Supply chain coordination mechanisms new approaches for collaborative planning

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 id

Founding Editors:

Lecture Notes in Economics

and Mathematical Systems

SpringerHeidelbergDordrechtLondon New York

Library of Congress Control Number: 2009931327

c

 Springer-Verlag Berlin Heidelberg 2010

This work is subject to copyright All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks Duplication of this publication

or parts thereof is permitted only under the provisions of the German Copyright Law of September 9,

1965, in its current version, and permission for use must always be obtained from Springer Violations are liable to prosecution under the German Copyright Law.

The use of general descriptive names, registered names, trademarks, etc in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use.

Cover design: SPi Publisher Services

Printed on acid-free paper

Springer is part of Springer Science+Business Media (www.springer.com)

For Rita and Amalia Isabel

Inter-organizational supply chains have to coordinate their material, information,and financial flows efficiently to be competitive However, legally independent sup-ply chain (SC) partners are often reluctant to share critical data such as costs orcapacity utilization, which is a prerequisite for central planning or hierarchicalplanning – the planning paradigm of today’s Advanced Planning Systems (APS).Consequently, concepts for collaborative planning are needed, considering a jointdecision 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 Albrechtbecause little is known about how to design a solution for this difficult decisionproblem Starting from an initial solution – that may be generated by upstream plan-ning – improved solutions are looked for This is achieved by computer-supportednegotiations, i.e., an exchange of different order proposals within the planning in-terval among the SC partners involved, where partners are free to accept or rejectproposals

One challenge in this negotiation process is to find new proposals and proposals which have a good chance of acceptance while improving the competitiveposition of a SC as a whole Here, Albrecht devised new generic coordinationschemes for planning tasks which can be modeled either by Linear Programming(LP) or Mixed Integer Linear Programming For the LP case finite convergence tothe optimum has been proved

counter-While previous research on collaborative planning stopped with a clever ordination scheme Albrecht also considered a further, very important aspect ofnegotiations: How to get the partners to tell the truth when exchanging informationand to accept a very promising solution for the supply chain as a whole Formallyspeaking, coordination mechanisms are needed where the coordination schemes can

co-be emco-bedded One of the coordination mechanisms advocated by Albrecht is thesurplus sharing by an initially agreed upon lump sum payment to one party He hasbeen able to show that the corresponding mechanism results in truth-telling as aweakly dominant strategy The reader can expect both analytical results as well ascomputational tests of collaborative planning schemes for various lot-sizing prob-lems 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 excellentthesis a wide audience of interested and very satisfied readers and a large impact oncollaborative planning

informa-I have developed mechanisms, which achieve coordination despite self-interestedbehavior of parties Without wanting to relativize the importance of this contribu-tion, I would like to point out the existence of a particular real-world team: Thepeople supporting me when I was writing this thesis.

First of all, I am indebted to Prof Dr Hartmut Stadtler He not only set the ple for my research, but also provided (sometimes incredibly) generous advice andprofessional and personal support Among many other things, he has patiently read

exam-my papers many times and supplied several insightful suggestions at all stages ofthis 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 orating researchers Particularly, I want to thank Carolin P¨uttmann for her greatteamwork in the EU-project InCoCo-S, for listening to many of my (not always fullyworked out) ideas, and for carefully proofreading the whole dissertation Dr BerndWagner and Volker Windeck also read parts of the thesis and provided many valu-able suggestions Last, but not least, I am thankful to Prof Dr Heinrich Braun andBenedikt Scheckenbach from the SAP AG for challenging discussions and for mak-ing available the real-world test data used in this work

collab-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 notinterested in supply chain management at all My parents supported my education,without expecting anything in return My wife Rita not only renounced to muchshared time, but encouraged me with all her love to keep on researching until I have(finally) been satisfied with this work

Thank you, everybody

ix

Abbreviations xiii

Nomenclature xv

1 Introduction 1

1.1 Motivation and Goals of This Work 1

1.2 Methodology 2

1.3 Outline 2

2 Supply Chain Planning and Coordination 5

2.1 Supply Chain Planning 5

2.1.1 Definitions and Overview 5

2.1.2 Master Planning 8

2.2 Model Formulations for Master Planning 9

2.2.1 Generic Master Planning Model 10

2.2.2 Extension to Lot-Sizing 12

2.3 Decentralized Planning and Coordination 20

2.3.1 Basic Definitions 20

2.3.2 Decentralized Supply Chain Planning 24

2.3.3 Upstream Vs Collaborative Planning 30

3 Coordination Mechanisms for Supply Chain Planning 35

3.1 Symmetric Information 35

3.1.1 Non-cooperative Game Theory 36

3.1.2 Cooperative Game Theory 41

3.2 One-Sided Information Asymmetry 43

3.2.1 Signaling 43

3.2.2 Screening 45

3.3 Multilateral Information Asymmetry 48

3.3.1 Auctions and Their Application to Supply Chain Coordination 48 3.3.2 Mechanisms with Focus on Proposal Generation 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

