Supply chain coordination mechanisms new approaches for collaborative planning

Lecture Notes in Economics
and Mathematical Systems
Founding Editors:
M. Beckmann
H.P. Künzi
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Fachbereich Wirtschaftswissenschaften
Fernuniversität Hagen
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Institut für Mathematische Wirtschaftsforschung (IMW)
Universität Bielefeld
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628



Martin Albrecht

Supply Chain
Coordination Mechanisms
New Approaches for Collaborative Planning

ABC

Dr. Martin Albrecht
PAUL HARTMANN AG


ISSN 0075-8442
ISBN 978-3-642-02832-8
e-ISBN 978-3-642-02833-5
DOI 10.1007/978-3-642-02833-5
Springer Heidelberg Dordrecht London New York
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c Springer-Verlag Berlin Heidelberg 2010
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For Rita and Amalia Isabel


Foreword

Inter-organizational supply chains have to coordinate their material, information,
and financial flows efficiently to be competitive. However, legally independent supply chain (SC) partners are often reluctant to share critical data such as costs or
capacity utilization, which is a prerequisite for central planning or hierarchical
planning – the planning paradigm of today’s Advanced Planning Systems (APS).
Consequently, concepts for collaborative planning are needed, considering a joint
decision making process for aligning plans of individual SC members with the aim
of achieving coordination in the light of information asymmetry.
This is the starting point and challenge of the PhD thesis of Martin Albrecht
because little is known about how to design a solution for this difficult decision
problem. Starting from an initial solution – that may be generated by upstream planning – improved solutions are looked for. This is achieved by computer-supported
negotiations, i.e., an exchange of different order proposals within the planning interval among the SC partners involved, where partners are free to accept or reject
proposals.
One challenge in this negotiation process is to find new proposals and counterproposals which have a good chance of acceptance while improving the competitive
position of a SC as a whole. Here, Albrecht devised new generic coordination
schemes for planning tasks which can be modeled either by Linear Programming
(LP) or Mixed Integer Linear Programming. For the LP case finite convergence to
the optimum has been proved.
While previous research on collaborative planning stopped with a clever coordination scheme Albrecht also considered a further, very important aspect of
negotiations: How to get the partners to tell the truth when exchanging information
and to accept a very promising solution for the supply chain as a whole. Formally
speaking, coordination mechanisms are needed where the coordination schemes can
be embedded. One of the coordination mechanisms advocated by Albrecht is the
surplus sharing by an initially agreed upon lump sum payment to one party. He has
been able to show that the corresponding mechanism results in truth-telling as a
weakly dominant strategy. The reader can expect both analytical results as well as
computational tests of collaborative planning schemes for various lot-sizing problems including some from industrial practice – and there is a lot more to be gained

vii

viii

Foreword

from reading this thesis but I will not reveal more details here. I wish this excellent
thesis a wide audience of interested and very satisfied readers and a large impact on
collaborative planning.
Hamburg, April 2009

Hartmut Stadtler


Preface

When I started my research, most known collaborative planning approaches dealing
with mathematical programming models were based on a serious oversimplification
of reality: They presumed a team setting, where parties honestly disclose information and sometimes even accept deteriorations if this benefits the supply chain as a
whole. One of the major contributions of this work has been to relax this assumption.
I have developed mechanisms, which achieve coordination despite self-interested
behavior of parties. Without wanting to relativize the importance of this contribution, I would like to point out the existence of a particular real-world team: The
people supporting me when I was writing this thesis.
First of all, I am indebted to Prof. Dr. Hartmut Stadtler. He not only set the example for my research, but also provided (sometimes incredibly) generous advice and
professional and personal support. Among many other things, he has patiently read
my papers many times and supplied several insightful suggestions at all stages of
this work. I am also grateful to Prof. Dr. Karl-Werner Hansmann for his willingness
to serve as the co-referee for this thesis.
Apart from my academic advisers, I am indebted to my colleagues and collaborating researchers. Particularly, I want to thank Carolin P¨uttmann for her great
teamwork in the EU-project InCoCo-S, for listening to many of my (not always fully
worked out) ideas, and for carefully proofreading the whole dissertation. Dr. Bernd

