DATA-DRIVEN SUPPLY CHAIN FORECASTING AND

INVENTORY OPTIMIZATION: MACHINE LEARNING

BASED MODELS AND METHODOLOGIES

SUSHIL PUNIA

DEPARTMENT OF MANAGEMENT STUDIES

INDIAN INSTITUTE OF TECHNOLOGY DELHI
©Indian Institute of Technology Delhi-2020
All rights reserved.

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DATA-DRIVEN SUPPLY CHAIN FORECASTING AND
INVENTORY OPTIMIZATION: MACHINE LEARNING
BASED MODELS AND METHODOLOGIES

by

SUSHIL PUNIA
Department of Management Studies

Submitted
in fulfilment of the requirements of the degree of Doctor of Philosophy

to the

Indian Institute of Technology Delhi

October 2020
 CERTIFICATE

This is to certify that the thesis entitled “Data-driven Supply Chain Forecasting and

Inventory Optimization: Machine Learning Based Models and Methodologies” being

submitted by Sushil Punia to the Indian Institute of Technology Delhi for the award of the

degree of Doctor of Philosophy is a bonafide record of original research work carried out by

him. He has worked under our supervision and has fulfilled the requirements for the

submission of the thesis, which has reached the requisite standard.

The results contained in this thesis have not been submitted, in part or full, to any other

University or Institute for the award of any degree or diploma.

(Prof. Surya Prakash Singh) (Prof. Jitendra Madaan)

Department of Management Studies Department of Management Studies
Indian Institute of Technology Delhi Indian Institute of Technology Delhi
New Delhi-110016, India. New Delhi-110016, India.

Date: October 2020

ii
 ACKNOWLEDGEMENTS

I would like to express my profound respect and a great sense of gratitude to my Ph.D.

supervisors, Prof. Surya Prakash Singh and Prof. Jitendra Madaan, for their support during

my research journey and making it possible to finish the writing of this thesis on time. I would

also like to thank my Student Research Committee members, Chairperson - Prof. P.

Vigneswara Illavarasan (Dept. of Management Studies, IIT Delhi), Internal Expert - Prof.

Arpan Kar (Dept. of Management Studies, IIT Delhi); External Expert - Prof. Abhijit

Majumdar (Dept. of Textile Technology, IIT Delhi) for their time, encouragement, and

support during various phases of the research work.

I would also like to thank the faculty of IIT Delhi for enhancing my knowledge through

various courses that they taught, and the administration and staff members of IIT Delhi for

all the support during my stay at IIT Delhi. I am highly grateful to the timely support provided

by Prof. T. C. Kandpal (CES), Prof. Shantanu Roy (Dean Academics, IIT Delhi), Prof. S. D.

Joshi (Electrical Engineering), Prof. Bhim Singh (Electrical Engineering), and Dr. Sanjay

Pande (IIT Delhi) at various stages of my Ph.D. journey. I would also like to thank Prof.

Konstantinos Nikolopoulos (Durham University, UK) for guiding me through the basics of

forecasting analysis. A special thanks to all my colleagues at IIT Delhi, Ph.D. scholars at

DMS, and my friends at Vindhyachal House.

Last but not the least, I would like to thank my family for supporting me throughout the

course of my Ph.D.

Sushil Punia

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 ABSTRACT

Firms are building their strategies to harness data and use artificial intelligence to manage

complex and competitive business environments. The growing availability of large datasets

(“big data”) and recent advances in the area of machine learning have led to the increased

focus of firms on developing data-driven solutions to the problems in the Operations and

Supply Chain Management (OSCM) field. Traditionally, problems of OSCM were largely

tackled through mathematical modeling and optimization, and in a few cases, through

empirical studies. In recent years, research focuses on using data and data modeling, known

as (data) analytics, for solving their business problems. The integration of data analytics and

the domain knowledge of OSCM has the potential to derive rules for effective direction and

optimization of the operations and supply chain.

In analytics, decision-makers develop data-based models to extrapolate the patterns in

historical data to get insights about the future, and then use them into optimization models to

obtain an effective solution to the business problems. Deriving the insights about future

outcomes is known as predictive analytics. Using predictive analytics results in the

optimization model to obtain actionable insights is known as prescriptive analytics. The

predictive analytics and prescriptive analytics are complete within themselves. However,

their combined use (called predict-then-optimize) leads to a true data-driven decision support

system that can create value.