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

CLSP Capacitated lot-sizing problem

CLSPL Capacitated lot-sizing problem with linked lot sizes

CSLP Continuous setup lot-sizing problem

DLSP Discrete lot-sizing and scheduling problem

GLSP General lot-sizing and scheduling problem

GS Gap after the application of the scheme

IGFR Increasing generalized failure rate

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

xiii

SOS2 Special ordered set of type 2

TC Time for solving the centralized model

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

iE Set of cost changes associated with proposals for central resource use

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

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

JS Set of items produced by the supplier

Jm Set of items produced on resource m

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

PB Set of supply proposals optimal for the buyer subject to anyN B

Rj Set of predecessor items of item j

S Set of customer classes

Sj Set of immediate successors of item j in the BOM

st Superindex indicating the starting solution

Xis Subset of feasible solutions to CS1i

XiE Set of proposals found so far

Xivd Subset of vertex solutions to DPi

Xiv Set of vertex solutions identified so far

Parameters and Random Variables

tB

i Periods between subsequent setups of the buyer

tS

i Periods between subsequent setups of the supplier

 Unit penalty costs for arbitrary deviations

O; A; B; C Weights

i e Scalars

i e Scalars

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

PB Proposal out of PB with the same NB and NS as in the systemwideoptimal solution

ie Proposal e for the central resource use by party i

ij Resource use for the j th proposal generated by party i

 p Production lead time of PPM p

 aj Transportation lead time for item j along arc a

j Lead time for item j

hB Lower bound for the probability distribution of hB

b

blcj Maximum costs for backorders that are caused by a shortage in the supply

or the production of item j

e

blcj Potential cost impact of backorders in the supply of item j

e

i Cost effects of the proposal e by party i

a; b Lower and upper bounds for S

Nomenclature xvii

Ai Use of the central resources by decisions xi

amj Capacity needed on resource m for one unit of item j

amp Capacity needed on resource m for one unit of PPM p

Bk1,Bk2 Prior knowledge of parties #1, #2 about the other party’s bids for proposals

k (upper bounded by bj1,bj2)

b1k,b2k Bids by parties #1, #2 for proposal k

b0 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 inperiod t

bl0

j 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 atlocation 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

cBPB Buyer’s costs for the proposal out of PB with the same NB and NS as inthe 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 

csysCS Costs for the best solution out of CS

csysPB Costs of an implementation of the best proposal out ofPB

planning)

cam0j Initial campaign quantity for item j

cbe Buyer’s costs change of the previous proposal e compared to the initialsolution

conoc Average ratio between backorder and overtime costs

cp Unit penalty costs

cpiB Penalty costs for supplier i

cse Supplier’s costs change of the previous proposal e

csei 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

xviii Nomenclature

ctaj Transportation costs for one unit of item j along arc a

cvp Variable production costs of PPM p

dj0 Value of the j -th dimension of Ai

xsti  xi

djt Primary, gross demand for item j in period t

dljst Primary, gross demand for item j of customer class s in period t at tion l

loca-dlbe

jt Deviation of proposal e that is due to lost sales and relevant for the buyer

dlse

jt Deviation of proposal e due to lost sales for the supplier

ejtcum Cumulated secondary demand for item j in period t

F / Cumulated density function

f / Probability density function

fmt Randomly generated factor determining capacity profiles

gmax Expected surplus of the best solution identified by the scheme

gmech 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

i0

j Inventory of item j at the beginning of the planning interval

ijtP rev 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 cemax

l 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 kTi

kmt Available capacity of resource m in period t

L; OL Lump sum payment

l; Ol Markup (above the lump sum)

L1,L2 Prior knowledge of parties #1, #2 about the leeway in general, (upperbounded by lj1)

L1k,L2k Prior knowledge of parties #1, #2 about the leeway for proposals k(upperbounded by lj1)

Li Lump sum required by party i

lk Markup for proposal k

Nomenclature xix

lbdj0 Lower bound for dj0

lbkj0 Lower bound for k0j

lmaxljs Maximum lateness for demand fulfillment of item j of customer class s atlocation 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

m1

k,m2k Markdowns chosen by parties #1, #2 for proposal k

Mi Vector made up of big numbers that exceed marginal cost savings resultingfrom increases in central resource use

mjt Big number, denoting the maximum cost change per unit deviation in thesupply quantities

mfjp Material flow of item j from PPM p

minlotp Minimum lot size for item p

NB;up Number of setups in the upstream planning solution

NkB Number of buyer’s setups in the planning interval for items k 2 SJD\ JB

NjS Number of supplier’s setups in the planning interval for items j 2 JD

nprek Number of items preceding item k

oi Number of the buyer’s orders within

tS

i ; tS iC1



ocm Overtime costs for one unit of resource m

P Set of decentralized parties

P Q/ Purchase price dependent on the purchase quantity Q

r Parameter denoting the ratio between NBand NS (rounded down)

r l/ Function that maps the expected reduction of S with l

rj kcum Number of units of item j required to produce one unit of the (direct orindirect) successor item k

rj k Number of units of item j required to produce one unit of the immediatesuccessor item k

