DYNAMIC SUPPLY CHAIN FORMATION WITH
MULTI-DIMENSIONAL UTILITIES
PANCHAL GAJANAN BHANUDASRAO
DEPARTMENT OF MECHANICAL ENGINEERING
INDIAN INSTITUTE OF TECHNOLOGY DELHI
JULY 2013
© Indian Institute of Technology Delhi (IITD), New Delhi, 2013
DYNAMIC SUPPLY CHAIN FORMATION WITH
MULTI-DIMENSIONAL UTILITIES
by
PANCHAL GAJANAN BHANUDASRAO
Department of Mechanical Engineering
Submitted in fulfillment of requirements for the degree of
Doctor of Philosophy
to the
INDIAN INSTITUTE OF TECHNOLOGY DELHI
JULY 2013
Dedicated to my niece and nephew
Riva & Omkar
CERTIFICATE
This is to certify that the thesis entitled “Dynamic Supply Chain Formation with Multidimensional Utilities” submitted by Panchal Gajanan Bhanudasrao to the Indian Institute of
Technology Delhi for the award of the degree of Doctor of Philosophy is a record of original
research work carried out by him. He has worked under my guidance and supervision and has
fulfilled the requirements for the submission of this thesis, which to my best knowledge 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.
Dr. Vipul Jain
Assistant Professor,
Department of Mechanical Engineering,
Indian Institute of Technology Delhi,
New Delhi-110016, INDIA.
i
ACKNOWLEDGEMENTS
I express my deep sense of respect and gratitude to my supervisor Dr. Vipul Jain. Throughout my
Ph.D., he mentored me with friendly, creative, an enlightened research environment that helped
me to come up with immense research ideas. I will cherish in all my life the time that I worked
with him for my research. He is a great inspiration for me who always motivated me to think out
of the box and to feel the amazing experience of being good researcher. The crystal clear ideas,
focused aim, right depth of research, significant contributions, sharp analytical demonstration are
a few of the many inputs from him. He evaluated my writings with critical analysis that helped
me to improve with the time. He always gave importance to the timeline set for my research,
which helped me to finish my work within the optimal time duration. I will be indebted
throughout my life for his guidance par excellence. Above all he was the backbone of this
research, standing firm for gaining beliefs, faith and goodness in the research.
I am grateful to Prof. J.P. Subrahmanyam, Prof. S.R. Kale (Head of the Department) and Dean
PGS&R for being supportive during my research work. I am grateful to my SRC members, Late
Prof. Arun Kanda, Prof. S.G. Deshmukh, Prof. A.D. Gupta, Dr. M.S. Kulkarni and Dr. Munawar
Shaik for their valuable suggestions and comments. The motivational examples given by Late
Prof. Kanda will always remain in my conscious mind. I am also thankful to Dr. Kiran Seth and
Dr. Nomesh Bolia for their support during my stay at IIT Delhi. I had the privilege to assist some
of the faculty members in their courses, which helped me to connect the different streams of
research. I must thank our industry collaborator, Mr. Prem Narayan (IRCTC), for showing his
interest in our research and provide us the industry inputs that helped me to analyze the real life
scenarios. I am also thankful to our international collaborators, Prof. Naoufel Cheikhrouhou
(EPFL, Switzerland) and Prof. Sameer Kumar (University of St. Thomas, USA), for their
ii
valuable inputs to my research. I take this opportunity to express my special gratitude to Prof.
Cheikhrouhou for his support and help in visiting LGPP laboratory of EPFL for collaborative
work under Indo-Swiss Joint Research Program.
My family members, especially my parents, deserve special mention for their inseparable support
and prayers. I would like to express my love to my niece and nephew, whose presence in my life
means an angelic feel, which helped me to get through some difficult times. I would like to
mention my great respect to my maternal grandfather Late Mr. Dattatray Mudholkar, I am sure
his blessings are and will be with me for my entire life.
I would like to express my thanks to my colleagues Dr. Avinash Samvedi, Mr. Umang Soni, Mr.