Wagner and Volker Windeck also read parts of the thesis and provided many valuable suggestions. Last, but not least, I am thankful to Prof. Dr. Heinrich Braun and
Benedikt Scheckenbach from the SAP AG for challenging discussions and for making available the real-world test data used in this work.
I also thank the Gesellschaft f¨ur Logistik und Verkehr for subsidizing the printing
of this work.
Certainly most important for this dissertation has been my family, although not
interested in supply chain management at all. My parents supported my education,
without expecting anything in return. My wife Rita not only renounced to much
shared time, but encouraged me with all her love to keep on researching until I have
(finally) been satisfied with this work.
Thank you, everybody.
Heidenheim, May 2009

Martin Albrecht
ix



Contents

Abbreviations .. . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . xiii
Nomenclature .. . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . xv
1

Introduction .. . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . .
1.1 Motivation and Goals of This Work . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . .
1.2 Methodology .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . .
1.3 Outline . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . .

1
1

2
2

2

Supply Chain Planning and Coordination .. . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . .
2.1 Supply Chain Planning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . .
2.1.1 Definitions and Overview .. . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . .
2.1.2 Master Planning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . .
2.2 Model Formulations for Master Planning . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . .
2.2.1 Generic Master Planning Model .. . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . .
2.2.2 Extension to Lot-Sizing .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . .
2.3 Decentralized Planning and Coordination .. . . . . . . . . . . . . . . . . . .. . . . . . . . . . .
2.3.1 Basic Definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . .
2.3.2 Decentralized Supply Chain Planning .. . . . . . . . . . . . . . .. . . . . . . . . . .
2.3.3 Upstream Vs. Collaborative Planning . . . . . . . . . . . . . . . .. . . . . . . . . . .

5
5
5
8
9
10
12
20
20
24
30

3

Coordination Mechanisms for Supply Chain Planning . . . . . . . .. . . . . . . . . . .
3.1 Symmetric Information .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . .
3.1.1 Non-cooperative Game Theory .. . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . .
3.1.2 Cooperative Game Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . .
3.2 One-Sided Information Asymmetry . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . .
3.2.1 Signaling .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . .
3.2.2 Screening . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . .
3.3 Multilateral Information Asymmetry .. . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . .
3.3.1 Auctions and Their Application to Supply Chain Coordination
3.3.2 Mechanisms with Focus on Proposal Generation .. . .. . . . . . . . . . .

35
35
36
41
43
43
45
48
48
51

xi


xii

Contents

4

New Coordination Schemes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . 63
4.1 Generic Scheme for Linear Programming and Analytical Results . . . . . 64
4.1.1 Version with Iterative, Unilateral Exchange
of Cost Information . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . 64
4.1.2 Version with One-Shot Exchange of Cost Information .. . . . . . . . 80
4.2 Scheme for Uncapacitated Dynamic Lot-Sizing
and Analytical Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . 82
4.3 Application to Master Planning .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . 99
4.3.1 Linearization .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . 99
4.3.2 Adaptation to Master Planning . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . .103
4.3.3 Generic Modifications.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . .111
4.3.4 Modifications for Master Planning . . . . . . . . . . . . . . . . . . .. . . . . . . . . . .114
4.4 Customizations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . .120
4.4.1 Master Planning with Lot-Sizing . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . .120
4.4.2 Voluntary Compliance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . .122
4.4.3 Lost Sales . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . .123
4.4.4 Multiple Suppliers .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . .126

5

New Coordination Mechanisms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . .129
5.1 Surplus Sharing Determined by the Informed Party . . . . . . . . .. . . . . . . . . . .130
5.2 Surplus Sharing Determined by Lump-Sum Payments . . . . . .. . . . . . . . . . .133
5.3 Surplus Sharing by a Double Auction . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . .141
5.4 Comparison of Mechanisms and Discussion . . . . . . . . . . . . . . . . .. . . . . . . . . . .149
5.5 Application with Rolling Schedules . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . .151

6

Computational Tests of Coordination Schemes . . . . . . . . . . . . . . . . .. . . . . . . . . . .155
6.1 General Master Planning Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . .155
6.1.1 Generation of Test Instances and Performance Indicators.. . . . .155
6.1.2 Analysis of Solutions for the Generic Scheme .. . . . . .. . . . . . . . . . .162
6.1.3 Analysis of Solutions for the Modified Scheme . . . . .. . . . . . . . . . .164
6.2 Uncapacitated Lot-Sizing Problem . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . .169
6.2.1 Generation of Test Instances .. . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . .169
6.2.2 Analysis of Solutions.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . .171
6.3 Multi-level Capacitated Lot-Sizing Problem . . . . . . . . . . . . . . . . .. . . . . . . . . . .174
6.4 Models for Campaign Planning .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . .179
6.4.1 Generation of Test Instances .. . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . .179
6.4.2 Analysis of Solutions.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . .180
6.5 Real-World Supply Chain Planning Problems . . . . . . . . . . . . . . .. . . . . . . . . . .184
6.5.1 Planning Problems and Model Formulation . . . . . . . . .. . . . . . . . . . .185
6.5.2 Analysis of Solutions.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . .192