S Subset of decentralized parties

S Systemwide surplus from coordination (random variable)

s Share of the revenue generated

sk1,s2k Savings by parties #1, #2 for proposal k

Si Marginal surplus from coordination for party i defined within the interval

ai; bi

(random variable)

Ssys Expected surplus for the whole system (random variable)

sji Savings of party i with proposal j

Sk Systemwide surplus for proposal k (random variable)

scB Setup cost of the buyer

scj Setup cost for a lot of item j

scS Setup cost of the supplier

xx Nomenclature

stj Setup time for item j

tiB Periods in which setups of the buyer occur

TL Time horizon in setting L

TU Time horizon in setting U

tiS Periods in which setups of the supplier occur

t cCB Reservation value of the buyer

t cCS Reservation value of the supplier

u Prices for central resource use

j Upper bound for kj0

ut Average capacity utilization

v S/ Surplus from forming set S

w Target for the reduction of the number of setups for the items supplied

w0

j Initial setup state of item j

X Random variable denoting perturbation

xnjtf;C Node n (x-coordinate) for the linearization of ff

xie Solution previously found (in step e of the scheme)

xiv Value taken by variables xiin the vertexv identified so far

xO; xA; xB; xC Breakpoints

xtjt0 Modified target supply quantity of item j in period t

xte

jt Amount of item j supplied in period t in the previous proposal e

xtjte;i Supply quantity of item j in period t delivered by supplier i and specified

by proposal e

xtajmax Maximum transportation quantity of item j along arc a in a period

xtajmi n 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 NB(rounded down)

Nomenclature xxi

i e Decision variables defining a linear combination of previous proposalsabout 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

Cjtp;C Penalties or bonuses for greater supply of item j in period t

Cjtp; Penalties or bonuses for less supply of item j in period t

Cd

B Costs for the decisions of the buyer’s planning domain

Cd

S Costs for the decisions of the supplier’s planning domain

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 paign up to period t )

cam-Djtls Difference in the supply quantity of item j in period t due to lost sales

gB 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

I CElt Increase of storage capacity at location l in period t

I Sjt Inventory of item j at the supplier’s site in period t

ki Prices for changes in central resource use

KjtC Endogenously determined unit prices for positive deviations from the ing proposal xjtst of item j in period t

start-Kjt Unit prices for negative deviations of item j in period t

Kjtls Penalty costs for lost sales of item j in period t

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

QB Optimal order quantity for the buyer

QS C 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

jt 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 )

Xe

pt Production quantity of PPM p that is not produced at the beginning ofperiod t

xi Decision variables in the generic LP model

Xjt Production amount of item j in period t

XBjt Amount of item j delivered to the buyer in period t

XSjt Amount of item j delivered by the supplier in period t

X TjtC Increase in the supply of item j in period t compared to xjtst

X Tjt Decrease in the supply of item j in period t

X Tajt Transportation quantity of item j along arc a in period t

Yjt Binary setup variable (=1 if item j is produced in period t , =0 otherwise)

Ypt Binary setup variable (=1, if PPM p is produced in period t , =0 otherwise)

Y Imt Setup operation indicator for resource m in period t (=1 if a setup occurs

on resource m in period t , =0 otherwise)

Y Sjt Indicator variable, =1 if item j is ordered in period t , =0 otherwise

ZCS1i Objective function value of CS1i

Zij Binary variable (=1 if proposal i of party j is implemented, =0 otherwise)

Chapter 1

Introduction

1.1 Motivation and Goals of This Work

Supply chain planning is concerned with the determination of integrated operationalplans for all functional areas and members within a supply chain Depending on theorganizational structure of the supply chain, this task can either be considered as thestate-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 thelast decades as well as modeling tools, APS (Advanced Planning Systems), whichare 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 fordata exchange between parties, but do not support inter-organizational collaborativeplanning In APS, an integrated planning requires a (central) entity equipped withall relevant data and the decision authority to implement the systemwide optimalplan However, this approach comes with a number of downsides: The need for dis-closing potentially confidential information by the decentralized parties, the conflict

of central targets with the incentive structure in decentralized organizations, and themissing 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 beenwidely recognized as one of the key drivers of supply chain performance in the last10–15 years A large number of papers evaluating the benefits from coordinationand proposing new coordination mechanisms have been produced Unfortunately,these mechanisms have severe limitations making it impossible to apply them tointer-organizational supply chain planning Among these limitations are a completeknowledge about the others’ model data and team behavior by the participatingparties as well as the restriction on economic order quantity or newsvendor models