Anirban Kundu, Mr. Sumit Sakhuja and special thanks to Mr. Vedpal for sharing elite moments
during my research work. These people provided me all the comforts required to stay away from
the family. I shall be failing in my duties if I do not express my thankfulness for the continuous
help extended to me during research work by Dr. Divya Pandey, Dr. Bhupesh Lad, Mr. Prashant
Ambad, Md. Asjad, Mr. Pravin Tambe, Mr. Pankaj Zine, Mr. Amit Upadhyay, Ms. Monica
Tanwar. The discussions during the tea breaks were fruitful to cherish the time in my entire life. I
would like to also express my deep respect to Dr. Nitin Chaphalkar (CoE, Pune) who has given
me immense support in keeping the fighting spirit to achieve higher limits of success.
I am also thankful to Mr. S.C. Sharma and Mr. Naveen for providing all the facilities in the CIM
lab and Industrial Engineering lab. Finally, I would like to thank everyone, who were important
to the successful realization of this thesis.
Date:
Panchal Gajanan Bhanudasrao
iii
ABSTRACT
In modern supply chain, managing three important flows, namely information, finance, and
material, come with the responsibility of desired efficiency. For the information flow, the
information asymmetry is the result of lack of efficiency in managing it. The information
asymmetry is also because of the rational and self-centered behavior of supply chain players in
the supply chain. The diluted relationship among the supply chain players demands for the use of
novel concepts like utility theory, game theory to elicit the true information from the players.
The prerequisite for this is a distinct differentiation between the public and the private
information. The revelation of true public information is in the hands of individual players in the
supply chain. An intelligent mechanism is indeed required to elicit the information along with
the incentives for each individual for agreeable incentive design. The concept of incentive
design is inspired by the process of internalization of externalities experienced in the supply
chain. The positive externalities like promoting the use of conventional energy sources requires
the incentives in the form of subsidies provided in order to achieve the social outcome. Similarly,
another example, which can be seen is the negative externalities experienced in over use of
nicotine based product should be slashed down by putting a heavy tax duty on their sale. In both
the cases, arriving at the social solution is vital in order to run steady operations of the supply
chain.
In the game theoretical approach of the problem, players’ utility of choosing any strategy lead to
quantification of their preference order of strategies. Usually, the utility depends on single
parameter or dimension as a representation of preference order. In supply chain, on the other
hand, decision over the preference order should incorporate multiple parameters or dimensions in
utility analysis. These strategic decisions relate to the operational decisions in the supply chain.
iv
The two important decisions are quantity of interest (ordered quantity, order fulfillment) and
price per unit (quoted price per unit, initial offered price per unit). Although these two
operational decisions look clean with each other, there exists a unique non-linear relationship
between them once the concept of rationality is introduced. Apart from these two, there are many
other decisions like quality requirement, lead time, service level etc. However, in this thesis, the
multi-dimensional utilities are analyzed with two major parameters or dimensions; price per unit
and quantity of interest. Including these two, the resultant utility analysis becomes the multidimensional utility analysis. The proposed approach is validated with real life industry example
of the procurement process in the two-tier supply chain of Indian Railways Catering and Tourism
Corporation (IRCTC) Limited. These two parameters, in fact, are the most concerned issues for
the organizations like IRCTC. Moreover, in this thesis, the supplier-buyer relation is well studied
to analyze and compare the individual utilities of the supply chain players and the designed
multidimensional social utility in IRCTC case. Based on the procurement data, the individual
utilities are appeared to be the conflicted utilities with which supply chain design fails. On the
contrary, the multidimensional social utility gives the maximum throughput in utility gain. Based
on the results the framework for the procurement process of IRCTC has been proposed, which
includes the incentives for the players participating in the supply chain design process.