In this research, predictive and prescriptive analytics models are developed to address various

challenges in supply chain forecasting and inventory optimization. This research work

addresses the demand (sales) forecasting problem in a complex environment by proposing

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big data analytics and machine (and deep) learning based on a Demand Forecasting Model

(DFM). The proposed DFM consists of a novel forecasting method that ensembles long-

short-term-memory networks and random forest through an evolutionary optimization

algorithm. DFM is capable of modeling the model time and covariates-based variations, and

thus, it has better accuracy than standalone state-of-the-art forecasting methods. A sample of

4235 demand series with structured and unstructured data (also known as “big data”) is used

for the analysis. It has been observed that DFM is suitable to provide accurate forecasts to

develop demand plans for operational and tactical decisions.

The research work is further extended by developing a novel Demand Forecasting Decision

Model (DFDM) to provide the forecasts for relatively long-term forecasts where big data

models are not applicable. The proposed DFDM mathematically integrates judgmental

estimates from experts and quantitative forecasts from econometric time-series and machine

learning models. Through this work, it has been explored whether the human judgment is still

apposite in the era of artificial intelligence, i.e., machine learning.

Further, it is known that the supply chain requires short-term up to long-run aggregated

forecasts for making strategic, tactical, and operational decisions. These forecasts need to be

accurate and coherent. However, using different predictive analytics methods for short-term

up to long-run forecasts in a supply chain leads to incoherency in forecasts at different

planning and decision levels. It leads to the misalignment in management and wastage of

resources of the organization. Thus, a novel supply chain forecasting framework, a

combination of temporal and cross-sectional hierarchical forecasting, is proposed to generate

coherent forecasts at all levels of a supply chain. The proposed framework also provides more

accurate forecasts than forecasts at different levels of supply chains.

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In the final model, predictive analytics is linked to the prescriptive analytics model. A data-

driven inventory optimization model is developed. The multi-item inventory optimization

problem with limited capacity/budget is solved using the machine learning and optimization

model. The mathematical solutions to the newsvendor problem are available in the literature

on inventory management. However, these available solutions make several assumptions

about demand distributions and other parameters, which are often incorrect and lead to errors

in inventory optimization. The proposed model provides a distribution-free and data-driven

solution approach to the problem to overcome the shortcomings of the mathematical model.

In a supply chain, demand forecasting and inventory optimization directly impact the

production, distribution, routing, scheduling, and many more decisions. In this context, the

proposed models and methodologies have numerous applications across supply chains of

various industries, including fashion, food, energy, electronics, and media.

Keywords: Data-driven Decision Models; Artificial Intelligence; Demand Forecasting;

Inventory Optimization; Big Data; Predictive Analytics; Prescriptive Analytics; Judgmental
Forecasting; Time series methods; Deep Learning; Machine Learning; Evolutionary
Optimization Algorithm; Temporal Aggregation; Cross-temporal Aggregation; Retail;
Manufacturing.

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 सार

व्यवसाय जटिल और प्रटिस्पर्धी व्यावसाटयक वािावरण के कुशल प्रबंर्धन के टलए डे िा की शक्ति का उपयोग

करने और कृटिम बुक्तिमत्ता की िकनीकों का उपयोग करने के टलए अपनी रणनीटि बना रहे हैं । टवशाल डे िा

की बढ़िी उपलब्धिा और मशीन टशक्षण के क्षे ि में हाटलया प्रगटि ने संचालन और आपूटिि श्ृंखला प्रबंर्धन क्षे ि में

समस्याओं के टलए डे िा-संचाटलि समार्धान टवकटसि करने पर फमों का ध्यान केंटिि टकया है । परं परागि रूप

से, संचालन और आपूटिि श्ृंखला प्रबंर्धन क्षेि की समस्याओं को बडे पैमाने पर गटणिीय मॉडटलं ग, अनु कूलन

और अनु भवजन्य अध्ययनों के माध्यम से टनपिाया जािा है । हाल के वर्षों में , व्यावसाटयक समस्याओं को सुलझाने

के टलए अनु संर्धान का ध्यान डे िा और डे िा मॉडटलं ग पर गया है । टजसे डे िा टवश्लेर्षण टवद्या के रूप में जाना

जािा है । डे िा टवश्लेर्षण टवद्या और संचालन और आपूटिि श्ृं खला प्रबंर्धन क्षे ि के ज्ञान के एकीकरण से संचालन

और आपूटिि श्ृं खला के अनु कूलन के टनयमों को प्राप्त टकया जा सकिा है ।

डे िा टवश्लेर्षण टवद्या में , टनणियकिाि भटवष्य के बारे में जानकारी प्राप्त करने के टलए ऐटिहाटसक डे िा में पैिनि को