1 See, e.g., the case studies reported by Stadtler and Kilger ( 2007 , p 367).

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 severalgeneric 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

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 programmingmodels We assume that such models are used by the parties for their decentralizedplanning and develop extensions, which can be applied in an iterative manner forthe generation and identification of potentially coordinating supply proposals; the

single steps undertaken for this purpose are called a coordination scheme The

effec-tiveness of the schemes proposed is demonstrated by analytical and computationalresults We analytically prove the convergence of the schemes for specific modelclasses, and show by computational tests that the schemes are able to substantiallymitigate the suboptimality from decentralized planning

To determine the incentives for the decentralized parties to follow the rules of theschemes, the mechanisms rely on concepts from the area of game theory Strategic(and potentially untruthful) behavior of decentralized parties is explicitly taken intoaccount We build on insights and ideas from bilateral bargaining and behavioralresearch to design several mechanisms that can be applied in different organiza-tional structures For two of these mechanisms, upper bounds for the losses due toinformation asymmetry will be derived

1.3 Outline

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

mecha-1.3 Outline 3

Planning and corresponding mathematical model formulations Second, we definebasic terms used in this work and discuss the consequences of decentralized plan-ning We show how the resulting planning processes can be modeled mathematicallyand identify drivers for the systemwide suboptimality of unilateral targets, whichare established without coordination Finally, we outline upstream planning, which

we assume as the standard planning procedure without coordination, as well as ourconcept for collaborative planning

Chapter3surveys the literature on coordination mechanisms We have structuredthis review according to the assumptions on the knowledge about the other parties’data, i.e., we distinguish between symmetric, one-sided asymmetric, and multilat-eral asymmetric information Moreover, we elaborate the basic ideas regarding thedesign of the related mechanisms and provide classifications for the literature ofthis area

Chapters4and5comprise the core contributions of this work In Chap.4, the ferent coordination schemes are outlined We begin with two versions of a genericscheme for coordinating decentralized parties running arbitrary linear program-ming models (in one version, even one of the parties may run a mixed-integerprogramming model) Moreover, we present a scheme for coordinating uncapaci-tated lot-sizing models in supply chains of one buyer and one or multiple suppliers.For both schemes, analytical results about their convergence behavior can be de-rived Apart from that, for a two-party supply chain, we present modified versions

dif-of these schemes with improved convergence rate and improved applicability forMaster Planning problems that include discrete decisions Amongst others, we coverextensions of these modified versions to voluntary compliance by the supplier, themodeling of lot-sizing and lost sales, and settings with multiple suppliers

As a second component of the coordination mechanisms, several contractualframeworks are outlined and analyzed in Chap.5 Resulting are mechanisms ap-plicable for different organizational structures and different distributions of thebargaining power between the decentralized parties The strategies adopted by thedecentralized parties using these mechanisms are discussed in light of behavioraltheories and analytical reasoning As a third issue in the chapter, we outline howthe mechanisms can be adapted for rolling schedules, which are frequently used inreal-world production planning

Computational tests are provided in Chap.6 We examine the performance of theschemes based on randomly generated test instances for different Master Planningmodels as well as for real-world Master Planning data provided by the SAP AG Forall problems investigated, significant improvements compared to upstream planningcan be identified after a modest number of iterations

Finally, Chap.7summarizes the contributions of this work and outlines nities for further research

opportu-Chapter 2

Supply Chain Planning and Coordination

The aim of this chapter is to familiarize the reader with the topic of this work,

how to coordinate mid-term planning in decentralized supply chains, i.e., supply

chains that comprise several independent, legally separated parties with their

own decision authorities We start with a description of planning in centralized

supply chains (Sect.2.1), where the decision authority and the knowledge of allrelevant planning data is hold by a single party In Sect.2.2we provide centralizedmathematical model formulations for mid-term supply chain planning (Master Plan-ning) Section2.3deals with supply chain planning in decentralized environments

We describe the differences in the planning processes compared to centralized ning, provide reasons for the potential suboptimality of decentralized planning andintroduce coordination and, more specifically, collaborative planning as approaches

plan-to mitigate this suboptimality

2.1 Supply Chain Planning

2.1.1 Definitions and Overview

We begin with an abstract and often cited definition of a supply chain: A supplychain is a “ network of organizations that are involved, through upstream anddownstream linkages, in the different processes and activities that produce value

in the form of products and services in the hands of the ultimate consumer.”1 As

an illustration, we depict in Fig.2.1a supply chain consisting of a set of vendors,plants, distribution centers, and customers that are linked by material flows.2

From a business economics perspective, supply chains require supply chainmanagement, that can be defined as “the task of integrating organizational unitsalong a supply chain and coordinating material, information and financial flows

in order to fulfill (ultimate) customer demands with the aim of improving the

1 Christopher ( 2005 , p 17).

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 2, c  Springer-Verlag Berlin Heidelberg 2010

