ABSTRACT
As the bar for service excellence keeps rising, especially in the request of
shorter lead times, higher service levels, lower costs and better customer
service support, the conventional models of spare parts inventory control are
increasingly becoming inadequate. Therefore, to tackle this challenge, in
this study, three novel models of spare parts inventory control have been
formulated, developed and packaged into a multi-model and multi-purpose
engineering computer software, called U-SPIC. Model 1 used mathematical
analysis to integrate 7 spare parts inventory policies together. Model 2
integrated the same inventory policies of Model 1, using stochastic simulation
while Model 3 expanded Model 2 by considering bulk demand and supply using
stochastic simulation. Chi-square goodness of fit inference statistical
technique was employed in the preliminary design to check the reasonableness
of using Poisson distribution for the demands and it gave 86% success.
Composite stepwise two dimensional graphical representations of the models
were formulated, which captured the stochastic demands and stepwise state
transitions. The inverse transform algebraic method was applied for the
generation of random numbers while next event method was used for the time
advancement of the simulation clock. Traces and structured walk through were
utilized for debugging the stochastic simulation models. Batch mean method was
used in determining the confidence intervals of the simulation models, with 105
days run time and 100 replications each. The developed models results were
validated with the case study (ANAMMCO) software package called IDIS which
uses standard (r;Q) inventory policy. Beyond that, the models results were
compared via an extensive simulation approach. 19 sensitivity parameters were
varied in the study, where at each instance of variation, the behaviour of the
fill rate of demands, as well as backorders (i.e. with regard to its average
number, mean response time and maximum queue length) were analysed. On the
average a saving of 18.51% demands in comparison with the conventional models
was found, which indeed will result in huge cost savings in absolute terms.
Beyond that, the insights from these models will increase the overall
efficiency of spare parts inventory control.
vi
Table of Contents
Page
Title Page – – – – – – – – – – – i
Certification – – – – – – – – – –
ii
Dedication – – – – – – – – – – –
iii
Acknowledgement – – – – – – – – – – iv
Abstract – – – – – – – – – – – v
Table of Contents – – – – – – – – – –
vi
List of Tables – – – – – – – – – – xi
List of Figures – – – – – – – – – –
xvi
List of Symbols and Abbreviations – – – – – – – xxii
CHAPTER ONE
INTRODUCTION 1
1.1 Spare Parts Inventory Control – Meaning – – – – – 1
1.1.1 Large Revenue and Investment on Spare Parts Inventory – – –
2
1.1.2 Overview of the Case Study – – – – – – – 3
1.1.3 Introduction to Service Differentiation – – – – – –
6
1.2 Statement of the Problem – – – – – – – –
8
1.3 Objective of the Study – – – – – – – – 9
1.4 Significance of the Study – – – – – – – –
10
1.5 Scope and Limitations – – – – – – – 11
vii
CHAPTER TWO
LITERATURE REVIEW 12
2.1 Service Differentiation and Rationing – – – – – –
13
2.1.1 Periodic Inventory Review – – – – – – – –
13
2.1.2 Continuous Inventory Review – – – – – – – 16
2.2 Backordering and Clearing Mechanism – – – – – –
21
2.3 Demand Lead-time – – – – – – – – – 22
2.4 Approximate Solutions of Spare Parts Inventory Models – – –
24
2.5 Simulation of Spare Parts Inventory Model – – – – –
25
2.6 Classification of Multi-Item Spare Parts Inventory – – – –
28
2.7 Summary of the Proposed Study and its Contribution to Knowledge
Informed from the Literature Review – – – – – –
31
CHAPTER THREE
RESEARCH DESIGN CONSIDERATIONS 34
3.1 Model Design Prerequisite – – – – – – – –
35
3.2 Use of Poisson Distribution for the Demands – – – – –
35
3.3 Service Differentiation and Rationing – – – – – –
38
3.4 Demand Lead Time – – – – – – – – – 38
3.5 Backordering and Clearing Mechanism – – – – – –
39
3.6 Manual Simulation Representation – – – – – – 40
3.7 Generation of Random Numbers – – – – – – – 41
viii
3.8 Time Advancement of the Simulation Clock – – – – –
43
3.9 Selection of the Programming Software – – – – – –
43
3.10 Development of the Algorithm – – – – – – – 44
3.11 Debugging of the Simulation Models – – – – – – 47
3.12 Determination of Confidence Intervals of Simulation Models Results –
47
3.13 Validation and Comparison of the Models – – – – – 48
3.14 Operation of the Software Package – – – – – – –
49
3.15 Variation of the Sensitive Parameters of the Models – – – –
50
CHAPTER FOUR
MODEL DEVELOPMENT 51
4.1 Determination of the Reasonableness of Using Poisson Distribution for
the Demands in the Models – – – – – – – 51
