Resource allocation problems in supply chains

RA variant in bi-objective capacitated SC network, RA variant in bi-objective bound driven capacitated SC network, RA variant in multiple measures driven capacitated multi echelon SC net

Supply Chains

Problems in Supply Chains

National Institute of Technology, Tiruchirappalli, India

United Kingdom North America Japan

India Malaysia China

First edition 2015

Copyright r 2015 Emerald Group Publishing Limited

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British Library Cataloguing in Publication Data

A catalogue record for this book is available from the British Library ISBN: 978-1-78560-399-0

Resource Allocation (RA) involves the distribution and

utiliza-tion of available resources in the system Because resourceavailability is usually scarce and expensive, it becomesimportant tofind optimal solutions to such problems Thus, RA pro-blems represent an important class of problems faced by mathemati-cal programmers Conventionally, such RA problems have beenmodeled and solved for allocation in single-echelon Supply Chain(SC), single-objective allocation, and allocation with certainty ofstatic input data, single-performance measure driven allocation, dis-integrated allocation and routing both in strategic and operationallevels Such models that consider the above assumptions/constraintsare nominal models and their solutions are denoted nominalsolutions However, in practice, these assumptions are rarely, ifever, true, which raises questions regarding the practicability andvalidity of the problems and solutions obtained under these assump-tions The allocation problems focusing bi- or multiple objectives,dynamic allocation bases on dynamic input data and constraints,multiple performance driven allocation and integrated allocationand routing context are complex combinatorial problems whichdemand high computational time and effort for deriving compro-mised near-optimal/optimal solutions In this research, we study RAproblems involving flow of resources over a typically, large-scalemulti-echelon SC network in an optimal manner

This research focuses on development of models and heuristicsfor six new and complex sub-classes of RA problems in SC networkfocusing bi-objectives, dynamic input data, and multiple perfor-mance measures based allocation and integrated allocation androuting with complex constraints This study considers six set ofvariants of the RA problems normally encountered in practice buthave not been given attention to hitherto These variants of the clas-sical RA are complex and pertaining to both manufacturing andservice industry RA variant in bi-objective capacitated SC network,

RA variant in bi-objective bound driven capacitated SC network,

RA variant in multiple measures driven capacitated multi echelon

SC network, RA variant in integrated decision and upper bound ven capacitated multi echelon SC network, RA variant in integrateddecision and time driven capacitated multi echelon SC network, RA

dri-v

variant in integrated decision, bound and time driven capacitatedmulti echelon SC network are the new variants proposed in thisresearch These variants have some applications that are of specialinterest, including those that arise in the areas of warehousing,transportation, logistics, and distribution These applicationdomains have important economic value, and high importance isattached to achieve efficient solutions.

The Non-deterministic Polynomial (NP)-hardness of these blems mandates the use of heuristics/meta-heuristics as solutionmethodology to solve these complex variants Mathematical pro-gramming model, genetic algorithms, simulated annealing, simula-tion modeling, and decision-making models are used as solutionmethodologies to address these variants The solution methodologiesare designed as unified methodology to solve the original or basevariant of the proposed variants The proposed unified solutionmethodologies are evaluated by comparing it with published resultsusing standard, derived, and randomly generated data sets In caseswhere benchmarks are not available, the published best results forthe simpler versions of RA are used as substitutes for the lowerbounds The solution methodologies performed exceedingly well inthe evaluations, recording better or equally good results in compari-son to the existing methodologies

pro-Keywords: Resource allocation problems; supply chain;

mathematical programming model; heuristic; meta-heuristic;