बाह्य गणन करने के टलए डे िा-आर्धाररि मॉडल टवकटसि करिे हैं , और टफर व्यावसाटयक समस्याओं का प्रभावी

समार्धान प्राप्त करने के टलए इन अंिर्दि टि का अनु कूलन मॉडल में उपयोग करिे हैं । भटवष्य के पररणामों के बारे

में अंिर्दि टि प्राप्त करना टियात्मक अंिर्दि टि के रूप में जाना जािा है , जबटक कारि वाई योग्य अंिर्दि टि प्राप्त करने

के टलए अनु कूलन मॉडल में भटवष्य कहने वाला टवश्लेर्षण के पररणामों का उपयोग टकया जािा है ।

इस शोर्ध कायि में , आपूटिि श्ृं खला पूवाि नुमान और संख्यापि इष्‍ििमीकरण में टवटभन्न चुनौटियों का सामना करने

के टलए भटवष्य कहने वाला और टियात्मक अंिर्दि टि मॉडल टवकटसि टकए गए हैं । यह शोर्ध कायि मां ग पूवाि नुमान

मॉडल के आर्धार पर बडे डे िा डे िा टवश्लेर्षण और मशीन टशक्षण का प्रस्ताव करके एक जटिल व्यावसाटयक

वािावरण में मां ग (टबिी) पूवाि नुमान समस्या का समार्धान करिा है । प्रस्ताटवि मां ग पूवाि नुमान मॉडल में एक नई

पूवाि नुमान पिटि टवकटसि की गई है जो एक सामू टहक प्रभाव कलनटवटर्ध के माध्यम से दीर्िकाटलक-

अल्पकाटलक-स्मृटि िंि और यार्दक्तिक वन को इकट्ठा करिी है । नई पूवाि नुमान पिटि समय सामटयक और

vii
कोवररएि् स दोनों प्रकार के जटिल संबंर्धों को मॉडल कर सकिा है , जो इसे अन्य अत्यार्धुटनक पूवाि नुमान टवटर्धयों

की सिीकिा में बढ़ि प्रदान करिा है । टवश्लेर्षण के टलए ४२३५ मां ग श्ृं खला टजसमें संरटचि और असंरटचि

डे िा (टजसे "टवशाल डे िा" कहा जािा है ) का एक बडा नमू ना उपयोग टकया गया है । यह दे खा गया टक प्रस्ताटवि

पूवाि नुमान पिटि पररचालन और सामररक टनणियों की मां ग योजनाओं को टवकटसि करने के टलए सिीक

पूवाि नुमान प्रदान में सक्षम है ।

आगे के अनु संर्धान कायि में , अपेक्षाकृि लं बी अवटर्ध के पूवाि नुमान प्रदान करने में सक्षम मां ग पूवाि नुमान टनणिय

मॉडल का टवस्तार टकया गया है । इन पररक्तथिटियों में टवशाल डे िा मॉडल लागू नहीं होिे हैं । प्रस्ताटवि टनणिय

मॉडल गटणिीय रूप से अििटमिीय समय-श्ृं खला और मशीन टशक्षण मॉडल से टवशेर्षज्ञों और मािात्मक

पूवाि नुमान से टनणिय अनु मानों को एकीकृि करिा है । इस काम के माध्यम से, यह पिा लगाया गया है टक क्या

मानव टनणिय का उपयोग अभी भी कृटिम बुक्तिमत्ता के युग, यानी मशीन टशक्षण में उपयुि है ।

यह ज्ञाि है टक आपूटिि श्ृं खला को रणनीटिक, सामररक और पररचालन टनणिय ले ने के टलए लं बे समय िक

समे टकि पूवाि नुमानों की आवश्यकिा होिी है । इन पूवाि नुमानों का सिीक और सुसंगि होना आवश्यक है।

हालां टक, आपूटिि श्ृंखला में लंबे समय िक चलने वाले पूवाि नुमानों के टलए भटवष्यवाटणयों के टवटभन्न िरीकों का

उपयोग करने से योजना और टनणियों के टवटभन्न स्तरों पर पूवाि नुमानों में असंगटि पैदा होिी है । यह प्रबंर्धन में

असंगटि और संगठन के संसार्धनों के अपव्यय की ओर ले जािा है । इस प्रकार, एक नये आपूटिि श्ृं खला पूवाि नुमान

चौखिा, जो अथिायी और िॉस-अनु भागीय श्ेणीबि पूवाि नुमान का एक संयोजन है , आपूटिि श्ृं खला के सभी