4.2.1 Manual Simulation of the (S, S-1) Models – – – – –
61
4.2.2 Manual Simulation of Model 3 – – – – – – –
66
4.3 Mathematical Model of (S, S-1) Model 1 – – – – –
71
4.3.1 Assumptions – – – – – – – – – –
71
4.3.2 Model Description – – – – – – – – – 71
4.3.3 Derivation of the Fill Rate of Low Priority Demand – – –
– 74
4.3.4 Derivation of the Fill Rate of High Priority Demand – – –
– 77
4.4 Stochastic Simulation of (S, S-1) Model 2 – – – – –
79
4.4.1 Stochastic Model Simulation – – – – – – – 79
ix
4.4.2 Natural Language Interpretation of Algorithm for the Stochastic
Model Simulation [Model] – – – – – – – –
81
4.5 Stochastic Simulation of Model 3 – – – – – – –
85
4.5.1 Stochastic Model Simulation of Model 3 – – – – –
85
4.5.2 Natural Language Interpretation of Algorithm for the Stochastic
Model Simulation – – – – – – – – – 87
4.6 Operation of the Developed U-SPIC Software – – – – –
92
CHAPTER FIVE
NUMERICAL STUDY 106
5.1.1 Determination of the Confidence Intervals of Models 2 and 3 – –
106
5.1.2 Models Validation With ANAMMCO Software called IDIS – – – 107
5.1.3 Parameter Variations of Models 1 and 2 and Comparison – – –
108
5.2.1 Base Stock Level Variation for Models 1 and 2 and Comparison – –
109
5.2.2 Critical Stock Level Variation for Models 1 and 2 and Comparison –
– 115
5.2.3 High Priority Arrival Rate Variation for Models 1 and 2 and Comparison
– 119
5.2.4 Low Priority Arrival Rate Variation for Models 1 and 2 and Comparison
– 125
5.2.5 Demand Lead Time Variation for Models 1 and 2 and Comparison – –
130
5.2.6 Replenishment Lead Time Variation for Models 1 and 2 and Comparison –
135
x
5.3 Comparison of Model 2 Output Results with Reduced Model 3 Results –
140
5.4 Comparison Analysis for Model 3 – – – – – –
144
5.4.1 Replenishment Level Variation for Model 3 – – – – –
145
5.4.2 Critical Stock Level Variation for Model 3 – – – – –
149
5.4.3 High Priority Arrival Rate Variation for Model 3 – – – –
155
5.4.4 Low Priority Arrival Rate Variation for Model 3 – – – –
160
5.4.5 Demand Lead Time Variation for Model 3 – – – – – 165
5.4.6 Replenishment Lead Time Variation for Model 3 – – – –
170
5.4.7 Quantity Demanded Variation for Model 3 – – – – – 175
5.5 Application of the Model Results to the Case Study Data – – –
180
5.6 Mathematical Formulation of Cost Savings – – – – – –
187
xi
CHAPTER SIX
SUMMARY CONCLUSION AND RECOMMENDATION FOR FURHTER STUDIES 189
6.1 Summary – – – – – – – – – – 189
5.2 Conclusion – – – – – – – – – – 193
5.3 Suggestions for Further Studies – – – – – –
195
REFERENCES – – – – – – – – – – 196
APPENDIXES – – – – – – – – – – 205
xii
List of Tables
Table
Pages
4.1a Summary of Demand History of 2-Year Period at Monthly Intervals
and Arrival Rates for Each of the Five Selected Class-A Spare Parts
– 52
4.1b Summary of Demand History of 1-Year Period at Weekly Intervals and
Arrival Rates for Each of the Five Selected Class-B Spare Parts – –
53
4.1c Summary of Demand History of 3-Month Period at Daily Intervals and
Arrival Rates for Each of the Five Selected Class-C Spare Parts –
– 53
4.2 Poisson Distribution of Each of the 15 Selected Spare Parts in the
3 Classes – – – – – – – – – – 55
4.3a Observations Frequency (Fn) and Theoretical Frequency (Tn) for Each of
the Spare Parts – – – – – – – – – 56
4.3b Formatted Observations Frequency (Fn) and Theoretical Frequency (Tn)
for Each of the Spare Parts – – – – – – – 58
4.4 Chi-Square Goodness of Fit Test Decision Table – – – –
59
5.0 Maximum and Minimum Results for High and Low Priority Fill Rates of
Models 2 and 3 in Confidence Interval Determination – – –
107
5.1 Validation Results of the Models with IDIS – – – – –
107
5.2 Fill Rate Results on Base Stock Level Variation for Models 1 and 2 –
109
5.3 Average Number of Backorder Results on Base Stock Level Variation for
Models 1 and 2 – – – – – – – – – 110
5.4 Mean Response Time of Backorder Results on Base Stock Level Variation
for Model 2 – – – — – – – – – 111
5.5 Maximum Queue Length of Backorder Results on Base Stock Level Variation
xiii
for Model 2 – – – – – – – – – 112
5.6 Fill Rate Results on Critical Stock Level Variation for Models 1 and 2
– 115
5.7 Average Number of Backorders Results on Critical Stock Level
Variation for Models 1 and 2 – – – – – – –
116
5.8 Mean Response Time of Backorders Results on Critical Stock Level
Variation for Model 2 – – – – – – – – 117
5.9 Maximum Queue Length of Backorders Results on Critical Stock Level
Variation for Model 2 – – – – – – – –
118
5.10 Fill Rate Results on High Priority Arrival Rate Variation for Models 1
and 2 – – – – – – – – – – 120
5.11 Average Number of Backorders Results on High Priority Demand
Variation for Models 1 and 2 – – – – – – – –
121
5.12 Mean Response Time of Backorders Results on High Priority Arrival Rate