genetic algorithms; simulated annealing; simulated modeling

1.3.1 Resource Allocation Variant in Bi-Objective

1.3.2 Resource Allocation Variant in Bi-Objective Bound

1.3.3 Resource Allocation Variant in Multiple Measures

Driven Capacitated Multi-Echelon Supply Chain

1.3.4 Resource Allocation Variant in Integrated Decision and

Upper Bound Driven Capacitated Multi-Echelon Supply

1.3.5 Resource Allocation Variant in Integrated Decision and

Time Driven Capacitated Multi-Echelon Supply Chain

1.3.6 Resource Allocation Variant in Integrated Decision,

Bound and Time Driven Capacitated Multi-Echelon

2.2 Review of the RA Variants Addressed in Current Research 142.2.1 Bi-Objective Generalized Assignment Problem 14

2.2.3 Multiple Measures Resource Allocation Problem 21

vii

2.2.4 Mixed Capacitated Arc Routing Problem 24

2.2.6 Vehicle Routing Problem with Backhauls with Time

SECTION3 Bi-Objective Capacitated Supply Chain Network 37

3.1 Bi-Objective Resource Allocation Problem with Varying

3.2.1 Mathematical Programming Model for

3.2.2 Simulated Annealing with Population Size Initialization

through Neighborhood Generation for GAP and

SECTION4 Bi-Objective Bound Driven Capacitated

4.1 Bi-Objective Resource Allocation Problem with Bound and

4.2.1 Recursive Function Inherent Genetic Algorithm

SECTION5 Multiple Measures Driven Capacitated

Multi-Echelon Supply Chain Network 75

5.1 Multiple Measures Resource Allocation Problem for

5.2.1 Simulation Modeling with Multiple Performances

5.2.5 Multiple Performance Measures of Multi-Echelon

5.4.1 Procurement Policy for all“A” Class Items 91

5.4.3 Procurement and Inventory Policy for all“B” “C”

SECTION6 Integrated Decision and Upper Bound Driven

Capacitated Multi-Echelon Supply Chain Network 97

6.1 Integrated Resource Allocation and Routing Problem with

6.2.1 Dijkstra’s Algorithm and Local Search Inherent

Genetic Algorithm (DIALING) for MCARP and

SECTION7 Integrated Decision and Time Driven Capacitated

Multi-Echelon Supply Chain Network 115

7.1 Integrated Resource Allocation and Routing Problem with

7.2.1 Clustering Inherent Genetic Algorithm (CLING) for

7.2.2 Parameter Settings for CLING 122

SECTION8 Integrated Decision, Bound and Time

Driven Capacitated Multi Echelon Supply Chain

8.1 Integrated Resource Allocation and Routing Problem with

8.2.1 Decision Support System Based on Mixed Integer

Linear Programming (DINLIP) for VRPBTW and

8.5 Decision Support System for Vehicle Routing at Sangam:

List of Tables

Section 2

Table 2.1 The Existing Solution Methods for VRPBTW 35

Section 3 Table 3.1 Comparison of SAPING and GA for BORAPVC for Benchmark Data Sets 44

Table 3.2 Comparison of SAPING and GA for Randomly Generated Datasets of BORAPVC 45

Section 4 Table 4.1 Comparison of REFING for 31 Randomly Generated Datasets of BAROPBVC with the Results of Brute Force Method 60

Table 4.2 Cost Difference among the Countries 62

Table 4.3 Patient Allocation 68

Table 4.4 Inputs for Patient Allocation 69

Table 4.5 Values and Reduced Cost of Variables 70

Table 4.6 Slack or Surplus and Dual Prices 71

Table 4.7 Optimum Patient Allocation 71

Section 5 Table 5.1 Input to the SIMMUM Model Program 83

Table 5.2 Output of the SIMMUM Model Program 84

Table 5.3 Min Max Inventory Levels 90

Table 5.4 ABC Always Better Control 91

Table 5.5 Level Comparisons on“A” Class 92

Table 5.6 Level Comparisons on“B” and “C” Classes 92

Table 5.7 Outsourcing decision based onABC analysis 93

xi

Section 6

Table 6.1 Comparison of DIALING for 34 Standard

Benchmark MCARP Datasets of Belenguer et al (2006) with the Lower Bound of Belenguer et al

(2006) 110

Table 6.2 Comparison of DIALING with 10 Derived Datasets of IRARPUB from Belenguer et al (2006) with the Lower Bound of Belenguer et al (2006) 111

Section 7 Table 7.1 Comparison of CLING for 25 Standard Benchmark VRPTW Datasets of Solomon (1987) 123

Table 7.2 Comparison of CLING with 25 Derived Datasets of IRARPTW from Solomon (1987) with the Lower Bound of Solomon (1987) 124

Section 8 Table 8.1 Comparison of Heuristics with Best-Known Solution Value of VRPBTW Problems Derived from VRPTW R101 and R102 Datasets 134

Table 8.2 Comparison of DINLIP with 25 Derived Datasets of IRARPBTW from Solomon (1987) with the Lower Bound of Solomon (1987) 135