7

Summary and Outlook .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . .197

References .. . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . .201


Abbreviations

AGC
Average gap closure achieved by the scheme
AGS
Average gap after the application of the scheme

AGU
Average gap of the uncoordinated solution
APO
Advanced planner and optimizer
APS
Advanced planning system
arb.
Arbitrary
B
Buyer
BOM
Bill of material
B2B
Business-to-business
CLSP
Capacitated lot-sizing problem
CLSPL Capacitated lot-sizing problem with linked lot sizes
cos.
Cosinus
CSLP
Continuous setup lot-sizing problem
CU
Capacity unit
DLSP
Discrete lot-sizing and scheduling problem
EOQ
Economic order quantity
GC
Gap closure achieved by the scheme
GLSP

General lot-sizing and scheduling problem
GM
Generic master planning model
GS
Gap after the application of the scheme
H
High
IGFR
Increasing generalized failure rate
IP
Informed party
L
Lot size (driver)
L
Low (type of demand forecast)
LB
Lower bound
LP
Linear programming
MLCLSP Multi-level capacitated lot-sizing problem
MLCLSPL Multi-level capacitated lot-sizing problem with linked lot sizes
MLPLSP Multi-level proportional lot-sizing and scheduling problem
MLULSP Multi-level uncapacitated lot-sizing problem
MINLP Mixed-integer nonlinear programming
MIP
Mixed-integer programming

xiii

xiv

MU
NLP
OEM
Q
RHS
RP
PPM
S
Sched.
SMP
SNP
SOS2
spl.
T
TBO
TC
TS
U
UB
UT

Abbreviations

Monetary unit
Nonlinear programming
Original equipment manufacturer
Quantity
Right-hand side

Reporting party
Production process model
Supplier
Scheduling
Single machine processor
Supply network planning
Special ordered set of type 2
Split
Time
Time between orders
Time for solving the centralized model
Time for running the scheme
Unit
Upper bound
Unit time


Nomenclature

Indices, Sets, and Index Sets
˘E
Set of proposals already found
˘iE
Set of proposals previously generated by the scheme
˘B
Set of proposals identified by the buyer
˘S
Set of proposals identified by the supplier
˘ up
Set of proposals identified by GMupS

E
Set of cost changes associated with proposals for central resource use
i
a
Arc linking two locations
ABa
Location at the beginning of arc a
AEa
Location at the end of arc a
Br .x/ r-neighborhood of x
CS
Set of solutions identified by the scheme for the MLULSP
DS
Set of proposals with delayed supply compared to the starting proposal
ES
Set of proposals with early supply compared to the starting proposal
f
Superindex denoting the first proposal generated
i
Decentralized parties
i
Suppliers
init
Superindex denoting the initial solution
J
Set of items
j
Items or operations
JB
Set of items produced by the buyer

JD
Set of items supplied
JE
Subset of items sold to external customers
JlE
Items sold at location l
S
Set of items produced by the supplier
J
Jm
Set of items produced on resource m
L
Set of locations
l
Location, l 2 L
M
Set of resources
m
Resources (e.g., personnel, machines, production lines)
MB
Set of resources of the buyer
MS
Set of resources of the supplier
NDS Set of proposals without delayed supply compared to the starting proposal

xv


xvi

Nomenclature

NES
Set of proposals without early supply compared to the starting proposal
new
Superindex indicating a new proposal
P
Set of PPM
P
Set of parties
p
PPM, p 2 P
Pc
Set of parties for which coordinated proposals have been chosen
PS
Set of suppliers
PB
Set of supply proposals optimal for the buyer subject to any N B
Rj
Set of predecessor items of item j
S
Set of customer classes
s
Customer class, s 2 S
Sj
Set of immediate successors of item j in the BOM
st
Superindex indicating the starting solution
T
Set of periods