Variation for Model 2 – – – – – – – – 122
5.13 Maximum Queue Length of Backorders Results on High Priority Arrival
Rate Variation for Model 2 – – – – – – – 123
5.14 Fill Rates Results on Low Priority Arrival Rate Variation for Models 1
and 2 125
5.15 Average Number of Backorders Results on Low Priority Arrival Rate
Variation for Models 1 and 2 – – – – – – –
126
5.16 Mean Response Time of Backorders Results on Low Priority Arrival
Rate Variation for Model 2 – – – – – – – 127
5.17 Maximum Queue Length of Backorders Results on Low Priority Arrival Rate
Variation for Model 2 – – – – – – – – 128
5.18 Fill Rate Results on Demand Lead Time Variation for Models 1 and 2 –
130
5.19 Average Number of Backorders Results on Demand Lead Time Variation
for Models 1 and 2 – – – – – – – – 131
xiv
5.20 Mean Response Time of Backorder Results on Demand Lead Time
Variation for Model 2 – – – – – – – – 132
5.21 Maximum Queue Length of Backorders Results on Demand Lead Time
Variation for Model 2 – – – – – – – – 133
5.22 Fill Rate Results on Replenishment Lead Time Variation for Models 1 and
2 135
5.23 Average Number of Backorders Results on Replenishment Lead Time
Variation for Models 1 and 2 – – – – – – –
136
5.24 Mean Response Time of Backorders Results on Replenishment Lead Time
Variation for Model 2 – – – – – – – 137
5.25 Maximum Queue Length of Backorders Results on Replenishment Lead
Time Variation for Model 2 – – – – – – – 138
5.26 Fill Rate Results for Reduced Model 3 Compared with Model 2 – –
140
5.27 Average Number of Backorders Results for Reduced Model 3 Compared
with Model 2 – – – – – – – – – 141
5.28 Mean Response Time of backorders Results for Reduced Model 3 Compared
with Model 2 – – – – – – – – – 142
5.29 Maximum Queue Length of backorders Results for Reduced Model 3
Compared with Model 2 – – – – – – – –
143
5.30 Fill Rate Results on Replenishment Level Variation for Model 3 –
– 145
5.31 Average Number of Backorders Results on Replenishment Level Variation
for Model 3 – – – – – – – – – 146
5.32 Mean Response Time of Backorders Results on Replenishment Level
Variation for Model 3 – – – – – – – –
147
5.33 Maximum Queue Length of Backorders Results on Replenishment
Level Variation for Model 3 – – – – – – – 148
5.34 Fill Rate Results on Critical Stock Level Variation for Model 3 –
– 150
xv
5.35 Average Number of Backorders Results on Critical Stock Level Variation
for Model 3 – – – – – – – – – 151
5.36 Mean Response Time of Backorders Results on Critical Stock Level
Variation for Model 3 – – – – – – – – 152
5.37 Maximum Queue Length of Backorders Results on Critical Stock Level
Variation for Model 3 – – – – – – – – 153
5.38 Fill Rate Results on High Priority Arrival Rate Variation for Model 3
– 155
5.39 Average Number of Backorders Results on High Priority Arrival Rate
Variation for Model 3 – – – – – – – –
156
5.40 Mean Response Time of Backorders Results on High Priority Arrival
Rate Variation for Model 3 – – – – – – – 157
5.41 Maximum Queue Length Results on High Priority Arrival Rate Variation
for Model 3 – – – – – – – – – 158
5.42 Fill Rate Results on Low Priority Arrival Rate Variation for Model 3
– 160
5.43 Average Number of Backorders Results on Low Priority Arrival Rate
Variation for Model 3 – – – – – – – – 161
5.44 Mean Response Time of Backorders Results on Low Priority Arrival
Rate Variation for Model 3 – – – – – – – 162
5.45 Maximum Queue Length of Backorders Results on Low Priority
Arrival Rate Variation for Model 3 – – – – – –
163
5.46 Fill Rate Results on Demand Lead Time Variation for Model 3 – –
165
5.47 Average Number of Backorders Results on Demand Lead Time Variation
for Model 3 – – – – – – – – – 166
5.48 Mean Response Time of Backorders Results on Demand Lead Time
Variation for Model 3 – – – – – – – – 167
5.49 Maximum Queue Length of Backorders Results on Demand Lead Time
Variation for Model 3 – – – – – – – – 168
xvi
5.50 Fill Rate Results on Replenishment Lead Time Variation for Model 3 –
170
5.51 Average Number of Backorders Results on Replenishment Lead Time
Variation for Model 3 – – – – – – – – 171
5.52 Mean Response Time of Backorders Results on Replenishment Lead
Time Variation for Model 3 – – – – – – – 172
5.53 Maximum Queue Length of Backorders Results on Replenishment Lead
Time Variation for Model 3 – – – – – – – 173
5.54 Fill Rate Results on Quantity Demanded Variation for Model 3 – –
175
5.55 Average Number of Backorders Results on Quantity Demanded Variation
for Model 3 – – – – – – – – – 176
5.56 Mean Response Time of Backorders Results on Quantity Demanded
Variation for Model 3 – – – – – – – – 177
5.57 Maximum Queue Length of Backorders Results on Quantity Demanded
Variation for Model 3 – – – – – – – – 178
