.4;2.2.4 Combinations of Heuristics and Exact Algorithms;76
8.2.5;2.2.5 Selected Approaches for Lot-Sizingwith Sequence-Dependent Setups;80
8.3;2.3 Transshipment Problems;81
8.3.1;2.3.1 Basics;81
8.3.2;2.3.2 Classification of Models;82
8.4;2.4 Solution Techniques for Transshipment Problems;85
8.4.1;2.4.1 Existing Approaches for Transshipment Problems;85
8.4.2;2.4.2 Simulation-Based Optimization;87
8.4.2.1;2.4.2.1 SBO Applications;88
8.4.2.2;2.4.2.2 Elements of an SBO Model;89
8.4.2.3;2.4.2.3 Classification of SBO Models;91
8.4.2.4;2.4.2.4 Specifics of SBO;92
8.4.2.5;2.4.2.5 Common Random Numbers;94
8.4.2.6;2.4.2.6 SBO Algorithms: Taxonomy and Selection Criteria;95
8.4.2.7;2.4.2.7 Direct Search: Pattern Search;96
8.4.3;2.4.3 Robust Optimization;97
9;3 Graphical Modeling of Substitutions and Flexible Bills-of-Materials;99
9.1;3.1 Applications;99
9.2;3.2 Modeling Approaches;102
9.2.1;3.2.1 Blending Models;103
9.2.2;3.2.2 Substitution Graphs;103
9.2.2.1;3.2.2.1 Substitution Structures;104
9.2.2.2;3.2.2.2 Demand Class-Specific Substitution Options;104
9.2.2.3;3.2.2.3 Modeling Transitive Substitution Options;105
9.2.2.4;3.2.2.4 Substitution Ratio;106
9.2.2.5;3.2.2.5 Substitution Triangle Inequality;107
9.2.3;3.2.3 Substitution Hypergraphs;107
9.2.3.1;3.2.3.1 Modeling Approach;107
9.2.3.2;3.2.3.2 Classification Criteria;110
9.2.4;3.2.4 Task-Oriented Modeling;112
9.2.5;3.2.5 Comparison of Modeling Approaches;115
9.3;3.3 Model Classification Criteria;116
9.3.1;3.3.1 Demand;116
9.3.1.1;3.3.1.1 Information and Activeness of Customers Regarding Substitutions;116
9.3.1.2;3.3.1.2 Substitution Acceptance;118
9.3.1.3;3.3.1.3 Linkage of Substitutions to Customer Orders;120
9.3.2;3.3.2 Model Context;120
9.3.2.1;3.3.2.1 Planning Level of Substitution;120
9.3.2.2;3.3.2.2 Substitute Sources;120
9.3.3;3.3.3 Substitution Characteristics;121
9.3.3.1;3.3.3.1 Substitute Preference Order;121
9.3.3.2;3.3.3.2 Partial vs. Exclusive Substitution;121
9.3.4;3.3.4 Conversions;121
9.3.4.1;3.3.4.1 Interpretations of Conversion Costs;121
9.3.4.2;3.3.4.2 Setup Times;122
9.3.4.3;3.3.4.3 Production and Conversion Capacities;122
9.3.4.4;3.3.4.4 Product Type Quantities;123
9.3.4.5;3.3.4.5 Time of Conversion;123
9.3.5;3.3.5 Production;124
9.3.5.1;3.3.5.1 Yield;124
9.4;3.4 Implementing Product Substitution;124
10;4 Literature Review;128
10.1;4.1 Assortment Problems;128
10.2;4.2 Lot-Sizing with Substitutions;129
10.2.1;4.2.1 The Requirements Planning Problem with Substitutions;130
10.2.2;4.2.2 Substitution with/without Conversion Problems;133
10.2.3;4.2.3 The Multi-level Lot-Sizing Problem with Flexible Production Sequences;134
10.2.3.1;4.2.3.1 Assumptions;135
10.2.3.2;4.2.3.2 Formulation;135
10.2.3.3;4.2.3.3 Transformation of RPS and SWCP into Special Case of MLFP;137
10.3;4.3 Related Aspects;138
11;5 Efficient Reformulations for Uncapacitated and Capacitated Lot-Sizing with Substitutions and Initial Inventories;142
11.1;5.1 Introduction;142
11.2;5.2 Outline;143
11.3;5.3 The Lot-Sizing Problem with Substitution and Initial Inventory;143
11.3.1;5.3.1 Model Formulation;144
11.3.2;5.3.2 Facility Location Based Reformulation;145
11.3.3;5.3.3 Valid Inequalities;148
11.4;5.4 The Multi-Resource Capacitated Lot-Sizing Problem with Substitution;148
11.5;5.5 Computational Experiments;150
11.5.1;5.5.1 Problem Instances;151
11.5.2;5.5.2 Solution Approaches;153
11.5.3;5.5.3 Experimental Designs, Results and Interpretation;153
11.5.3.1;5.5.3.1 LSP-SI: Influence of Substitution Structure, Initial Inventories and Problem Size;153
11.5.3.2;5.5.3.2 Larger LSP-SI Instances: Approximate Extended Formulations;156
11.5.3.3;5.5.3.3 MR-CLSP-S: Lost Sales vs. Overtime;157
11.5.3.4;5.5.3.4 MR-CLSP-S: Scarcity of Production Capacity;158
11.5.3.5;5.5.3.5 MR-CLSP-S: Number of Resources;159