t
Periods
Xis
Subset of feasible solutions to CS1i
XiE
Set of proposals found so far
Subset of vertex solutions to DPi
Xivd
Xiv
Set of vertex solutions identified so far
Parameters and Random Variables
tiB
Periods between subsequent setups of the buyer
tiS
Periods between subsequent setups of the supplier
Unit penalty costs for arbitrary deviations
O ; A ; B ; C Weights
Scalars
ie
Scalars
ie
aj
Cumulated capacity requirements of an item j
ei
Number of different solutions found so far for party i
ej
Average secondary demand for item j
Proposal
PB
Proposal out of PB with the same N B and N S as in the systemwide

optimal solution
e
Proposal e for the central resource use by party i
i
Resource use for the j th proposal generated by party i
ij
Production lead time of PPM p
p
Transportation lead time for item j along arc a
aj
Lead time for item j
j
Type of demand forecast
hB
Lower bound for the probability distribution of hB

b
be
lc

blcj
j

e
i

a; b

Maximum costs for backorders that are caused by a shortage in the supply
or the production of item j

Potential cost impact of backorders in the supply of item j
Cost effects of the proposal e by party i
Lower and upper bounds for S


Nomenclature

Ai
amj
amp
b
Bk1 ,Bk2

xvii

Use of the central resources by decisions xi
Capacity needed on resource m for one unit of item j
Capacity needed on resource m for one unit of PPM p
Purchase price
Prior knowledge of parties #1, #2 about the other party’s bids for proposals

(upper bounded by bj1 ,bj2 )
Bids by parties #1, #2 for proposal k
Total amount of the central resources
Bi
Use of the decentralized resources by decisions xi
bi
Total amount of the decentralized resources
bjt
Large number, not limiting feasible lot size of item j in period t

bpt
Big number indicating the maximum production quantity of PPM p in
period t
blj0
Amount of backorders for item j at the beginning of the planning interval
bljT
Amount of backorders for item j at the end of the planning interval
blcj
Backorder costs for one unit of item j in a period
blljs
Backorder costs for one unit of item j of customer class s in a period at
location l
bsj
Batch size for item j
bsp
Batch size for PPM p
cB
Buyer’s costs of the systemwide optimal solution
csys
Overall costs in the systemwide optimum
PB
cB
Buyer’s costs for the proposal out of PB with the same N B and N S as in
the systemwide optimal solution
c0
Production costs at the supplier’s site
ci
Costs associated with decisions xi
cce n;n Costs of the solution to the centralized model for test instance n
ccor;n;i Costs after i iterations of the scheme

csys . / Systemwide costs resulting from an implementation of
CS
csys
Costs for the best solution out of CS
PB
csys
Costs of an implementation of the best proposal out of PB
cunc;n Costs of the uncoordinated solution (usually determined by upstream
planning)
cam0j Initial campaign quantity for item j
cb e
Buyer’s costs change of the previous proposal e compared to the initial
solution
conoc Average ratio between backorder and overtime costs
cp
Unit penalty costs
i
cpB
Penalty costs for supplier i
cs e
Supplier’s costs change of the previous proposal e
csie
Costs of proposal e for supplier i
csel
Costs for one unit of storage capacity increase at location l
csslj Penalty costs for one unit of stock below the required safety stock of item
j at location l
k

bk1 ,bk2

b0


xviii

Nomenclature

ctaj
cvp
D
d
dj0
djt
dljst

Transportation costs for one unit of item j along arc a
Variable production costs of PPM p
Demand (random variable)
Demand per unit time
Value of the j -th dimension of Ai xist xi
Primary, gross demand for item j in period t
Primary, gross demand for item j of customer class s in period t at location l
dlbejt Deviation of proposal e that is due to lost sales and relevant for the buyer
dlsejt
Deviation of proposal e due to lost sales for the supplier
cum
ejt
Cumulated secondary demand for item j in period t
F ./
Cumulated density function

f ./
Probability density function
fmt
Randomly generated factor determining capacity profiles
g max Expected surplus of the best solution identified by the scheme
g mech Expected surplus that can be realized by the mechanism
gRP .l/ Gains of the RP from coordination subject to l
h
Unit holding cost per unit time
hB
Limit for acceptable hB
hj
Holding cost for one unit of item j in a period
hS
Holding cost of the supplier
hlj
Holding cost for one unit of item j at location l in a period
hbj
Buyer’s unit costs for inventory holding of the supplied item j
ij0
Inventory of item j at the beginning of the planning interval
P rev
ijt
Inflow of item j in period t originating from earlier production periods
i clmax Maximum storage capacity at location l
i clj
Consumption of storage capacity at location l by one unit of item j
i celmax Maximum extension of storage capacity at location l
i nilj Inventory of item j at location l at the beginning of the planning interval
K