5.58 The Demands, Rates and Costs of the Selected Spare Parts for
Class A – – – – – – – – – – 180
5.59 Fill Rates and Percentages Savings for Different Optimization
Levels and Priorities – – – – – – – – 182
5.60 Average Number of Backorders for Different Priorities of
Demand and Optimization Levels – – – – – – 183
5.61 Mean Response Time of Backorders for Different Priorities
of Demands and Optimization Levels – – – – – –
184
5.62 Maximum Queue of Length Backorders for Different Priorities
of Demand at Different Optimization Levels – – – – –
185
xvii
List of Figures
Figure
Pages
3.1 Design Algorithm Summary Flow Diagram – – – – – 46
3.2 Distinctive Diagram for Debugging and Validation – – – –
49
4.1a Observations Composite Graph for Class A – – – – –
57
4.1b Theoretical Composite Graph for Class A – – – – –
57
4.1c Observations Composite Graph for Class B – – – – –
57
4.1d Theoretical Composite Graph for Class B – – – – –
57
4.1e Observations Composite Graph for Class C – – – – –
57
4.1f Theoretical Composite Graph for Class C – – – – –
57
4.2 Composite Step-wise Graphical Representation of (S,S-1) Model – –
61
4.3 Composite Step-wise Graphical Representation of Model 3 – – –
66
4.4a Schematic Diagrams for Derivation of Low Priority Fill Rate – –
74
4.4b Schematic Diagrams for Derivation of High Priority Fill Rate – –
77
4.5a A Typical Flowchart of Model 2 (for LR variation only) – – –
80
4.5b A Typical Flowchart of Model 3 (for λ1 variation only) – – –
86
4.6 The Flash Window and the Progress Bar in Action – – – –
92
4.7 Security Login Dialogue Box – – – – – – – 93
xviii
4.8 Main Menu Dialogue Box for the Models – – – – – 94
4.9 Input Dialogue Box for Model 1 – – – – – – –
95
4.10 Variation Dialogue Box for Model 1 – – – – – –
96
4.11 Variation Parameter Maximum Value Dialogue Box – – – –
96
4.12 Input Dialogue Box for Model 2 – – – – – – –
98
4.13 Start or Continue Simulation Request Dialogue Box – – – –
99
4.14 Variation Dialogue Box for Model 2 – – – – – –
99
4.15 Start or Continue Simulation Request Dialogue Box – – – –
100
4.16 Simulations Output Event List – – – – – –
101
4.17 Dynamic Digital Tracing Output of Event type – – – – 102
4.18 Intermediate Simulation Output Results – – – – –
102
4.19 Final Simulation Output Results – – – – – – –
102
4.20 Input Dialogue Box for Model 3 – – – – – – –
104
4.21 Variation Dialogue Box for Model 3 – – – – – –
105
5.0 Validation Results of the Models with IDIS – – – – –
108
5.1 Fill Rate Results on Base Stock Level Variation for Models 1 and 2 –
109
5.2 Average Number of Backorders Results on Base Stock Level Variation
for Models 1 and 2 – – – – – – – – 110
5.3 Mean Response Time of Backorders Results on Base Stock Level Variation
xix
for Model 2 – – – – – – – – – 111
5.5 Maximum Queue Length of Backorders Results on Base Stock Level
Variation for Model 2 – – – – – – – – 112
5.5 Fill Rates Results on Critical Stock Level Variation for Models 1 and 2
– 115
5.6 Average Number of Backorders Results on Critical Stock Level
Variation for Models 1 and 2 – – – – – – –
116
5.7 Mean Response Time of Backorders Results on Critical Stock Level
Variation for Model 2 – – – – – – – – 117
5.8 Maximum Queue Length of Backorders Results on Critical Stock Level
Variation for Model 2 – – – – – – – 118
5.9 Fill Rate Results on High Priority Arrival Rate Variation for Models 1
and 2 120
5.10 Average Number of Backorders Results on High Priority Arrival Rate
Variation for Models 1 and 2 – – – – – – –
121
5.11 Average Number of Backorders Results on High Priority Arrival Rate
Variation for Model 2 – – – – – – – – 122
5.12 Maximum Queue Length of Backorders Results on High Priority
Arrival Rate Variation for Model 2 – – – – – –
123
5.13 Fill Rate on Low Priority Arrival Rate Variation for Models 1 and 2
– 125
5.14 Average Number of Backorders Results on Low Priority Arrival
Rate Variation for Models 1 and 2 – – – – – –
126
5.15 Mean Response Time of Backorders Results on Low Priority
Arrival Rates Variation for Model 2 – – – – – –
127
5.16 Maximum Queue Length of Backorders Results on Low Priority
Arrival Rates Variation for Model 2 – – – – – –
128
xx
5.17 Fill Rate on Demands Lead Time Variation for Models 1 and 2 – –
130
5.18 Average Number of Backorders Results on Demand Lead Time
Variation for Models 1 and 2 – – – – – – –
131
5.19 Mean Response Time of Backorders Results on Demand Lead Time
Variation for Model 2 – – – – – – – – 132
5.20 Maximum Queue Length of Backorders Results on Demand Lead
Time Variation for Model 2 – – – – – – – 133
5.21 Fill Rate on Replenishment Lead Time Variation for
Models 1 and 2 – – – – – – – – – 135
5.22 Average Number of Backorders Results on Replenishment Lead
Time Variation for Models 1 and 2 – – – – – –
136
5.23 Mean Response Time of Backorders on Replenishment Lead Time