स्तरों पर सुसंगि पूवाि नुमान उत्पन्न करने के टलए प्रस्ताटवि टकया गया है । प्रस्ताटवि चौखिा आपूटिि श्ृं खलाओं

के टवटभन्न स्तरों पर सिीक और सुसंगि पूवाि नुमान प्रदान करिा है ।

अंटिम मॉडल में , भटवष्य टवश्लेर्षण टवद्या को टियात्मक टवश्लेर्षण टवद्या मॉडल से जोडा गया है और डे िा-

संचाटलि संख्यापि इष्‍ििमीकरण मॉडल टवकटसि टकया गया है । मशीन टशक्षण और इष्‍ििमीकरण मॉडल का

उपयोग करके एक क्षमिा अवरोर्ध के साि बहु-उत्पाद संख्यापि प्रबंर्धन समस्या का समार्धान टकया गया है ।

viii
समाचार संख्यापि प्रबंर्धन समस्या के गटणिीय समार्धान संख्यापि प्रबंर्धन साटहत्य में उपलब्ध हैं । हालां टक, ये

उपलब्ध समार्धान मां ग टविरण और अन्य मापदं डों के बारे में कई र्धारणाएं बनािे हैं , जो अक्सर गलि होिी हैं

और संख्यापि इष्‍ििमीकरण में िु टियों का कारण बनिे हैं। प्रस्ताटवि मॉडल गटणिीय मॉडल की कटमयों को दू र

करने के टलए एक र्धारणा-मु ि और डे िा-संचाटलि समार्धान प्रदान करिा है । आपूटिि श्ृंखला में , मां ग पूवाि नुमान

और संख्यापि इष्‍ििमीकरण का उत्पादन, टविरण, रूटिं ग, शे ड्यूटलं ग और कई और फैसलों पर सीर्धा प्रभाव

पडिा है । इस संदभि में , प्रस्ताटवि मॉडल और कायिप्रणाली के टवटभन्न उद्योग जै से टक खाद्य, ऊजाि , स्वास्थ्य

दे खभाल और अन्य की आपूटिि श्ृं खलाओं में कई अनु प्रयोग हैं ।

संकेिशब्द : डे िा-संचाटलि टनणिय मॉडल, कृटिम बुक्तिमत्ता; मां ग पूवाि नुमान; संख्यापि इष्‍ििमीकरण; भटवक्तष्यक

टवश्लेर्षण टवद्या; टियात्मक टवश्लेर्षण टवद्या; पूवाि नुमान; न्याटयक पूवाि नुमान; समय श्ृं खला; मशीन टशक्षण; समय

सामटयक एग्रीगेशन; िॉस- समय सामटयक एग्रीगेशन; खु दरा; टवटनमाि ण।

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 TABLE OF CONTENTS

CERTIFICATE II
ACKNOWLEDGEMENTS III
ABSTRACT IV
सार VII
LIST OF VARIABLES AND PARAMETERS XVI
LIST OF ABBREVIATION XVIII
LIST OF FIGURES XXI
LIST OF TABLES XXIII

CHAPTER 1: INTRODUCTION 1
1.1 Background 1
1.2 Demand Forecasting in a Supply Chain 3
1.2.1 Accuracy of Demand Forecasts 5
1.2.2 Coherency of Demand Forecasts 7
1.3 Predictive to Prescriptive Analytics: Using Demand Forecasting for Inventory
Management 9
1.3.1 Inventory Management 10
1.4 Data-driven Decision Making in Supply Chain 11
1.5 Machine Learning in Supply Chain Management 13
1.5.1 Machine Learning for Demand Forecasting 13
1.5.2 Machine Learning for Inventory Optimization 15
1.6 Scope of the Thesis 15
1.7 Organization of the Thesis 16

CHAPTER 2: LITERATURE REVIEW 17

2.1 Introduction 17
2.2 Review on Demand Forecasting in Supply Chains 18
2.2.1 Data for Forecasting: Factors and Features 20
2.2.2 Time Series Methods 22

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 2.2.3 Machine Learning and Deep Learning Methods 25
2.2.4 Hybrid Methods 27
2.2.5 Judgmental Forecasting 28
2.3 Review on Hierarchical Forecasting: Methods and Approaches 30
2.3.1 Cross-sectional Hierarchical Forecasting 30
2.3.2 Temporal Hierarchical Forecasting 32
2.3.3 Cross-temporal Hierarchical Forecasting 35
2.3.4 Hierarchical Demand Forecasting in Supply Chains 35
2.4 Review on Data-driven Newsvendor Inventory Optimization in Supply Chains 36
2.5 Research Gaps 39
2.6 Research Questions 42
2.7 Research Objectives 44
2.8 Concluding Remarks 44