Constant of an arbitrary value (e.g., 1) used for the correct transformation
of the unit of aj
k
Parameter for surplus sharing in the sealed bid double auction
kj0
Value of the j -th dimension of kiT
kmt
Available capacity of resource m in period t
L; LO
Lump sum payment
l; lO
Markup (above the lump sum)
L
Optimal lump sum
L1 ,L2 Prior knowledge of parties #1, #2 about the leeway in general, (upper
bounded by lj1 )
1
2
Lk ,Lk Prior knowledge of parties #1, #2 about the leeway for proposals k (upper
i

L
lk
lb

bounded by lj1 )
Lump sum required by party i
Markup for proposal k
Lower bound

Nomenclature
0

xix

lbjd
Lower bound for dj0
0
lbjk
Lower bound for kj0
lmaxljs Maximum lateness for demand fulfillment of item j of customer class s at
location l
lscj
Costs for lost sales of one unit of item j in a period
lsljs
Costs for lost sales of item j of customer class s at location l
m
Number of approximation intervals
m1 ,m2 (General) markdowns chosen by parties #1, #2
m1k ,m2k Markdowns chosen by parties #1, #2 for proposal k
Mi
Vector made up of big numbers that exceed marginal cost savings resulting
from increases in central resource use
mjt
Big number, denoting the maximum cost change per unit deviation in the
supply quantities
mfjp Material flow of item j from PPM p
minlotp Minimum lot size for item p
N B;up Number of setups in the upstream planning solution

NkB
Number of buyer’s setups in the planning interval for items k 2 SJ D \ J B
NjS
Number of supplier’s setups in the planning interval for items j 2 J D
pre
nk
Number of items preceding item k
Number of the buyer’s orders within tiS ; tiSC1
oi
Overtime costs for one unit of resource m
ocm
P
Set of decentralized parties
p
Selling price
P .Q/ Purchase price dependent on the purchase quantity Q
r
Parameter denoting the ratio between N B and N S (rounded down)
r .l/
Function that maps the expected reduction of S with l
cum
rjk
Number of units of item j required to produce one unit of the (direct or
indirect) successor item k
rjk
Number of units of item j required to produce one unit of the immediate
successor item k
S
Subset of decentralized parties
S

Systemwide surplus from coordination (random variable)
s
Selling price
s
Share of the revenue generated
sk1 ,sk2 Savings by parties #1, #2 for proposal k
Si
Marginal surplus from coordination for party i defined within the interval
ai ; b i (random variable)
sys
S
Expected surplus for the whole system (random variable)
sji
Savings of party i with proposal j
Sk
Systemwide surplus for proposal k (random variable)
sc
Setup cost
scB
Setup cost of the buyer
scj
Setup cost for a lot of item j
scS
Setup cost of the supplier


xx

Nomenclature

stj
tiB
TL
TU
tiS
C
tcB
tcSC
u
u
ub
0
ubjd
0
ubjk
ut
v
v .S /
w
w
w0j
X
f;C
xnjt

Setup time for item j
Periods in which setups of the buyer occur
Time horizon in setting L
Time horizon in setting U
Periods in which setups of the supplier occur

Reservation value of the buyer
Reservation value of the supplier
Prices for central resource use
Utility vector
Upper bound
Upper bound for dj0
Upper bound for kj0
Average capacity utilization
Salvage value
Surplus from forming set S
Target for the reduction of the number of setups for the items supplied
Wholesale price
Initial setup state of item j
Random variable denoting perturbation
ÁÁ
C
st
Node n (x-coordinate) for the linearization of f f Kjt
; XBjt xbjt
ÁÁ
f;
st
xnjt
Node n (x-coordinate) for the linearization of f f Kjt ; XBjt xbjt
ÁÁ
s;C
C
st
xnjt
Node n (x-coordinate) for the linearization of f s Kjt

; XBjt xbjt
ÁÁ
s;
st
xnjt
Node n (x-coordinate) for the linearization of f s Kjt ; XBjt xbjt
Solution previously found (in step e of the scheme)
xie
xiv
Value taken by variables xi in the vertex v identified so far
xO ; xA ; xB ; xC Breakpoints
0
xtjt
Modified target supply quantity of item j in period t
e
xtjt
Amount of item j supplied in period t in the previous proposal e
e;i
xtjt