Variation for Model 2 – – – – – – – – 137
5.24 Maximum Queue Length of Backorders Results on Replenishment
Lead Time Variation for Model 2 – – – – – – 138
5.25 Fill Rate Results for Reduced Model 3 Compared with Model 2 – –
140
5.26 Average Number of Backorders Results for Reduced Model 3 Compared
with Model 2 – – – – – – – – – 141
5.27 Mean Response Time of Backorders Results for Reduced Model 3
Compared with Model 2 – – – – – – – – 142
5.28 Maximum Queue Length of Backorders Results for Reduced Model 3
Compared with Model 2 – – – – – – – – 143
5.29 Fill Rate Results on Replenishment Level Variation for Model 3 –
– 145
5.30 Average Number of Backorders Results on Replenishment Level
Variation for Model 3 – – – – – – – – 146
5.31 Mean Response time of Backorders Results on Replenishment Level
Variation for Model 3 – – – – – – – –
147
xxi
5.32 Maximum Queue Length of Backorders Results on Replenishment
Level Variation for Model 3 – – – – – – – 148
5.33 Fill Rate Results on Critical Stock Level Variation for Model 3 –
– 150
5.34 Average Number of Backorders Results on Critical Stock
Level Variation for Model 3 – – – – – – – 151
5.35 Mean Response Time of Backorders Results on Critical Stock
Level Variation for Model 3 – – – – – – – 152
5.36 Maximum Queue Length of Backorders Results on Critical Stock
Level Variation for Model 3 – – – – – – – 153
5.37 Fill Rate Results on High Priority Arrival Rate Variation for Model 3
– 155
5.38 Average Number of Backorders Results on High Priority Arrival
Rate Variation for Model 3 – – – – – – – 156
5.39 Mean Response Time of Results on High Priority Arrival Rate
Variation for Model 3 – – – – – – – – 157
5.40 Maximum Queue Length of Backorders Results on High Priority
Arrival Rate Variation for Model 3 – – – – – –
158
5.41 Fill Rate Results on Low Priority Arrival Rate Variation
for Model 3 – – – – – – – – – 160
5.42 Average Number of Backorders Results on Low Priority Arrival
Rate Variation for Model 3 – – – – – – – –
161
5.43 Mean Response Time of Backorders Results on Low Priority Arrival
Rate Variation for Model 3 – – – – – – – 162
5.44 Maximum Queue Length of Backorders Results on Low Priority Arrival
Rate Variation for Model 3 – – – – – – – 163
5.45 Fill Rate Results on Demand Lead Time Variation for Model 3 – –
165
5.46 Average Number of Backorders Results on Demand Lead Time
Variation for Model 3 – – – – – – – –
166
xxii
5.47 Mean Response Time of Backorders Results on Demand Lead Time
Variation for Model 3 – – – – – – – –
167
5.48 Maximum Queue Length of Backorders Results on Demand Lead
Time Variation for Model 3 – – – – – – – 168
5.49 Fill Rates Results on Replenishment Lead Time Variation
for Models 3 – – – – – – – – – 170
5.50 Average Number of Backorders Results on Replenishment Lead
Time Variation for Model 3 – – – – – – – 171
5.51 Mean Response Time of Backorders Results on Replenishment Lead
Time Variation for Model 3 – – – – – – – 172
5.52 Maximum Queue Length of Backorders Results on Replenishment
Lead Time Variation for Models 3 – – – – – – 173
5.53 Fill Rates Results on Quantity Demanded Variation for Models 3 –
– 175
5.54 Average Number of Backorders Results on Quantity Demanded
Variation for Model 3 – – – – – – – – 176
5.55 Mean Response Time of Backorders Results on Replenishment Lead
Time Variation for Model 3 – – – – – – – 177
5.56 Maximum Queue Length of Backorders Results on Replenishment
Lead Time Variation for Models 3 – – – – – – 178
5.57 Percentages Savings for Different Optimization Priorities of
Demands and Optimization Levels – – – – – – 182
5.58 Average Number of Backorders for Different Priorities of
Demands and Optimization Levels – – – – – – 183
xxiii
5.59 Mean Response Time of Backorders of Different Priorities
at Different Optimization Levels – – – – – – 184
5.60 Maximum Queue of Length Backorders of Different Priorities
at Different Optimization Levels – – – – – – 185
xxiv
List of Symbols and Abbreviations
Symbol Meaning
λ1 High Priority Arrival Rate
λ2 Low Priority Arrival Rate
β1 Fill rate of high priority demand
β2 Fill rate of low priority demand
ini
1
Initial High Priority Fill Rate
opt
1
Optimized High Priority Fill Rate
ini
2
Initial Low Priority Fill Rate
opt
2
Optimized Low Priority Fill Rate
2o
bserved Observed Value of Chi Square
2
Df , Critical Value of the Chi Square
Level of Statistical Significance
x
k A Arrival of xth demand of kth Class
C period A S Average Cost Savings for a given period
period AQD Average Quantity Demanded for a given period
ANAMMCO Anambra Motor Manufacturing Company
ANB1 Average Number of High Priority Backorders
ANB2 Average Number of Low Priority Backorders
C AU Average Unit Cost of Spare Parts
x
k
cB Clearing of xth backorder of kth Class