5

6 2 Supply Chain Planning and Coordination

Fig 2.1 Sketch of a supply chain (example)

competitiveness of a supply chain as a whole.”3One of the building blocks of supplychain management is (advanced) supply chain planning.4The aim of supply chainplanning is to determine an integrated plan for the whole supply chain; referring toFig.2.1, such a plan comprises appropriate quantities of the raw materials procured,

of the products manufactured in the plants, of the products distributed, and of theproducts sold to the customers

Of course, this is a very complex task especially for real-world organizations,which may comprise a large number of facilities, customers, and products There-fore, it has been proposed in the literature5to organize (production) planning in a

hierarchical way.6The basic idea of hierarchical planning is the separation of cisions according to their impact, e.g., on the profitability of the supply chain Thedecisions at the upper levels, i.e., those with greater impact, are determined firstand implemented as targets for the planning of the lower levels Further importantcharacteristics are the aggregation of data and decisions at the upper levels and theprovision of feedback by the lower levels.7

de-A common representation for the individual tasks of supply chain planning

is the Supply Chain Planning Matrix (see Fig.2.2).8 Frequently, these planningtasks are supported by software tools in practice As a standard software, Ad-vanced Planning Systems (APS) have been developed by different companies (e.g.,SAP, Oracle9) Each APS contains several modules that cover in part the plan-ning tasks stated in Fig.2.2 The Advanced Planning Matrix provides an overview

of these modules (see Fig.2.3).10 Long-term planning is the object of Strategic

8 See Fleischmann et al ( 2007 , p 102).

below).

2.1 Supply Chain Planning 7

• lot-sizing

• machine scheduling

• shop floor control

salesdistribution

productionprocurement

• product programme

• strategic sales planning

• capacity planning

flow of goods

• distribution planning

• warehouse replenishment

• transport planning

• mid-term sales planning

• short-term sales planning

information flows

Fig 2.2 Supply Chain Planning Matrix

Production Planning

Distribution Planning

Demand Planning Purchasing

&

Material Requirements

Planning

Demand Fulfillment

production procurement

Fig 2.3 Advanced Planning Matrix

Network Design, whereas the mid-term planning tasks are covered by Purchasing &Material Requirements Planning, Master Planning, Production Planning, Distribu-tion Planning, and Demand Planning Analogously, the short-term planning tasksare tackled by Purchasing & Material Requirements Planning, Production Plan-ning, Scheduling, Transport Planning, Demand Fulfillment & Available-To-Promise(ATP) Note that Fig.2.3differs from the original Advanced Planning Matrix by the

8 2 Supply Chain Planning and Coordination

overlap of Master Planning into sales (see the shadowed area in Fig.2.3) In ouropinion, this is more concise than the original representation since Master Planningfrequently involves sales-related decisions like backorders and lost sales.11

In the following, we will provide a more detailed description of Master Planning,which is the main focus of this work For an in-depth explanation of the othermodules, we refer to the textbook ofStadtler and Kilger(2007).12

2.1.2 Master Planning

Master Planning means mid-term operational decision-making carried outsimultaneously for all functional areas participating in the order fulfillment process:Procurement, production, distribution, and sales In this work, we focus on thisplanning level since the potential financial impact for collaborating enterprises islargest here

Master Planning is based on monthly or weekly time buckets; hence, planninghorizons of, e.g., 12, 24, or 52 periods are used It is important that the planninghorizon is chosen such large that effects due to seasonal demand are considered.This requires that the planning interval comprises one seasonal cycle at least.Table2.1provides an overview about the basic decisions made within MasterPlanning Most of these decisions are likewise mentioned in other descriptions ofMaster Planning.13 A somewhat ambiguous role in this context plays lot-sizing,

Table 2.1 Basic decisions of Master Planning

Resource utilization Inventory levels Utilization of overtime Lot-sizing

Inventory levels

(including backorders and lost sales)

11 See also Sect 2.1.2 The importance of (lost) sales for integrated mid-term planning is further supported by the practitioner-oriented literature, where mid-term planning models with the aim of

12 See Stadtler and Kilger ( 2007 , p 117).

13 See Rohde and Wagner ( 2007 , p 160) and G¨unther ( 2006 , p 20).

2.2 Model Formulations for Master Planning 9

which is often regarded as a short-term planning task in the literature.14 Indeed,lot-sizing is not an issue for mid-term planning in many industries.15 A notewor-thy exception, however, are process industries, where lot-sizing decisions have asubstantial impact on the quality of the resulting plans Due to large setup timesand expensive setup activities, practical mid-term planning model formulationsoriginating from this area usually include lot-sizing.16