Table 8.3 Cost Data for the Case Study 144

Table 8.4 Travel Distance Data for the Case Study 147

Table 8.5 Demand Data for the Case Study 150

Table 8.6 Vehicle Data for the Case Study 150

Table 8.7 Results and Comparison for the Case Study 151

Section 9 Table 9.1 RA Variants and Nature of Supply Chain Network 156

List of Figures

Section 1

Figure 1.1 Complications in Supply Chain 2

Figure 1.2 Various Elements Driving Complexity of Supply Chain 3

Figure 1.3 Decision Framework for Supply Chain 4

Figure 1.4 Elements Involved in Decisions Required for Supply Chain 4

Figure 1.5 Diagrammatic Representation of Resource Allocation in Supply Chain 6

Section 2 Figure 2.1 Conceptual Framework for Resource Allocation Problems 13

Section 4 Figure 4.1 Network Flow Diagrams 50

Figure 4.2 BORAPBVC Network 51

Figure 4.3 Allocation Based on the Formulation 53

Figure 4.4 Chromosome of Solution in GA 56

Figure 4.5 Two Point Crossover 56

Figure 4.6 Cycle Crossover First Step 57

Figure 4.7 Cycle Crossover Second Step 57

Figure 4.8 Inputs to the Central Body 64

Figure 4.9 Flow Chart for the Allocation of Patient 64

Section 5 Figure 5.1 Simplified Multi-Echelon Supply Chain Model 77

Figure 5.2 Logic Diagram of Simulation Model 86

Figure 5.3 Activities at Node 1 87

Figure 5.4 Activities at Node 2 88

Figure 5.5 Activities at Node 3 88

Figure 5.6 Activities at Factory Node 89

Figure 5.7 Bullwhip Effect 89

xiii

Section 6

Figure 6.1 Flow Chart of Proposed Heuristic DIALING to

Solve MCARP and IRARPUB Problems 102

Figure 6.2 Chromosome Representation for MCARP and IRARPUB Problems 104

Figure 6.3 Two-Point Crossovers (C1) 107

Figure 6.4 Two-Point Crossovers (C2) 107

Figure 6.5 Simple Inversion Mutations 108

Figure 6.6 Solid Waste Management Collection of Refuse/Waste to Refuse Dumpsite 112

Figure 6.7 Networks for Case Study 5 Vehicles, with 12 Nodes 113

Figure 6.8 Convergence of Solution for Case Study 114

Section 7 Figure 7.1 Chromosome Representation for VRPTW and IRARPTW Problems 118

Figure 7.2 Two-Point Crossovers (C1) 121

Figure 7.3 Two-Point Crossovers (C2) 121

Section 8 Figure 8.1 Procurement (Amul Pattern) 136

Figure 8.2 Organization Structure Diagram 137

Figure 8.3 Flow Chart of Critical Processes 138

Figure 8.4 Process Flow Diagram of Milk Processing and Packaging 139

Figure 8.5 Order Taking and Distribution Processes 140

List of Symbols and

Abbreviations

ASPSA Augmented Simultaneous Perturbation Stochastic

ApproximationBGAP Bi-Objective Generalized Assignment Problem

BMWAP Bi-Criteria Multiple Warehouse Allocation Problem

BORAPVC Bi-Objective Resource Allocation Problem with

Varying CapacityBORAPBVC Bi-Objective Resource Allocation Problem with

cij Cost of Assigning Jobj to Agent i

Cij Revenue Generated from theith Patient by the jth

Hospital for a Particular Diseases

ck

ij Per Unit Cost of Commodityk on arc ij

xv

DC Distribution Center

DIALING Dijkstra’s Algorithm and Local Search Inherent

Genetic AlgorithmDINLIP Decision Support System Based on Mixed Integer

Linear Programming

dij Travel Distance between Retailerj to Distributor i

Div The Load Remaining to be Delivered by Vehiclev

When Departing from Nodei

E Set of Arcs Linking Any Pair of Node; (i, j) ∈ E

EPDOCP Evaluation Process Using Dynamic Optimal Cost

Procedure

g(sj) Objective Function Value of Chromosomesj.

gðsj 0Þ Total Allocation Cost

IRARPTW Integrated resource Allocation and Routing Problem

with Time WindowIRARPBTW Integrated Resource Allocation and Routing

Problem with Bound and Time WindowISWMS Integrated Solid Waste Management SchemeIRARPUB Integrated Resource Allocation and Routing

Problem with Upper Bound

JIT Just-In-Time

MCARP Mixed Capacitated Arc Routing Problems

MMRAPMSC Multiple Measures Resource Allocation Problem for

Multi-Echelon SC

Piece-Wise Linear Concave Cost

O(k) [D(k)] Origin [Destination] Node for Commodityk

Piv The Cumulative Load Picked Up by Vehiclev When

Departing from Nodei

pop size Population Size

Ps Probability of Stochastic Hill Climbing Search

PVRP1 Periodic Vehicle Routing Problem

R Tasks

REFING Recursive Function Inherent Genetic Algorithm

Rj Total Revenue Generated by thejth Hospital

SAPING Simulated Annealing with Population Size

Initialization through Neighbourhood Generation

Si Maximum Cost Spend by theith Patient for having

the Treatment

SIMMUM Simulation Modeling with Multiple Performance

Measures

sj Current Solution in Feasible Space

Tiv The Starting Time of the Service of the Vehiclev at

Nodei

tij Travel Time between Retailerj to Distributor i

uij Total Capacity on Arcij (assume uijkis Unlimited

for Eachk and Each ij)