CAD Computer Aided Design
CNHD Cumulative Number of High priority Demands
CNLD Cumulative Number of Low priority Demands
CNB1 Cumulative Number of High Priority Backorders
CNB2 Cumulative Number of Low Priority Backorders
x D Due time of xth low priority demand
DL Degree of Freedom
DTLD Due time of the Low Priority Demand
EPC Electronic Parts Catalogue
Fn Observations Frequency
FHD Filled High Priority Demand
FLD Filled Low Priority Demand
H0 Null Hypothesis
H1 Alternate Hypothesis
HC High Priority Class
HD High Priority Demand
H Hitting Time (arrival time of [S – S * ]th total order)
IDIS Integrated Dealer Importer System
Symbol Meaning
xxv
Lr Replenishment Lead Time
Ld Demand Lead Time
LD Low Priority Demand
LPA Low Priority Arrival
LC Low Priority Class
M λ1 Maximum Variation for High Priority Arrival Rate
MQLB1 Maximum Queue Length of High Priority Backorder
MQLB2 Maximum Queue Length of Low Priority Backorder
MLr Maximum Replenishment Lead Time
MRTB1 Mean Response Time of High Priority Backorder
MRTB2 Mean Response Time of Low Priority Backorder
MS* Maximum Critical Level
MST Maximum Simulation Time
MSTE Maximum Simulation Time Exceeded?
n Number of Observations
NB1 Current Number of High Priority Backorder
NB2 Current Number of Low Priority Backorder
NROT Number of Replenishment Order in Transit
NLAD Number of Low Priority Arrivals Not Yet Due
NTHD Next Time of High Priority Demand
NTLD Next Time of Low Priority Demand
NTRO Next Time of Replenishment Order
Pn Poisson Distribution
PI Physical Inventory
QD1 Current Quantity Demanded for High Priority
QD2 Current Quantity Demanded for Low Priority
QR Quantity Replenished
QDI Quantity Demanded Interval
RL Replenishment Level
Rx Arrival of xth replenishment
S Base Stock Level
S * Critical Stock Level
S,S-1 One to one lot
C period T S Total Cost Savings for a given period
Tn Theoretical Frequency
x
k B xth Backorder of kth Class
TWTB 1 Total Waiting Time of High Priority Backorder
TWTB2 Total Waiting Time of Low Priority Backorder
WTx
Waiting time of xth backorder
CHAPTER ONE
INTRODUCTION
1.1 Spare Parts Inventory Control – Meaning
To establish a common understanding, ‘Spare parts’ refers to the
parts requirement for keeping both owned equipment/machine or
service needs of customers in healthy operating condition by
meeting repair and replacement needs imposed by breakdown and
preventive maintenance. The term spare parts in this study
therefore, is used to connote both spare parts and service parts
as applied to a firm handling both internal and
external spare and service needs. On the other hand, ‘Inventory
Control’ refers to the management of the supply, storage and
accessibility of items, in this case spare parts, in order to
ensure an adequate supply without excessive supply.
Spare parts inventory models differ substantially from regular
inventory models. The key reason for this difference is that
spare parts provisioning is not an end in itself, but a means to
guarantee up-time of equipment. With respect to spare parts
inventory, the customer’s sole interest is that his systems are
not down due to lack of spare parts because equipment downtime is
lost production capacity.
1.1.1 Large Revenue and Investment on Spare Parts Inventory
In today’s technological environment, the importance of aftersales
service which basically concerns the use of spare parts for
maintenance purposes, is high. Lost revenues due to disservice
are enormous. Not only is after-sales service valuable as a
competitive advantage for manufacturers and service providers,
direct revenues in this service are also remarkably high.
Companies that provide the after-sales service have to invest a
lot on spare parts inventory. In 2006, Koudalo1 investigated
revenues of spare parts in the service business over a period of
one year, and he reports combined revenues of more than $1.5
trillion. Flint2 stated that the world’s spare parts inventory in
the aviation industry in 1995 amounted to $45 billion at that
time. Any means to downsize this stock, without decreasing
customer service, would be more than welcomed by the aviation
industry. Also in other industries, large amounts of money are
invested in spare parts inventory and this has increased over the
years. Heather3 reported that the spare parts market of U.S.
represents $700 billion and 8 percent of the U.S. gross domestic
product. Many manufacturers find that profit margins for services
can top 40 percent, whereas margins for finished goods top out at
around 13 percent. Cohen et al4 and AberdeenGroup5 also report
that profitability in service is much higher than profitability
for initial products. Because of these large amounts of money
involved, savings of a few percent only constitute large cost
savings in absolute terms.