The results of these decisions (e.g., the planned amount of stock or the planneduse of overtime17) constitute targets for the lower-level modules Purchasing &Material Requirements Planning, Production Planning, and Distribution Planning.Note that, according to the principles of hierarchical planning, the correspondingdata has to be disaggregated for this purpose

The input data for Master Planning is deterministic Real-world data, especiallydemand forecasts, however, always comprise some uncertainty Because of that,mid-term planning models incorporating stochastic data have been elaborated inthe literature.18In practice, however, stochastic decision models are rarely used for

mid-term planning Instead, planning is done based on rolling schedules.19 Thismeans that only the first periods of plans (i.e., the periods before the frozen horizon)are implemented; the rest is determined later by re-planning, which is undertakenperiodically (e.g., once a month) This approach provides the flexibility to react withplan changes if uncertainty is revealed in future periods

2.2 Model Formulations for Master Planning

In this section, we present mathematical model formulations for Master Planningthat are used throughout this work (among others, for the computational verifica-tion of the coordination schemes proposed) First of all, we provide a generic linearprogramming (LP) model in Sect.2.2.1 Compared to mixed-integer programming(MIP) or nonlinear programming (NLP), the mathematical structure of LP is muchsimpler, which makes approaches based on LP particularly suited for structuralanalyses However, results valid for LP do not necessarily extend to other modelclasses.20 These classes include MIP models, which are required for modeling

14 As an example, see the Supply Chain Planning Matrix on p 7 of this work.

which yields the optimal solution to, e.g., MIP models only in case of the total unimodularity of

the simplex algorithm and of solution procedures for MIP models such as branch and bound, see,

10 2 Supply Chain Planning and Coordination

lot-sizing decisions at the Master Planning level Therefore, we additionally providemodel formulations accounting for lot-sizing in Sect.2.2.2.21

2.2.1 Generic Master Planning Model

Before presenting the mathematical formulation of the generic Master Planningmodel (GM), we state its underlying assumptions:

 Several items are arranged in a general bill of material (BOM) and produced onone or more specific resources Production results in variable capacity loads

 The capacities of the resources are finite and can be extended by costly, infinitelyavailable overtime

 Demand is dynamic and deterministic for all items

 Unfulfilled demand can either be backlogged or lost; both actions incur additionalcosts

 Inventory holding of items is possible and results in holding costs

j 2J

Xt2T

hjIjtC X

m2M

Xt2T

ocmOmtC X

j 2J E

Xt2T

2.2 Model Formulations for Master Planning 11

Indices and Index Sets

j Items or operations (e.g., end products, intermediate products, raw

materials), j 2 J ; JEis the subset of (end) items sold to external customers

m Resources (e.g., personnel, machines, production lines), m 2 M

t Periods, t 2 T , with T D 1; : : : ;jT j

Sj Set of immediate successors of item j in the BOM

Data

amj Capacity needed on resource m for one unit of item j

blcj Backorder costs for one unit of item j in a period

bl0j 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

djt Primary, gross demand for item j in period t

ij0 Inventory of item j at the beginning of the planning interval

hj Holding costs for one unit of item j in a period

kmt Available capacity of resource m in period t

lscj Costs for lost sales of one unit of item j in a period

ocm Overtime costs for one unit of resource m

rjk Number of units of item j required to produce one unit of the

immediate successor item k

Variables

BL jtAmount of backorders for item j in period t

Ijt Inventory of item j at the end of period t

LS jt Amount of lost sales of item j in period t

Omt Amount of overtime on resource m in period t

Xjt Production amount of item j in period t

The objective function minimizes the costs for inventory holding, overtime,backorders, and lost sales Constraints (2.1) determine the quantities of the externaldemand that are backlogged and lost Constraints (2.2) ensure the fulfillment ofthe secondary demand.22Constraints (2.3) limit the capacity used for production tothe sum of normal capacity and overtime Constraints (2.4)–(2.6) fix the amounts

of backorders and inventories at the borders of the planning interval.23 Finally,(2.7)–(2.11) determine the nonnegativity of the decision variables

Note that due to its generic character, this model formulation does not coverall decisions potentially relevant for Master Planning.24For lot-sizing, we refer to

22 For ease of exposition, we have separated items into two groups: End items with external demand (J E ) and intermediate items used for production (J nJ E ) In a setting where an item is used for production and has external demand, this model formulation would have to be adapted accordingly.

23 This fixation seems the most straightforward possibility for the modeling of backorders Note that when planning is based on rolling schedules, the modeling of maximum latenesses may be more adequate.