CHAPTER 3: MACHINE AND DEEP LEARNING FOR DEMAND

FORECASTING 45
3.1 Introduction 45
3.2 Notations Used 47
3.3 Deep Learning for Demand Forecasting 47
3.3.1 The LSTM Network 48
3.4. Experimental Setup 52
3.4.1. The Data 52
3.4.2 Hardware and Software 52
3.4.3 Evaluation Metrics 53
3.5. Empirical Results 54
3.5.1 Implementation 55
3.5.2 Results for the Online Channel: The Online Store 56
3.5.3 Results for the Offline Channel: The Physical Stores 58
3.5.4 Discussions 60
3.6. Concluding Remarks 61

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CHAPTER 4: BIG DATA AND DEEP LEARNING BASED
PREDICTIVE ANALYTICS FOR DEMAND FORECASTING 63
4.1 Introduction 63
4.2. Data Collection 65
4.2.1. Factors Influencing the Sales 65
4.2.2 Data Properties 67
4.3 Methodology 70
4.3.1 Dimensionality Reduction: Principal Component Analysis (PCA) 71
4.3.2 Time-series Data Modelling: The LSTM Networks 72
4.3.3 For Multivariate Data Modelling: Random Forest (RF) 74
4.3.4 Ensemble: Genetic Algorithm (GA) 75
4.4 Data Analysis 76
4.4.1 Data and Summary Statistics 76
4.4.2 Big Data Framework for Data Management and Modelling 78
4.4.3 Data Conversion: Principal Component Analysis (PCA) 79
4.4.4 The Benchmarking Methods and Performance Metrics 80
4.4.5 Results and Discussions 81
4.5 Managerial Implications 83
4.6 Concluding Remarks 86

CHAPTER 5: INTEGRATING MACHINE LEARNING AND HUMAN

JUDGMENT FOR PREDICTIVE ANALYTICS 89
5.1 Introduction 89
5.2 Structure of Demand Forecasting Decision Model (DFDM) 92
5.2.1 Judgmental Forecasts 93
5.2.2 Statistical Forecasts 94
5.2.3 Independent Variables 95
5.2.4 The Forecasting Model 95
5.2.5 Bias Adjustment Mechanism (BAM) 97
5.3 Empirical Analysis 97
5.3.1 Data and Summary Statistics 97

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 5.3.2 Empirical Results for Manufacturing Dataset 99
5.3.3 Empirical Results for Retail Product Data 101
5.3.4 Impact of Independent Variables on Forecasting 104
5.3.5 Impact of Bias Adjustment Mechanism (BAM) on Forecasting 105
5.4 Discussions 106
5.5 Concluding Remarks 107

CHAPTER 6: A FORECASTING FRAMEWORK FOR PREDICTIVE

ANALYTICS IN A SUPPLY CHAIN 109
6.1 Introduction 109
6.2 Hypothesis Development 111
6.3 Methodology 113
6.3.1 The LSTM Network 115
6.3.2 The Forecasts from Temporal Hierarchies 115
6.3.3 The Forecasts from Cross-sectional Hierarchies 118
6.4 Results and Analysis 120
6.4.1 Data 120
6.4.2 The Metrics of Evaluations 122
6.4.3 The Implementation of Forecasting Method 122
6.4.4 Results and Discussions 123
6.4.4.1 Results for the Cross-temporal Hierarchical Forecasts 124
6.5 Hypothesis Testing and Insights 126
6.6 Concluding Remarks 129

CHAPTER 7: FROM PREDICTIVE TO PRESCRIPTIVE

ANALYTICS: A DATA-DRIVEN INVENTORY OPTIMIZATION 131
7.1 Introduction 131
7.2 Notations Used 133
7.3.1 Problem Description 134
7.3.2 Demand Estimation through Machine/Deep Learning 135
7.3.3 Inventory Optimization 137