The above indicates that the control of spare parts for aftersales
service deserves substantial corporate attention, which is
even more true, since customer requirements have tightened.
AberdeenGroup5 indicates that 70% of the respondents in its study
have seen service response times as required in service level
3
agreements shrinking to 48 hours or less, and Koudalo1 states
that customers keep raising the bar for service excellence by
requesting shorter lead times, higher service levels, lower
costs, and better customer service support.
1.1.2 Overview of the Case Study
The first insight on the importance of spare parts inventory
control by the researcher was made while carrying out another
study, Okonkwo6, on stochastic queueing behaviour of vehicles in
a maintenance workshop which eventually resulted in the
development of a computer software: Ugoo Multi-Purpose Computer
Qeueuing Model Simulator (Ugoo MC-QMS).
However, the primary motivation that finally triggered off this
research is an experience with the spare parts complex of a
leading motor assembling/manufacturing company in Nigeria. The
Anambra Motor Manufacturing Company (ANAMMCO) Enugu, Nigeria –
This company is a product of a joint venture of the Federal
Government of Nigeria and Daimler-Chrysler of Germany, and was
commissioned in 1980. The spare parts complex of ANAMMCO provides
considerable after-sales service which is impacted significantly
by the spare parts control. The company has a very large spare
parts complex that stores and manages spares various models of
Mercedes Benz heavy duty vehicles. Specifically, besides the
selling of vehicles, the spare parts of various models of heavy
duty vehicles listed below are stored and managed by the company.
Trucks: MB-711, MB-1418, MB-1520, MB-1518, MB-1720, MB-1620,
MB-1718, MB-1634, MB-2423
Actros: MB-2031, MB-2035, MB-3340, MB-4031
4
Freightliner: MB-M21126X4, MB-M21124X2
Axor: MB-1823
Buses: MB-712, MB-812, MB-1721, MB-O400, MB-O500
The management of these models which is complex was further
complicated by the vast number of parts required in each model.
In fact, more than 30,000 active parts needed to be controlled.
The management of these parts can only be done with the aid of a
computer, hence the spare parts complex has a computerized spare
parts inventory database. Each of the parts that is supplied or
replenished is continuously keyed into the computer and the
inventory stock parameters are updated automatically.
The company uses two software for its inventory control. The
first is the Electronic Parts Catalogue (EPC) which is used to
identify the part number of the spare parts. Once the engine and
chassis number is inputted, it invokes a dialogue box from where
spare parts section is selected and from the pull down menu, the
particular spare part is chosen. The software will search and pop
up the part number of the spare part, a 3-D AutoCAD drawing of
the required part, a CAD drawing guide on how it can be fixed
into the vehicle and in some cases an alternative part to be used
in case the said part is out of stock. From the part number, the
location of the spare parts in the stock room is identified. The
second software is Integrated Dealer Importer System (IDIS). It
is a software that determines the stock level for each part in
the stock complex. It has a database showing the orders and
replenishments that have been made. It also indicates when to
replenish and the quantity. It uses continuous review (r,Q)
inventory policy. It should also be noted that the complex
5
observes the well known A-B-C classification in its spare parts
inventory.
The company faces two major demands of spare parts from the
complex, the first is demand from the maintenance section of the
company. The second is from the external customers that directly
buy spare parts from the complex for their personal use. Demand
from the maintenance section is as a result of spare parts
demands for maintaining their vehicles, for maintaining aftersales
service of vehicles whose owners had service level
agreement with the company as well as those that just take their
vehicles to their maintenance workshop for either regular
servicing or for repairs when they have broken down completely.
Notwithstanding the fact that the company’s inventory system is
computerized, yet the computerized system does not observe
service differentiation through rationing and demand lead time.
However, in some exceptional cases, the company observes demand
lead time manually though, But, more than ever before, this
method can no longer withstand the challenges of modern standards
of spare parts inventory control. These standards have risen to
such levels that it is difficult, if not impossible to attain it
by manual form of optimization.
Therefore, this study provides improved models which when
implemented, find solution to the company’s spare parts network
challenge. These models will not only provide immediate and
significant benefit to the company under study, but can be
adapted to very many other systems.
1.1.3 Introduction to Service Differentiation
6
In spare parts inventory, just as different customers may require
different product specifications, they may also require different
service levels. For instance, for a single product, different
customers may have different stockout costs and/or different
minimum service level requirements or different customers may
simply be of different importance to the supplier by similar
measures. Therefore, it can be imperative to distinguish between
classes of customers thereby offering them different services. In
this setting, different product demands from different customers
can no longer be handled in a uniform way. This, in turn, gives
rise to multiple demand classes and customer differentiation.
In this system of multiple demand classes the easiest policy
would be to use different stockpiles for each demand class. This
way, it would be very easy to assign a different service level to
each class. Also the practical implementation of this policy
would be relatively easy and will require less mathematical
analysis. But the drawback of this policy is that there is no
advantage from the so-called portfolio effect. In other words,
the advantage of pooling demand from different demand sources
together would no longer be utilized. Therefore, as a result of
the increasing variability of demand, more safety stock would be
needed to ensure a minimum required service level which in turn
means more inventory.