24 I.e., those listed in Table 2.1 (see p 8 ).

12 2 Supply Chain Planning and Coordination

the following subsection Moreover, an exemplary modeling of storage capacitiesand transportation is included in the model for the real-world planning problemspresented in Sect.6.5

2.2.2 Extension to Lot-Sizing

A broad variety of models incorporating lot-sizing decisions has been proposed inthe literature We begin with some basic formulations and discuss how to integratethem into Master Planning Built on this, we present a Master Planning model that

is extended to production campaigns Campaign planning is a variant of lot-sizingwith practical relevance for process industries and additional difficulties for supplychain coordination,25which makes this extension particularly suited for examiningthe performance of the coordination schemes proposed in this work

2.2.2.1 Basic Models

One of the first production planning problems analyzed in the literature is thedetermination of the economic order quantity (EOQ),26 i.e., the optimal orderquantity of an item based on a number of restrictive assumptions The mostimportant assumptions are:27

 One single item is considered

 Demand is deterministic and constant

 The replenishment lead time is zero

 Inventory holding is possible and results in holding costs

 Each replenishment requires fixed ordering costs

Then the total relevant costs per unit time can be expressed by

c Q/D sc d

Q C hQ

2 :

Data

d Demand per unit time

h Unit holding cost per unit time

sc Cost for one replenishment order (D setup cost)

Variables

Q Order quantity

25 See Example 2.6 as an illustration of this issue.

26 See Harris ( 1913 , p 135).

2.2 Model Formulations for Master Planning 13

c Q/ is a convex function It takes its minimum with the EOQ QDp

2sc d= h

Due to the restrictive assumptions, direct applications of this model are rather rare

in practice.28In spite of that, this model has proved useful as a basis for analyzinglot-sizing decisions in broader contexts, which include the potential cost impact ofdeviations of lot sizes from the EOQ29and supply chain coordination mechanisms.30

The term lot-sizing also means the determination of optimal order quantities,

but – in contrast to the EOQ – without the limitation to constant demand.31The mostbasic lot-sizing model is the uncapacitated dynamic single-item lot-sizing modeldeveloped byWagner and Within(1958).32Since the applicability of this model isagain rather limited, we state a more relevant extension to several items and sev-eral levels of the BOM, the MLULSP (D Multi-Level Uncapacitated Lot-SizingProblem).33

j 2J

Xt2T

hjIjtCX

j 2J

Xt2T

scjYjt (2.12)

s.t (2.2), (2.6), (2.8), (2.11)(MLULSP) Ijt1C Xjt D djtC Ijt 8j 2 JE

hj Holding cost for one unit of item j in a period

scj Setup cost for a lot of item j

Variables

Yjt Binary setup variable (D 1, if item j is produced in period t , D 0 otherwise)The objective function (2.12) minimizes the sum of inventory holding and setupcosts Constraints (2.2), (2.6), (2.8), and (2.11) are taken from GM Constraints(2.13) ensure together with (2.2) the fulfillment of external and secondary demand,respectively Setup constraints (2.14) enforce variables Yjtto 1 if a lot of item j isproduced in period t Constraints (2.15) define variables Yjtas binary

28 Note that this only holds for this model in its pure form presented above For some extensions (e.g., to a multi-level BOM), real-world applications have been reported, see, e.g., Muckstadt and Roundy ( 1993 , p 61) for an automotive manufacturer and Stadtler ( 1992 , p 217) for a light alloy foundry.

differ from each other in case of dynamic demand.

32 See Wagner and Within ( 1958 , p 89).

14 2 Supply Chain Planning and Coordination

Combining the MLULSP and GM, we obtain a Multi-Level CapacitatedLot-Sizing Problem (MLCLSP) with backorders and lost sales as a generic MasterPlanning model that includes decisions related to lot-sizing This model differs fromthe original MLCLSP developed byBillington et al.(1983)34 by the negligence ofpenalties for undertime and by the inclusion of backorders and lost sales

j 2J

Xt2T

hjIjtCX

j 2J

Xt2T

scjYjtC

m2M

Xt2T

ocmOmtC X

j2J E

Xt2T

blcjBL jtC X

j 2J E

Xt2T

lscjLS jt

s.t (2.1)–(2.11), (2.14), (2.15):

Variables

CMLCLSPValue of the objective function of the MLCLSP

2.2.2.2 Extension to Campaign Planning

Campaign planning is a variant of lot-sizing, which raises additional challenges for

an efficient mathematical modeling and is of great importance in process tries.35Analogously to a production lot, a campaign means the production of severalunits of items without performing any additional setup operation.36 The sizes ofthese units usually cannot be chosen continuously; due to technical restrictions, e.g.,

indus-fixed tank or reaction volumes, whole batches, i.e., prespecified amounts of items,

have to be produced Hence, a campaign length corresponds to an integer number

of batch sizes.37

For the modeling of campaign planning, the MLCLSP has to be altered in two spects First, of course, we have to assure that only complete batches are produced.Second, the MLCLSP contains a representation defect, which affects the applica-bility of this model for campaign planning The MLCLSP comprises the restrictiveassumption that, whenever an item is produced in a period, a setup has to be per-formed for this item The setup is required irrespectively whether the resource hasalready been set up for this item at the end of the preceding period, i.e., the setupstate could have been preserved This representation defect can affect the optimality

re-of the resulting production plans in general.38For campaign planning, this effect issignificantly aggravated, particularly if the production of a single batch requires aconsiderable share of the available capacity