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 7.3.3.1 The Maximal Approximation Model 137
7.3.3.2 Empirical Demand Distribution Model 138
7.3.3.3 Proposed Inventory Optimization Model: QR-ML 138
7.3.4 The Multi-item Inventory Optimization with a Capacity Constraint 140
7.4 Empirical Evaluation 144
7.4.1 Data and Descriptive Statistics 144
7.4.2 Forecasting Methods, Parameter Setup, and Performance Metrics 145
7.4.2.1 Time-series Methods 145
7.4.2.2 Machine Learning Methods 147
7.4.2.3 Performance Metrics 148
7.4.3 Demand Estimation: Results and Discussions 149
7.4.4 Inventory Analysis 152
7.4.4.1 Effects of Demand Estimation on Inventory Costs 152
7.4.4.2 Effects of Inventory Optimization Techniques on Inventory Cost 154
7.4.4.3 The multi-item capacity allocation 155
7.5 Concluding Remarks 157

CHAPTER 8: CONCLUSIONS, RECOMMENDATIONS, AND

DIRECTIONS FOR FUTURE RESEARCH 159
8.1 Introduction 159
8.2 Conclusions and Summary of the Research Work 159
8.2.1 Summary of the Research Work 159
8.2.2 Revisiting the Research Questions 164
8.3 Contributions to the Literature 167
8.4 Recommendations for Academicians and Practitioners 169
8.4.1 Implications for Academicians 169
8.4.1 Implications for Industry Practitioners 171
8.5 Limitations and Directions for Future Research 173
8.6 Concluding Remarks 175

REFERENCES 177

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Appendix A: Variables and Data Summaries 201
Appendix B: Methodologies for disaggregated and aggregated forecasts 204
Appendix C: Proof of Theorem 7.1 208

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 LIST OF VARIABLES AND PARAMETERS

Chapter 3

• 𝑋𝑡 : the input vector at time step t

• ℎ𝑡 : the output vector at time step t
• 𝑠𝑡 : the vector for cell state t
• 𝑠̃𝑡 : the vector for a candidate value for input gate
• 𝑏𝑓 , 𝑏𝑖 , 𝑏𝑠̃ , 𝑏𝑜 : bias vectors
1
• (. ) : denotes the sigmoid function (𝑓(𝑥) = 1+𝑒 −𝑥 )

• 𝑊𝑓,𝑥 , 𝑊𝑓,ℎ , 𝑊𝑖,𝑥 , 𝑊𝑖,ℎ , 𝑊𝑜,𝑥 , 𝑊𝑜,ℎ , 𝑊𝑠̃ ,𝑥 , 𝑊𝑠̃,ℎ : weight matrices for input and outputs
for the three gates (forget gate, input gate, and output gate), and cell state
• 𝑓𝑡 , 𝑖𝑡 , 𝑜𝑡 : vectors of values obtained after activation of the three gates

Chapter 4

• 𝑆𝑡,𝑖 : represent the number of searches with selected keywords (𝑘𝑡,𝑖 )

• 𝑅𝑡,𝑖 : total number of search queries in geographical area 𝑖 in total 𝑁𝑤 weeks
• 𝐺𝐼𝑡,𝑖 : Google search index
• 𝑌𝑡 : time-series vector
• 𝑦̂𝑡 : predictions from the LSTM networks
• 𝑦𝑟𝑓 : predictions from the RF

Chapter 5
• {𝐿𝐸𝑡+1 , 𝑀𝑡+1
𝐸 𝐸
, 𝑈𝑡+1 }: lower, most likely, and upper bound, respectively, of the interval
for the expert’s forecast
• I_F : Internal expert’s judgmental demand forecasts
• E_F : External expert’s judgmental demand forecasts
• 𝑋 𝑐 : interval mid-point series
• 𝑋 𝑟 : half range interval series
• 𝑤1 and 𝑤2 : weights given to forecasts of expert 1 and expert 2

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 • 𝐶𝐹1 : combined experts forecast
• 𝐶𝐹2 : combined statistical forecast

Chapter 6

• 𝐶𝑋 : Total Quantity sold on all channels

• 𝑃𝑖 : Product 𝑖 , 𝑖 ∈ 1,2, … , 𝑛
• 𝐶𝑃 : Total Quantity sold of a specific product on all channels
• 𝐶𝑂𝑁 : Online Channel
• 𝐶𝑂𝐹𝐹 : Offline Channel
• 𝑆𝑂𝑁 : Online Store
• 𝑆𝑂𝐹𝐹(𝑗) : Offline Store 𝑗 , 𝑗 ∈ 1,2, … , 𝑀
• 𝑆𝑃 : Total quantity sold of a specific product at a specific store.
• 𝑦̂ℎ : base forecast for each level with horizon ℎ can be represented by
• 𝑆 : summing matrix
• 𝑆𝐺 : reconciliation matrix