The utility comparison also depicts two major observations, namely non-participation and
dominance of the players. The results of the utility comparison show that the individual utility,
which is non-dominating player’s utility is non-increasing throughout the contract period as
against the increasing dominating player. The distinction based on the dominance level of the
players lead to the non-dominant player to back out from the competition and thus the nonparticipation. The players’ non-participation leads to barging into non-capable supplier (player)
v
in the supply chain. The non-participation also leads to the monopoly of the unqualified supplier
and hence the possibility of the bad quality product in the sake of making profit. The
consequences of barge-in supplier are also huge in terms of externalities, which are difficult to
internalize.
The supply chain players’ non-participation or reluctance to participate in supply chain contracts
is influenced by the dynamics of the system evolving with many competitive players in the
supply chain. In this thesis, with the objective of maximizing the social utility, efforts have been
made to access behavioral issues of supply chain as well. In doing so, the reluctance or
conservativeness of player, due to the information asymmetry, is measured in the form of inertia
experienced in the anxious and dynamic supply chain market. To represent the anxious and
dynamic supply chain market, distinguished cases are considered based on the supply chain
players’ level of risk and variety of product. The cases considered are accommodated in two tests
or experiments designed to model the inertia and study its impact on total utility gained in the
supply chain. The expected outcome of these experiments is in the form of threshold analysis of
the parameters. This threshold analysis is helpful in extrapolating inclination of the players on
parametric negotiation. This is because while negotiating with the supply chain players it is
required to devise a mechanism with which the one can trace more on the parameter which has a
greater impact on the total supply chain throughput.
From the literature, it is seen that most of supply chains are a combination of an oligopoly
market or sometime a duopoly market at each echelon of the supply chain with rational players.
The allocation of the tasks in these market conditions at each echelon of the supply chain is an
important activity in the supply chain formation process with incomplete or partial information
vi
setting of the supply chain. The market situations along with the nature of players give rise to a
dynamic environment in a supply chain, which becomes difficult to manage causing the
spillovers in the transaction; i.e. externalities. Along with tasks allocation, it is also required to
assign the incentives to each supply chain players. These incentives are an outcome of the
internalization process of externalities with which the total supply chain utility is maximized.
The role of a supply chain manager is to facilitate a mechanism devised for allocating the
identified tasks with efficient incentive system keeping the focus on the multi-echelon supply
chain. The focus on complete supply chain is required to avoid the bullwhip effect of uneven
utility resulting in non-participation and conflict in the supply chain. Utility analysis is the
measure of the efficiency in supply chain, which is the function of strategy decided by supply
chain players. However, setting the optimal strategy for rational and intelligent players with
conflicting interests is a challenging task for the supply chain manager.
In today’s growing economy, it has also been found that there is a shift in the paradigm of
getting the optimal solutions to the problems, especially the conflict related problems. The shift
is from optimality to the strategic and heuristic solutions. For example, choosing strategic
location gives rise to the minimization of the transportation costs and thus making more profit. In
this thesis, the major internalization methods considered are Lagrange relaxation and Vickery
Clarke Groves (VCG) mechanism. These methods have been developed to incorporate a
universal framework incorporating every possible incentive scheme related to the supply chain
environment. The proposed mechanism includes the possible internalization methodologies in
the form of incentive design to offer the universal supply chain formation process for supply
chain managers. The proposed mechanism also contributes in analyzing two-way competitions, a
Bertrand and Cournot competition, where Price per unit and Quantity are the two parameters for
vii
the utility analysis. The final framework as an outcome of the thesis is the proposed universal
multi-stage auction mechanism for supply chain formation with multi-dimensional utilities of
supply chain players.