11.6;5.6 Conclusions;162
11.7;5.7 Transformation of LSP-SI into a CFLP;163
11.8;5.8 Proof that LSP-SI is NP-Hard;165
11.9;5.9 Proof for Product Substitution (l,S)-Cuts;166
12;6 MIP-Based Heuristics for CapacitatedLot-Sizing with Sequence-DependentSetups and Substitutions;168
12.1;6.1 Introduction;168
12.2;6.2 Outline;169
12.3;6.3 The Capacitated Lot-Sizing Problemwith Sequence-Dependent Setups and Substitutions;170
12.3.1;6.3.1 Assumptions;170
12.3.2;6.3.2 Formulation;171
12.4;6.4 Determining Efficient or Good Sequences;174
12.5;6.5 MIP-Based Heuristics;175
12.5.1;6.5.1 Subproblems with Relaxed or Fixed Binary Variables;175
12.5.2;6.5.2 Decompositions;177
12.5.2.1;6.5.2.1 Time-Oriented Decompositions;177
12.5.2.2;6.5.2.2 Product-Oriented Decompositions;179
12.5.2.3;6.5.2.3 Substitute-Oriented Decompositions;182
12.5.3;6.5.3 Relax&Fix;182
12.5.4;6.5.4 Fix&Optimize;183
12.5.4.1;6.5.4.1 Algorithm Scheme;184
12.5.4.2;6.5.4.2 Priority Rules;185
12.5.4.3;6.5.4.3 Generating Initial Feasible Sequences;186
12.5.5;6.5.5 Two-Stage Relax&Fix/Optimize Algorithm;186
12.5.6;6.5.6 Time Limit and Stopping Criterion for Subproblems;186
12.6;6.6 Computational Experiments;187
12.6.1;6.6.1 Problem Instances;187
12.6.2;6.6.2 Experimental Design;192
12.6.3;6.6.3 Solution Approaches;192
12.6.4;6.6.4 Results and Interpretation;194
12.7;6.7 Summary and Conclusions;199
13;7 Multi-Level Lot-Sizing Models with Flexible Bills-of-Materials;201
13.1;7.1 The Multi-Level Capacitated Lot-Sizing Problem with Substitutions;201
13.1.1;7.1.1 Assumptions;202
13.1.2;7.1.2 Formulation;203
13.1.3;7.1.3 Example of Substitution Hypergraph;205
13.1.4;7.1.4 Transformation into Special Case of MLFP;206
13.1.5;7.1.5 Echelon Stocks and Flexible BOMs;207
13.2;7.2 The General Lot-Sizing and Scheduling Problem for Multiple Production Stages with Flexible Production Sequences;207
13.2.1;7.2.1 Assumptions;207
13.2.2;7.2.2 Formulation;209
13.2.3;7.2.3 Ensuring Temporal Feasibility within Micro-Periods;213
13.2.3.1;7.2.3.1 Calculating Minimal and Maximal Values for Gozinto Factors;215
13.2.3.2;7.2.3.2 Constraints for Potentially Faster Successors;216
13.2.3.3;7.2.3.3 Constraints for Potentially Slower Successors;218
13.2.4;7.2.4 Transformation of GLSPMS into Special Case of GLSPMS-FPS;219
14;8 Blood Inventory Control with Transshipments and Substitutions;221
14.1;8.1 Introduction;221
14.1.1;8.1.1 Analogy Between Transshipments and Substitutions;221
14.1.2;8.1.2 Outline;223
14.2;8.2 Combining Transshipments and Substitutions;223
14.3;8.3 Blood Bank Inventory Control;224
14.4;8.4 Blood Bank Simulation Model;227
14.4.1;8.4.1 Assumptions;227
14.4.2;8.4.2 Replenishment, Substitution and Transshipment Policies;228
14.5;8.5 Simulation-Based Optimization Approach;230
14.5.1;8.5.1 Optimization Problem;230
14.5.2;8.5.2 Pattern Search Algorithm;231
14.5.3;8.5.3 Adaption of PS Algorithm;233
14.6;8.6 Computational Experiments;234
14.6.1;8.6.1 Setup;234
14.6.1.1;8.6.1.1 Simulation Model Parameters;234
14.6.1.2;8.6.1.2 PS Algorithm Parameters;236
14.6.2;8.6.2 Experiment Designs, Results and Interpretation;236
14.6.2.1;8.6.2.1 Impact of Transshipments and Substitutions;236
14.6.2.2;8.6.2.2 Pattern of Search Directions;238
14.6.2.3;8.6.2.3 Difference Between Small and Large Hospitals;239
14.7;8.7 Conclusions;241
14.8;8.8 Limitations;241
15;9 Conclusions and Future Research;243
15.1;9.1 Conclusions;243
15.2;9.2 Future Research;245
15.2.1;9.2.1 Multi-Location Inventory Control with Transshipments and Substitutions;245
15.2.2;9.2.2 Production Planning with Substitution and Flexible BOMs;246
15.2.3;9.2.3 Substitutions and Flexible BOMs in Advanced Planning Software;247
16;Appendix A Additional Related Literature;247
17;Bibliography;251
18;Index;268