34 See Billington et al ( 1983 , p 6).

2.2 Model Formulations for Master Planning 15

Table 2.2 Comparison of lot-sizing models with the preservation of setup states

In the literature, several model formulations have been developed that overcomethe above mentioned representation defect by allowing lot sizes that overlap periodboundaries.39 These models differ by their scope and their computational com-plexity Table 2.2provides a comparison of five basic models with this property,the DLSP (Discrete Lot-sizing and Scheduling Problem),40the CSLP (ContinuousSetup Lot-sizing Problem),41 the PLSP (Proportional Lot-sizing and SchedulingProblem),42 the GLSP (General Lot-sizing and Scheduling Problem),43 and theCLSPL (Capacitated Lot-Sizing Problem with Linked lot sizes).44

The scopes of these models differ by the maximum number of items that can beproduced per time period45and by the question whether sequence-dependent setupscan be modeled.46We choose the CLSPL as the basis for evaluating the coordinationschemes proposed The main reason for this is that the CLSPL allows the production

of an arbitrary number of items per period In anticipation to Sect.2.3, we want topoint out that coordination becomes most relevant if several items are ordered and

if decentralized parties have little leeway for adapting their production plans (e.g.,due to tight capacities and elevated costs for shortages) In such situation, partieswould hardly confine themselves to models which artificially restrict the production

to one or two items per period Potential modest increases in inventory holding andsetup costs with the CLSPL are of secondary relevance then Such increases may

be caused by the greater computational complexity of the CLSPL, which usuallyresults in larger optimality gaps compared to the DLSP, CSLP, and PLSP, providedthat a limit on the solution time is applied.47 Sequence-dependent setups, in turn,

39 For comprehensive surveys of these models see, e.g., Drexl and Kimms ( 1997 , p 221) and Jans and Degraeve ( 2008 , p 1619).

40 See Fleischmann ( 1990 , p 338).

41 See Karmarkar and Schrage ( 1985 , p 328).

42 See Drexl and Haase ( 1995 , p 75).

43 See Fleischmann and Meyr ( 1997 , p 12).

44 See Dillenberger et al ( 1993 , p 112) More recently, this model has been investigated by Gopalakrishnan et al ( 2001 , p 851) and Suerie and Stadtler ( 2003 , p 1039).

to capture the difference between the DLSP and the CSLP, which is the all-or-nothing condition required by the DLSP and relaxed in the CSLP.

47 See Suerie ( 2005c , p 164) for computational results for campaign planning models based on the PLSP and the CLSPL Regarding the best solutions found, however, the CLSPL can outperform

16 2 Supply Chain Planning and Coordination

are usually not included at the Master Planning level;48 hence, there is no need for

a computationally more demanding model like the GLSP that additionally coversthis issue

Concerning the restrictions on feasible campaigns, we limit here to single-itemcampaigns with fixed batch sizes.49 For sake of simplicity, we neither includeminimum campaign lengths50nor batch availability.51

Further discussion deserves the modeling of lead times in the multi-level version

of the CLSPL considered here Lead times of zero, which have implicitly been sumed for the MLCLSP, may cause infeasibility of solutions obtained by multi-levellot-sizing models with the preservation of the setup states Such infeasibility mayarise if a successor item is not produced at the end of a period (i.e., its setup state isnot carried over into the next period) and one of its predecessor items is produced

as-at the end of the same period (i.e., its setup stas-ate is carried over into the next riod) With insufficient inventories of the predecessor item at the beginning of theperiod, the secondary demand of the successor item might not be fulfilled in time.52

pe-In order to exclude the generation of infeasible solutions, we choose in analogy to

Kimms(1996)53lead times equal to or greater than one period length for diate items.54

interme-Below we present the adaptation of the MLCLSP to the preservation of setupstates and campaign restrictions This model extends the single-level formulationproposed bySuerie(2005b)55to a multi-level BOM structure

min CMLCLSP(MLCLSPL-C) s.t (2.4)–(2.11), (2.15)

hence, does not apply to the MLCLSP.

of zero lead times For multi-machine problems (like the problem considered here), however, we are not aware of any corresponding practicable formulation.

55 Suerie ( 2005b , p 102).

2.2 Model Formulations for Master Planning 17

; t D j C 1; : : : ; jT j (2.18)X

stjYjt  kmt C Omt 8m 2 M; t 2 T (2.19)

Xjtb  bjtWjt1 8j 2 J; t 2 T (2.21)

Wjt YjtC Wjt1 8j 2 J; t 2 T n fjT jg (2.22)X