The mechanism for supply chain formation is achieved through the algorithmic development of
the problem. The multi-stage auction mechanism is used for supply chain formation process. The
preferred values of the parameters are checked with the preference function of the auction
mechanism. The proposed auction mechanism is unique in developing ‘forward and reverse’
auction mechanism with value of price per unit, increasing with decreasing units of quantity of
interest alternatively. The algorithm for the task allocation is extending to assign incentives for
the supply chain players. Based on the algorithm, the framework for supply chain formation
process is proposed for its use in a variety of supply chain cases. The proposed framework is
compared with the conventional procurement process of IRCTC on the basis of procurement
data. The objective of the comparison is to critically analyze the conventional process of dealing
with information asymmetry, dynamics and product variety on the common platform of supply
chain formation process.
viii
TABLE OF CONTENTS
Item
Pages
Certificate
i
Acknowledgement
ii-iii
Abstract
iv-viii
Table of Content
ix-xii
List of Figures
xiii-xiv
List of Tables
xv
List of Abbreviations and Symbols
xvi-xix
Chapter 1: Introduction
1-21
1.1 Introduction to supply chain
1
1.2 Introduction to utility theory and game theory
5
1.2.1 Supply chain games
5
1.3 Multi-dimensional utilities
8
1.4 Internalization of externalities: Motivation for social outcome
9
1.5 Introduction to supply chain formation and mechanism design
13
1.6 Research problem and objectives
16
1.6.1 Objectives of research
17
1.7 Organization of thesis
20
Chapter 2: Literature review
22-43
2.1 Supply chain formation
23
2.1.1 Supply chain formation with channel contractual equilibrium
23
2.1.2 Negotiation models for supply chain formation
25
2.1.3 Quantity discount modeling for supply chain formation
27
2.1.4 Competitive equilibrium for supply chain formation
38
2.1.5 Other methodologies for supply chain formation
30
2.2 Multi-dimensional utility analysis
31
2.3 Auction mechanisms for supply chain formation with multi-dimensional
33
utilities
ix
2.4 Research gaps
39
2.5 Problem Statement and scope of research
41
2.5.1 Objectives of research
42
2.5.2 Methodological description
42
2.6 Concluding Remarks
43
Chapter 3: Multi-dimensional Utility Analysis for The Social Outcome
3.1 Introduction
44-73
44
3.1.1 Assumptions
47
3.2 Learning from the literature on multi-dimensional utility
3.2.1 Research gaps, key issues and challenges
3.3 Problem statement and model formation
49
50
51
3.3.1 Analysis of induced game
52
3.3.2 The multi-dimensional utility
53
3.3.3 Incentive design modeling: social outcome abetment
58
3.4 Industry case analysis for multi-dimensional utilities
3.4.1 Industry case-Indian Railways Catering and Tourism Corporation
59
59
Limited (IRCTC)
3.4.2 Supply chain and operational complexity of the procurement process in
61
IRCTC
3.4.3 Game theoretical structure of IRCTC
62
3.4.4 Data analysis for discount pattern and utilities
63
3.4.5 Superiority of the proposed framework
69
3.5 Managerial insights
70
3.6 Conclusion on multi-dimensional utility analysis for social outcome
71
Chapter 4: Equilibrium Analysis in Multi-echelon Supply Chain with Multi-
74-104
dimensional Utilities of Inertial Players
4.1 Introduction
74
4.2 Theoretical background
76
4.2.1 Utility and social utility function
76
4.2.2 Inertia in supply chain
77
4.2.3 Risk and inertia in supply chain
78
x
4.2.4 Novelty of the proposed methodology for behavioral analysis
4.3 Literature review
80
80
4.3.1 Review on supply chain formation in dynamic environment
80
4.3.2 Review on inertial amendments in utility analysis
81
4.4 Model formulation
83
4.4.1 Demand modeling for the players’ valuations
84
4.4.2 Inertia modeling
86
4.4.3 Discount modeling
87
4.5 Experimental design
91
4.5.1 Experiments for modeling inertia
91
4.5.2 Design of experiments for optimization
93
4.5.3 Results of optimization
96