Supply quantity of item j in period t delivered by supplier i and specified
by proposal e
max
xtaj
Maximum transportation quantity of item j along arc a in a period
mi n
xtaj
Minimum transportation quantity of item j along arc a in a period
xtjt
Target for the supply quantity of item j in period t

ysjup Number of orders for item j in the proposal from upstream planning
z
Parameter indicating the ratio between T and N B (rounded down)
Variables
ÁÁ
f;C
C
f
st
K
Weight
for
node
n
for
the
linearization
of
f
;
XB
xb
jt
njt
jt
jt
ÁÁ
f;
st
f

Kjt ; XBjt xbjt
Weight for node n for the linearization of f
njt
ÁÁ
s;C
C
st
Weight for node n for the linearization of f s Kjt
; XBjt xbjt
njt
ÁÁ
s;
s
st
K
Weight
for
node
n
for
the
linearization
of
f
;
XB
xb
jt
njt
jt

jt


Nomenclature

xxi

Decision variables defining a linear combination of previous proposals
about the central resource use of party i
BLjt Amount of backorders for item j in period t
BLljst Amount of backorders of item j of customer class s at location l in period t
p;C
Cjt
Penalties or bonuses for greater supply of item j in period t
p;
Cjt
Penalties or bonuses for less supply of item j in period t
CBd
Costs for the decisions of the buyer’s planning domain
Costs for the decisions of the supplier’s planning domain
CSd
CMLCLSP Value of the objective function of the MLCLSP
CAMjt Campaign variable for item j in period t (quantity of the current campaign
up to period t)
CAMpt Campaign variable for PPM p in period t (quantity of the current campaign up to period t)
ls
Djt
Difference in the supply quantity of item j in period t due to lost sales
B
g

Profit of the buyer
I .Q/ (Leftover) inventory
Ijt
Inventory of item j at the end of period t
Iljt
Amount of inventory of item j at location l at the end of period t
IBjt
Inventory of the (supplied) item j at the buyer’s site in period t
ICElt Increase of storage capacity at location l in period t
ISjt
Inventory of item j at the supplier’s site in period t
ki
Prices for changes in central resource use
C
Kjt
Endogenously determined unit prices for positive deviations from the startst
ing proposal xjt
of item j in period t
Kjt
Unit prices for negative deviations of item j in period t
ls
Kjt
Penalty costs for lost sales of item j in period t
ie

Kjagg;C Endogenously determined unit penalty costs for shifts of the supply of item
j to later periods compared to the starting supply pattern
Kjagg; Endogenously determined unit penalty costs for shifts of the supply of item
j to earlier periods compared to the starting supply pattern
LSjt Amount of lost sales of item j in period t

LSljst Amount of lost sales of item j of customer class s at location l in period t
M .Q/ Quantity sold to the market
Omt
Amount of overtime on resource m in period t
Q
Order quantity
QB
Optimal order quantity for the buyer
QSC Optimal order quantity for the supply chain
Rjt
Integer number of full batches produced in the current campaign of item j
up to period t
Rpt
Integer number of full batches produced in the current campaign of PPM p
up to period t
Sjt
Quantity of the last batch of item j in period t which is not finished in t
Spt
Quantity of the last batch of PPM p in period t which is not finished in t
S Sljt Undershot of safety stock of item j at location l in period t


xxii

Nomenclature

Wjt

Setup state indicator variable (=1 if item j is set up at the end of period t, 0,
otherwise)

Setup state indicator variable (=1 if PPM p is set up at the end of period
t, =0 otherwise)
Production quantity of item j at the beginning of period t (i.e., of the first
campaign in t)
Production quantity of PPM p at the beginning of period t
Production quantity of item j that is not produced at the beginning of period
t (i.e., not part of the first campaign in t)
Production quantity of PPM p that is not produced at the beginning of
period t
Decision variables in the generic LP model
Production amount of item j in period t
Amount of item j delivered to the buyer in period t
Amount of item j delivered by the supplier in period t
st
Increase in the supply of item j in period t compared to xjt
Decrease in the supply of item j in period t
Transportation quantity of item j along arc a in period t
Binary setup variable (=1 if item j is produced in period t, =0 otherwise)
Binary setup variable (=1, if PPM p is produced in period t, =0 otherwise)
Setup operation indicator for resource m in period t (=1 if a setup occurs
on resource m in period t, =0 otherwise)
Indicator variable, =1 if item j is ordered in period t, =0 otherwise
Objective function value of CS1i
Binary variable (=1 if proposal i of party j is implemented, =0 otherwise).

