ISBN: 3540430156
TITLE: Planning Stability in Material Requirement Planning
AUTHOR: Gerald Heisig
TOC:

1. Introduction 1
1.1 Research Motivations 1
1.2 Planning Stability in Material Coordination Systems 3
1.3 Objectives and Structure of Analysis 5
2. Material Requirements Planning and Inventory Control 7
2.1 Concepts for Material Planning 8
2.1.1 Stochastic Inventory Control (SIC) 8
2.1.2 Material Requirements Planning (MRP) 11
2.2 Types of Uncertainty in a Production Environment 13
2.3 Methods for Coping with Uncertainty 14
2.3.1 Planning Concepts in a Stochastic Environment 14
2.3.1.1 Stochastic Dynamic Programming 14
2.3.1.2 Rolling Horizons 15
2.3.2 MRP Logic in a Stochastic Environment 16
2.3.2.1 Safety Stocks, Safety Times, and Safety Capacities 16
2.3.2.2 Hedging and Overplanning 17
2.3.3 Alternative Concepts in a Stochastic Environment 18
2.3.3.1 Line Requirements Planning (LRP) 19
2.3.3.2 Flexible integral Requirements planning STrategy (FiRST) 19
2.4 Summary 20
3. Nervousness in Material Requirements Planning Systems 21
3.1 Rolling Horizon Planning Framework 23
3.1.1 General Approach 23
3.1.2 Characterization of Plan Revisions 25
3.2 Clarification of Terms: Robustness, Planning Stability, and Flexibility 29
3.3 Explanation of Technical Stability Measures 33
3.4 Concepts for Measuring Planning Stability 34
3.4.1 Setup-Oriented Stability 38
3.4.2 Quantity-Oriented Stability 41
3.4.3 Extensions 44
3.4.3.1 Throughput Times 44
3.4.3.2 Stability Measures in Multi-Stage Systems 45
3.5 Strategies for Reducing Nervousness 47
3.6 Influence of Operating Environment on Planning Stability 51
3.6.1 Rolling Horizon Schedule Parameters 51
3.6.1.1 Length of Planning Horizon 51
3.6.1.2 Freeze Interval Length 53
3.6.2 Lot-sizing 55
3.6.2.1 Schedule-Change Cost based Approaches 55
3.6.2.2 Comparison of Lot-Sizing Procedures 56
3.6.2.3 Analysis of Stochastic Inventory Control Rules 57
3.6.3 Buffering Methods 59
3.6.4 Forecast Accuracy 60
3.6.5 Comparison of Different Strategies 60
3.6.6 Comparison of MRP and LRP with respect to Nervousness 61
3.6.7 Filtering Processes 62
3.7 Summary 63
4. Single-Stage Production Systems 65
4.1 Motivation of Underlying Inventory Control Rules 65
4.2 Steady-State Analysis 66
4.2.1 Assumptions and Notation 66
4.2.2 General Results 68
4.2.2.1 Setup Stability of (s,S) Inventory Control Rules 69
4.2.2.2 Setup Stability of (s,nQ) Inventory Control Rules 82
4.2.2.3 Summary of General Results 91
4.3 Properties of Setup Stability 93
4.3.1 Stability Functions for Specific Demand Distributions 95
4.3.1.1 (s, S) Policy 95
4.3.1.2 (s, nQ) Policy 96
4.3.1.3 Basic Scenario for the Analysis of Stability Functions 97
4.3.2 Lot-Sizing and Demand Uncertainty Effects 99
4.3.3 Influence of Stability Horizon and Weight Parameter 105
4.3.4 Minimum Planning Stability 110
4.3.5 Forecast Accuracy 116
4.4 Summary and Managerial Implications 121
4.5 Extensions 123
5. Product Recovery Systems 127
5.1 Strategic Aspects of Product Recovery Management 127
5.2 Inventory Management and MRP Concept in Reverse Logistics 129
5.3 Basic Recovery Model 133
5.4 Recovery System without Disposal Option 135
5.4.1 Notation and Assumptions 136
5.4.2 General Results 139
5.4.3 Setup Stability for Exponentially Distributed Demand and Returns 142
5.4.4 Recovery System without Fixed Costs for Production 151
5.4.5 Summary 153
5.5 Recovery System with Disposal Option 154
5.5.1 Notation and Assumptions 154
5.5.2 General Results 155
5.5.3 Setup Stability for Exponentially Distributed Demand and Returns 158
5.5.4 Summary 163
5.6 Final Remarks and Extensions 164
6. Conclusions 167
6.1 Summary of Results 167
6.2 Further Research 170
A. Approximation for Renewal Function M(x) 171
A.1 Mixed-Erlang Distribution 172
A.2 Hyperexponential Distribution 173
B. (s,S) Policy 175
B.1 General Stability Functions 175
B.1.1 Q _< D 175
B.1.2 Q > D 176
B.2 Mixed-Erlang Distributed Demand 177
B.2.1 Q _<^D 177
B.2.2 Q > ^D 177
B.3 Exponentially Distributed Demand 186
B.3.1 Q _< ^D 186
B.3.2 Q > ^D 186
B.3.3 Properties of Stability Function 187
B.3.3.1 Simplification of Stability Function 187
B.3.3.2 Convexity of Stability Function for Q < ^D 193
B.3.3.3 Discontinuity of Stability Function for Q =D 193
B.3.3.4 Development of Stability Function for Q > D 194
B.3.3.5 Minimum Stability for long-term Setup Stability 203
B.4 Hyperexponentially Distributed Demand 207
B.4.1 Q _<D 207
B.4.2 Q > ^D 207
B.5 Short-term Planning Stability 210
C. (s,nQ) Policy 213
C.1 General Stability Functions 213
C.1.1 Q _< D 213
C.1.2 Q > D 213
C.2 Mixed-Erlang Distributed Demand 214
C.2.1 Q _< D 214
C.2.2 Q > D 215
C.3 Exponentially Distributed Demand 219
C.3.1 Q _< D 219
C.3.2 Q > D 220
C.4 Hyperexponentially Distributed Demand 220
C.4.1 Q _< D 220
C.4.2 Q > D 220
C.5 Short-Term Planning Stability 222
C.6 Proof of Algorithm I 224
D. Product Recovery Systems 231
D.1 (s,S) Policy 231
D.1.1 Stationary Density of (s, S) Policy 231
D.1.2 Exponentially Distributed Demand and Returns 233
D.2 (S,D) Policy 238
D.2.1 Stationary Density of (S, D) Policy 238
D.2.2 Exponentially Distributed Demand and Returns 241
List of Abbreviations 247
List of Symbols 249
List of Figures 254
List of Tables 255
References 257
END