4.5.4 Research findings and implications
99
4.6 Managerial insights
102
4.7 Conclusion on amendments in utility analysis with inertial effects of
103
enterprises
Chapter 5 Multi-stage Auction Based Mechanism Design for Supply Chain
105-133
Formation with Multi-dimensional Utilities
5.1 Introduction
105
5.1.1 Mechanism design and supply chain formation for social multi-
106
dimensional utilities
5.1.2 Need for supplier selection mechanism
108
5.1.2 Objectives of universal supplier selection mechanism
109
5.1.3 Assumptions
109
5.2 Summary of related work
111
5.2.1 Auction mechanism design for two-way competition (multi-dimensional
111
utility)
5.2.2 Multi-attribute auction mechanism in procurement process
113
5.2.3 Research gaps
114
5.3 Universal auction mechanism in two-way competition
5.3.1 Incentive design conceptualization
115
116
xi
5.4 Algorithm for winner determination function of auction mechanism
117
5.5 Incentive design in auction mechanism
120
5.6 Framework for universal supplier selection process with multi-dimensional
124
utility analysis for supply chain formation process
5.6.1 Expected outcome
125
5.7 A case example: Indian Railways Catering and Tourism Corporation Limited
127
5.8 Managerial insights
131
5.9 Conclusion on universal supplier selection model for supply chain formation
133
Chapter 6: Conclusion and Scope for Future Work
134-146
6.1 Salient contribution of the research
139
6.2 Managerial implications of the research
141
6.3 Limitations and future work
142
6.3.1 Scope for future work
143
References
146-154
Appendices
155-157
Appendix A: List of Publications from research
155
Appendix B: Biography of the researcher
156
xii
LIST OF FIGURES
Figure number
Title of the Figure
Page number
1.1
Vertical competition game
7
1.2
Horizontal competition game
8
1.3
Shape of utility function with price per unit and quantity of
9
interest
1.4
Supply chain: global and local perspective
1.5
Analogical
explanation
of
10
internalizing
the
positive
11
internalizing
the
negative
12
externalities in supply chain
1.6
Analogical
explanation
of
externalities in supply chain
1.7
Concept of social choice function
14
1.8
Information elicitation problem
14
1.9
Development of mechanism design by relaxing the truth
16
revelation of (i-1) players
2.1
Classification of methodology for supply chain formation
23
problem
3.3.1
Visual presentation of supplier-buyer game with respective
52
notations
3.3.2
Shape (non-scaled) of multi-dimensional utilities as non-
54
linear function of price per unit and quantity of interest
3.3.3
Mapping in the bijective function
55
3.3.4
Feasible area of Maximum utility
57
3.4.1
Flowchart of algorithm used conventionally for the selection
60
of supplier in IRCTC
3.4.2
Game theoretical structure of IRCTC showing interactions
62
3.4.3
Discount (in percentage) pattern asked by the buyer IRCTC)
64
3.4.4
Comparative analysis of individual utility (in INR) and
66
social utility (in INR) for the IRCTC case
3.4.5
Trends of individual utility against social utility
xiii
67
3.4.6
Proposed framework of algorithm for the procurement
68
process
4.2.1
Classification of supply chain players with associated risk
79
4.4.1
Distribution of consumption value of Supplier and Buyer
85
4.4.2
Feasible area of the discount function in the supply chain
89
formation
4.5.1
Histogram of quantity for three cases of players based on the
92
risk
4.5.2
Regression of quantity (q) against price per unit (p)
92
4.5.3
Comparative analyses of low-price and high-price products
99
for risk-based cases of supply chain players
4.5.4
Framework for the supply chain formation process with
101
inclusion of inertia of supply chain players
5.4.1
Bid profiles of players through auction mechanism with four
120
stages;
(a) price per unit profile in the bid
(b) quantity of interest profile in the bid
5.5.1
Types of incentives designed for in general task allocation
121
problem
5.6.1
Combined framework of monopoly and oligopoly market
126
supplier-buyer selection in two-way competition
5.7.1