On the other side, one could simply use the same pool of
inventory to satisfy demand from various customer classes without
differentiating them. In this case, the highest required service
level would determine the total inventory needed and thus the
inventory cost. The drawback of this policy is that higher
service level will be offered to the rest of the demand classes,
7
a deficiency that would lead to increased inventory costs.
Critical level policy essentially lies between these two
extremes. It requires complex mathematical analysis, but the
gains outweigh the task involved.
In the existing practice, the company studied failed to exploit
service differentiation (demand classes) of the various
customers. The company targets to achieve the maximum of the
service level requirements while considering the aggregated
demand. Moreover, the company does not recognize the possible
demand lead times (the difference between requested date and
shipment date of the request) for lead time orders. This study
develops spare parts inventory models that recognize the demand
lead times, multiple demand classes, allow for providing
differentiated service levels through rationing, as well as
optimizes the generated policy parameters, notwithstanding the
complex analysis that it entails.
1.2 Statement of the Problem
The complexities and the growing criticality of spare parts
inventory control in manufacturing and service operations are on
the increase. Factors like demand unpredictability, parts
indigenization, high service levels, large investments on and
revenues from parts, the imperative to accurately forecast spare
parts requirements and to optimize existing inventory policies
require significant decision support. This decision support can
only be achieved from the results generated from more efficient
novel decision models.
8
Unfortunately, many researchers from the third world shy away
from developing this type of models. Those who delve into it
limit themselves to the development of spare parts inventory
control database, using conventional models. These conventional
models are increasingly becoming ineffective in tackling spare
parts inventory control problems. On the other hand, the
advanced countries that have done a lot of work with regards to
developing novel spare parts inventory control models have not
been able to integrate either the 7 spare parts inventory
policies as was done in Models 1 and 2 of this study, or 9 spare
parts inventory policy as was done in Model 3 of this study, in
any of their developed models. The spare parts inventory policies
are listed in the objective of the study in section 1.3.
9
1.3 Objective of the Study
The objective of the study embraces the following:
Development of a novel analytical model (Model 1)
This integrates 7 spare parts inventory policies together.
The policies are continuous review, one to one lot, service
differentiation and rationing, backordering, demand lead
time, priority clearing mechanism and bounded enumerative
optimization.
Development of novel stochastic simulation models (Models 2 and 3)
Model 2 integrates the same 7 spare parts inventory policies
of model 1 using stochastic simulation while model 3 expands
model 2 by considering in addition to the to the policies of
modal 2, bulk demand and bulk replenishment of spare parts
using stochastic simulation.
Showcasing new insight in the behaviour of backorders of spare parts
inventory This is with regards to its maximum queue length,
mean response time and average number in the system.
Establishment of the magnitude of cost savings
This is done by the application of service differentiation
through rationing and demand lead time.
Formulation of composite graphical representations of the models
This is for pedagogical purposes.
Proposal of the models to the Management of ANAMMCO
This is for possible interfacing with their already existing
computer spare parts inventory model.
Uploading the active software to the internet
This is for easy subscription, access and run, from any part
of the world.
10
1.4 Significance of the Study
The envisaged significance of this study is laid on its applied
nature mainly. That is, the output results from these models have
foreseeable potentialities for immediate practical applications
to the on-going challenge of achieving above 99% service level at
minimum stock.
Specifically, the models can easily be applied in spare parts
inventory control Industries/Companies and even Institutions, for
the following purposes:
1. The models can be applied to the management of the spare
parts inventory system, requiring both preventive and
breakdown demands of spare parts.
2. Industries that have contractual agreements for servicing
machines/vehicles/airplanes with some of its customers can
also find the models very useful for the management of its
inventory. An example is an airline industry that has
contractual agreement with its major and minor airlines of
differentiated service levels.
3. Spare parts inventory systems that do not recognize both
service differentiation and positive demand lead time can
equally make use of these models. What is required is just
to remove the service differentiation and demand lead time
by setting critical service level and demand lead time to
zero value, accomplished through pressing few clicks on the
graphical user interface of the multi-model software
package.
4. Managing inventories for spare parts of equipments of
different criticality can make use of the models. In this
11
case the equipment criticality will determine the service
level.
5. The building blocks that will be provided in this study can
be adapted to solving other real-life spare parts inventory
control problems.
6. Finally, it can be very useful as an effective and
interesting spare parts inventory pedagogical tool, both in
the academic and commercial Institutions.
1.5 Scope and Limitations
The study of the operating realities of the Spare Parts Complex
of Anambra Motor Manufacturing Company Limited (ANAMMCO) informed
this work.
The thrust was on the continuous review inventory models, which
in any case are better than periodic review for spare parts
inventory. For effective control, continuous review models
require companies whose inventory database systems are
computerized.
The study did not set out to develop database inventory models
but the decision-support models using mathematical and simulation
approaches. These models will be compatible with the case study
inventory databases and indeed should be easily interfaced with
standard databases of leading software manufacturers Like
Microsoft and Oracle Corporations.
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