Chapter 7

• 𝑑𝑖 : random variable for the demand for an item 𝑖

• 𝑐𝑖 : purchasing cost for each unit of item 𝑖
• 𝑝𝑖 : selling price for each unit of item 𝑖
• ℎ𝑖 : overage cost for each unit of item 𝑖
• 𝑏 𝑖 : underage cost for each unit of item 𝑖
• 𝑚 : total no. of items/products
• 𝐺𝑛 : total no. of items in a product group
• 𝐶 : total resource capacity for all products of a product group
• 𝑄𝑖 𝑜𝑟 𝑄 𝑖 : order quantity for item 𝑖
• 𝜋𝑖 (𝑄𝑖 ) : total cost of inventory for item 𝑖
• 𝑄𝑖𝑢 : unconstrained order quantity for item 𝑖
• 𝛼 𝑖 : the critical fractile (optimal service level) for unconstrained newsvendor item 𝑖
• 𝛽 𝑖 : is the ratio of the capacity required to the marginal revenue for an item 𝑖

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 LIST OF ABBREVIATIONS

ACF: Auto-correlation function

ADAM: Adaptive moment estimation

AI: Artificial Intelligence

AIC: Akaike Information Criterion

ANN/ FNN: Artificial/Feedforward Neural Network

AR: Autoregression

ARIMA: Autoregressive integrated moving average

ARIMAX: Autoregressive integrated moving average with external regressors

ARMAE: Average relative mean absolute error

ARMAPE: Average relative mean absolute percentage error

ARME: Average relative mean error

ARMSE: Average relative mean squared error

BAM: Bias adjustment mechanism

BIC: Bayesian Information Criterion

CART: Classification and regression trees

CH: Cross-sectional Hierarchies

CS-HF: Cross-sectional hierarchical forecasting

CT-HF: Cross-temporal hierarchical forecasting

DFDM: Demand forecasting decision model

DFM: Demand forecasting model

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DL: Deep Learning

DM: Diebold and Mariano Test

DNN: Deep neural networks

ETS: Error, Trend, Seasonality

FMCG: Fast moving consumer goods

FVA: Forecast Value-added Analysis

GA: Genetic Algorithm

GLS: Generalised least square

HF: Hierarchical Forecasting

LSTM: Long-short-term-memory

MA: Moving Average

MAE: Mean absolute error

MAPE: Mean absolute percentage error

ME: Mean error

ML: Machine Learning

MLR: Multiple linear regression

NVM: Newsvendor Model

NVP: Newsvendor Problem

PACF: Partial auto-correlation function

PCA: Principal components analysis

POS: Point-of-sales

PT: Pesaran and Timmermann Test

QR: Quantile regression

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QR-ML: Quantile regression-machine learning

ReLU: Rectified linear unit

RF: Random Forest

RMSE: Root mean squared error

RMSPROP: Root mean square propagation

RNN: Recurrent Neural Network

SGD: Stochastic gradient descent

SKU: Stock keeping unit

SVM: Support Vector Machine

TA: temporal aggregation

TD: temporal disaggregation

TD-NVM: Top-down newsvendor model

TH: Temporal Hierarchies

TPR: Temporary price reduction

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 LIST OF FIGURES

Figure 1.1: Supply Chain Dimensions for Forecasting in a Supply Chain 8

Figure 2.1: The research framework for the study 43

Figure 3.1: Recurrent Neural Network 49

Figure 3.2: The memory cell architecture of an LSTM and the input data to the LSTM

networks 50

Figure 4.1: Independent Variables Related to Various Factors 67

Figure 4.2: Flow diagram for Demand Forecasting Framework 69

Figure 4.3: Flowchart of the Proposed Method 71

Figure 4.4: The LSTM Memory Cell Architecture 73

Figure 4.5: Input sequences for the LSTM (all sequences are transposed) 74

Figure 4.6: Big Data Framework for Modelling and Analysis 78

Figure 4.7: Weekly distribution of sales and forecast values for a sample series 82