Wpt
b
Xjt
b
Xpt

e
Xjt
e
Xpt

xi
Xjt
XBjt
XSjt
X TjtC
X Tjt
X Tajt
Yjt
Ypt
Y Imt
Y Sjt
ZCS1i
Zij


Chapter 1

Introduction

1.1 Motivation and Goals of This Work
Supply chain planning is concerned with the determination of integrated operational
plans for all functional areas and members within a supply chain. Depending on the
organizational structure of the supply chain, this task can either be considered as the
state-of-the-art or as a challenge for future supply chain excellence.
State-of-the-art is the planning in intra-organizational supply chains. This task

is supported by a broad range of procedures elaborated in the literature during the
last decades as well as modeling tools, APS (Advanced Planning Systems), which
are widely used by practitioners.1
This, however, is not the case for inter-organizational supply chains consisting
of multiple, legally independent parties. Current APS only provide interfaces for
data exchange between parties, but do not support inter-organizational collaborative
planning. In APS, an integrated planning requires a (central) entity equipped with
all relevant data and the decision authority to implement the systemwide optimal
plan. However, this approach comes with a number of downsides: The need for disclosing potentially confidential information by the decentralized parties, the conflict
of central targets with the incentive structure in decentralized organizations, and the
missing guarantee for truthful information disclosure; indeed, very few applications
of this approach have been reported so far.2
This result stands in sharp contrast to the literature, where coordination has been
widely recognized as one of the key drivers of supply chain performance in the last
10–15 years. A large number of papers evaluating the benefits from coordination
and proposing new coordination mechanisms have been produced. Unfortunately,
these mechanisms have severe limitations making it impossible to apply them to
inter-organizational supply chain planning. Among these limitations are a complete
knowledge about the others’ model data and team behavior by the participating
parties as well as the restriction on economic order quantity or newsvendor models.
1
2

See, e.g., the case studies reported by Stadtler and Kilger (2007, p. 367).
E.g., Shirodkar and Kempf (2006, p. 420).

M. Albrecht, Supply Chain Coordination Mechanisms: New Approaches
for Collaborative Planning, Lecture Notes in Economics and Mathematical Systems 628,
DOI 10.1007/978-3-642-02833-5 1, c Springer-Verlag Berlin Heidelberg 2010

1


2

1 Introduction

In this study, we augment the existing literature by new coordination
mechanisms, which lift the major limitations as needed for a potential practical
application. These mechanisms are the first to simultaneously include several
generic features like:
The assumption of multilateral information asymmetry about other parties’
detailed data (before, during, and after the application of the mechanism)
No need for involving a third party
Self-interest of parties
Complex mathematical programming models including discrete decisions run by
the decentralized parties
In addition to a theoretical development and foundation, computational tests for
randomly generated data as well as real-world data indicate that substantial savings
can be obtained by the mechanisms proposed.

1.2 Methodology
The coordination mechanisms have to identify an improvement compared to an
initial, uncoordinated solution and to include incentives to implement the improved
solution. For that purpose, this work combines methodologies from two different
areas of economic research: Operations research and game theory.
The improvements are identified by innovative mathematical programming
models. We assume that such models are used by the parties for their decentralized
planning and develop extensions, which can be applied in an iterative manner for
the generation and identification of potentially coordinating supply proposals; the

single steps undertaken for this purpose are called a coordination scheme. The effectiveness of the schemes proposed is demonstrated by analytical and computational
results. We analytically prove the convergence of the schemes for specific model
classes, and show by computational tests that the schemes are able to substantially
mitigate the suboptimality from decentralized planning.
To determine the incentives for the decentralized parties to follow the rules of the
schemes, the mechanisms rely on concepts from the area of game theory. Strategic
(and potentially untruthful) behavior of decentralized parties is explicitly taken into
account. We build on insights and ideas from bilateral bargaining and behavioral
research to design several mechanisms that can be applied in different organizational structures. For two of these mechanisms, upper bounds for the losses due to
information asymmetry will be derived.

1.3 Outline
The thesis is organized as follows. Chapter 2 provides the basis for the mechanisms developed in this work. First, we describe the task of Master (i.e., mid-term)