Process of short listing
128
5.7.2
Discount pattern and opportunities for supplier by bidding
130
xiv
LIST OF TABLES
Table number
3.4.1
Title of table
Page number
One calculation of individual and social utility in two-tier
64
supply chain (first month)
3.4.2
IRCTC data analysis for analyzing individual and social
65
utility
3.4.3
Relative difference of individual utility and social utility
67
4.5.1
Inputs for the high-price product
94
4.5.2
Inputs for the low-price product
94
4.5.3
Inputs for the discount function in the case of low-price
95
products
4.5.4
Inputs for the discount function in the case of high-price
95
products
4.5.5
Result of test I for the inertia analysis with high-price
96
products
4.5.6
Result of test I for the inertia analysis with low price product
97
4.5.7
Result of Low-price product case with tuple of outcome
98
(qi,pi,ui)
4.5.8
Result of High-price product case with tuple of outcome
98
(qi,pi,ui)
5.7.1
Two-phase demonstration of discount pattern and supplier
selection
xv
129
LIST OF ABBREVIATIONS AND NOTATIONS
Item
Description
CDA
Central design authority
GSCM
Global supply chain manager
LSCM
Local supply chain manager
VCG
Vickery-Clark-Groves
DSIC
Dominant strategy incentive compatibility
BIC
Bayesian incentive compatible
BIC-SCF
Bayesian incentive compatible-supply chain formation
IRCTC
Indian Railways Catering and Tourism Corporation
MAS
Multi-agent systems
TDN
Task dependency network framework
ABM
Agent-Based Modeling
MLT
Mean lead time
SDLT
Standard deviation of lead time
MAU
Multi-attribute utility
AMD
Automated mechanism
INR
Indian Rupees
w
wholesale price from seller
m
Buyer’s margin
q (w+m)
Quantity of interest as a function of wholesale price, W and margin, m
(in production games)
qi
Market share of ith supplier in supplier tier (in pricing games)
xvi
p (q1 +q2)
Price quoted on total market share (in pricing games)
i =(1,…,n)
Echelon of supply chain with n echelons
(i,-i)
Player profile of the supply chain consisting i and other players (-i)
  (1 ,..., n )  
Valuation or type profile of n echelons of supply chain from the
valuation set 
f 1 ,..., n 
i
Social choice function
True valuation of ith echelon player

Reported (non-truth) valuation of ith echelon player
x  f 1 ,..., n 
Outcome of the social choice function
{a, W}
Strategic pair of announcement and willingness
qi  Q
Quantity of the echelon i or quantity of interest of ith player
pi  P
Price of the echelon i
 pi , pi  , qi , qi 
Price per unit and quantity of interest profile
uiso ()
Social utility for ith echelon for any strategy profile
uio
Optimal utility for ith echelon
vi
Valuation of ith echelon
BR-i(si)
Best response of –ith player for si strategy of ith player
ci
Cost to the supplier (i)
hi ()
Payment for the each of the participating players
t T
Number of stage of the negotiation in supply chain
jJ
Number of parameters
i
xvii
Social utility for supply chain players’ profile
u(soi,i )
p
so
(i ,i )
, q(soi ,i ) 
Social price and social quantity profile for supply chain players’
profile
(pso, qso)
Social price and Social quantity pair
CiMax
Maximum capacity of supplier i
cmi
Cost to manufacture the product
i
ith echelon’s inertial effect
dimax
Maximum discount provided by ith supplier in IRCTC case from all
the discount di
Qi
Demand from supply chain player based on the consumption
distribution (i can be supplier (s or i) or buyer (b or –i))
Profit of ith player
ai0
Lower bound for the utility to ith player in supply chain
ai1
ith player’s weight for the quantity while modeling utility
ai2
ith player’s weight for price per unit while modeling utility
ai3
ith player’s weight for the social utility while modeling utility
h
Number of stages in the auction mechanism
k  n
Winner of the auction which is the subset of n
(bih , bhi )  ( p(hi ,i ) , qih,i ) )
Bidding profile of the supply chain player at hth stage of auction with
price and quantity ( p(hi ,i ) , qih,i ) )
xviii
Xh
Set of preference constraints at hth stage of auction
Δ
Threshold for the utility gain
xix