Figure 4.8: Relative importance of variables for sales prediction 84

Figure 4.9: Demand Forecasting Tool for an Operations Manager 86

Figure 5.1: Flow diagram for the proposed demand forecasting decision model 92

Figure 6.1: Supply Chain Dimensions for Forecasting 110

Figure 6.2: Hierarchical Tree Diagram for Multi-channel Retailer 114

Figure 6.3: Temporal Hierarchies for Weekly Series up to monthly aggregates 115

Figure 6.4: Weekly Series up to monthly aggregates (with Notations) 116

Figure 6.5: Flowchart for the proposed cross-temporal forecasting framework 119

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Figure 6.6a: A demand series (log of demand) for online channel and its temporal

aggregates 121

Figure 6.6b: A demand series (log of demand) for offline channel and its temporal

aggregates 121

Figure 7.1: Schematic diagram for a deep neural network – (a) the mathematical functions,

and (b) A deep neural network architecture 136

Figure 7.2: A Products' Hierarchy in a retail store 141

Figure 7.3: Comparison of inventory cost from the inventory optimization techniques using

different demand estimation techniques 154

Figure 7.4: Products hierarchies and their historical demand proportions 156

Figure 7.5: Comparison of total inventory cost from the inventory optimization techniques

and demand estimation techniques 157

Figure 8.1: Research Framework with research contributions of the study 166

Figure A.1: Some sample demand time-series 203

Figure B.1: Monthly distribution of sales and forecast values for a sample series 206

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 LIST OF TABLES

Table 3.1: Online channel; one-week ahead: ARME, ARMAE, and ARMSE 57

Table 3.2: Online channel; one-month (4 weeks) ahead: ARME, ARMAE, and ARMSE 57

Table 3.3: Online channel; Statistical significance tests for Product #1 (weekly forecast). 58

Panel A: DM test; Panel B: PT test. 58

Table 3.4: Offline channel; one-week ahead: ARME, ARMAE, and ARMSE 59

Table 3.5: Offline channel: one-month (4 weeks) ahead: ARME, ARMAE, and ARMSE 59

Table 3.6: Offline channel; Statistical significance tests for a random Product 60

Panel A: DM test; Panel B: PT test. 60

Table 4.1: Summary statistics of variables for each year 77

Table 4.2: Principal Component Analysis for Point-of-sales variables 79

Table 4.3: Principal Component Analysis for Promotion-related variables 80

Table 4.4: Principal Component Analysis for Weather-related variables 80

Table 4.5: Principal Component Analysis for Economy related variables 80

Table 4.6: Relative errors metrics for One-week ahead predictions (with ranking) 82

Table 5.1: Summary statistics 98

Table 5.2: 1-month, 3-months, and 6-months ahead: forecasting bias (ME), accuracy (MAE,

MAPE), and variance (RMSE) of manufacturing product 99

Table 5.3: Comparison of models by a t-test for independent samples at 5% significance

level (+/- means method i is better/worse than method j) 100

Table 5.4: 1-month, 3-months, 6-months, and 12-months ahead: forecasting bias (ME),

accuracy (MAE, MAPE), and variance (RMSE) of retail product 102

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Table 5.5: Comparison of models by a t-test for independent samples at 5% significance

level (+/- means method i is better/worse than method j) 103

Table 5.6: Forecasting results for univariate and multivariate models 104

Table 5.7: Comparison of forecasts from judgment forecasting and judgment forecasting

with bias adjustment mechanism (BAM) 106

Table 6.1: ARMAE, ARMSE, ARMAPE for Forecasts (the smaller, the better) 123

Table 6.2: Short-term (one week ahead) forecasts: ARMAE, ARMSE, ARMAPE 124

(the smaller, the better) 124

Table 6.3: Medium-term (one month ahead) forecasts: ARMAE, ARMSE, ARMAPE 125

(the smaller, the better) 125

Table 6.4: Long-term (one quarter ahead) forecasts: ARMAE, ARMSE, ARMAPE 125

(the smaller, the better) 125

Table 6.5: Forecasts errors comparisons of top-down (TD) and bottom-up (BU) approaches

127

Table 6.6: Forecasts errors comparisons of direct forecasts and forecasts with temporal

hierarchies 128

Table 6.7: Forecasts errors comparisons of cross-sectional hierarchical forecasts (CS-HF)

and with proposed cross-temporal hierarchical forecasts (CT-HF) 128

Table 7.1: Summary statistics of variables for each year 145

Table 7.2: Error metrics for demand estimation 151

Table 7.3: FVA Analysis 152

Table 7.4: Average inventory costs relative to the best approach for each product groups 153

Table 7.5: Optimal Order quantities 156

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Table A.1: Summary statistics of Transactional and Store variables for each year 201

Table A.2: Summary statistics of Promotional variables for each year 202

Table A.3: Summary statistics of Weather variables for each year 202

Table A.4: Summary statistics of Economic variables for each year 203

Table B.1: Real-time daily point-of-sales data 207

Table B.2: Error metrics for the Demand Sensing 207

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