VRPB Vehicle Routing Problem with Backhauls

VRPBTW Vehicle Routing Problem with Backhauls and Time

Windows

VRPTW Vehicle Routing Problem with Time Window

xk

ij Number of Units of Commodityk Assigned to Arc ij

Yij Cost of Travel from Nodei to Node j

Yij 0 or 1, for alli and j

Zij The Total Load on Vehiclev, to be Delivered to

Nodes Carried along Arc (i, j)

About the Authors

K Ganesh is working as Knowledge Expert at McKinsey &Company, Chennai, India Dr Ganesh has done B.E fromAnnamalai University, M.E from NIT Trichy and PhD from IITMadras He has more than 10 years of combined industry and aca-demic experience and has consulted many organizations in differentdomains such as logistics optimization and supply chain planning

He has authored/co-authored 6 books, more than 70 papers in national referred journals besides publications in different confer-ences His research interests include application of advancedanalytics, big data, heuristics, metaheuristics for supply chain, andlogistics problems

inter-R A Malairajan is currently Assistant Professor at Department ofMechanical Engineering, Anna University, Tuticorin Campus, India

He completed his M.I.B.A at Alagappa University, Karaikudi,Tamil Nadu and Doctorate in Supply Chain Management, AnnaUniversity, Chennai His research interests include resource alloca-tion problems, routing problems, and metaheuristics in supplychain He currently teaches both mechanical engineering and man-agement studies

Sanjay Mohapatra has a B.E from NIT Rourkela, MBA fromXIMB, M Tech from IIT Madras, India and PhD from UtkalUniversity Dr Mohapatra has more than 27 years of combinedindustry and academic experience He has consulted many organiza-tions in different domains such as Utilities, Banking, Insurance, andhealthcare sectors His teaching interests are in IT Strategy andManagement Information Systems and research interests are in thearea of IT enabled processes He has authored/co-authored 21books, more than 50 papers in national and international referredjournals besides publications in different conferences His contactdetails and list of publications can be found at http://ximb.acade-mia.edu/sanjaymohapatra

M Punniyamoorthy is currently the Dean-Institute Developmentand Professor at DOMS-NITT He completed his M Tech (IIT,Karagpur) in Industrial Engineering & Operations Research andDoctorate in Management at the Bharathidasan University,

xxi

Tiruchirappalli His research interests include Risk Management,Capital Markets, Supply Chain performance, Data Analysis,Performance Measurement, and Balanced Scorecard He currentlyteaches Data Analytics, Supply Chain Management, Logistics,Production and Operation Management, Project Managementamong others He has authored a book on Production Managementand his second book on Data Analytics is in press He is on theeditorial board of several journals and has been a reviewer formany others.

1 Introduction

1.1 Supply Chain Management

Several researchers attempted to define the essence of Supply ChainManagement (SCM) into a distinct definition Its elements are theobject of the management philosophy, the target group, the objec-tive(s), and the broad means for achieving these objectives Theobjective of SCM is the Supply Chain (SC), which represents a“net-work of organizations that are involved, through upstream anddownstream linkages, in the different processes and activities thatproduce value in the form of products and services in the hands ofthe ultimate consumer” (Christopher, 2005) In a wide logic, an SCconsists of two or more legally separated organizations, being asso-ciated by material, information, andfinancial flows These organiza-tions may befirms producing parts, components and end products,logistics service providers, and even the (ultimate) customer So, theabove definition of an SC also incorporates the target group
theultimate customer An SC is a network that typically will not onlyspotlight onflows within a chain but will also have to contract withdiffering and convergentflows within a complex network resultingfrom many different customer orders to be handled in parallel Inorder to ease complexity, a given organization may concentrate only

on a portion of the overall SC As an example, looking in the stream direction, the view of an organization may be limited by thecustomers of its customers while it ends with the suppliers of its sup-pliers in the upstream direction SCs have become increasingly moreglobal and complex presenting greater challenges Contemporarymarket drifts considerably have an impact on growing complications

down-of SCs and it has been detailed inFigure 1.1

1

Figure 1.1: Complications in Supply Chain.

Because of these growing complications, SC is under tal pressure with various elements as indicated inFigure 1.2.

fundamen-Various decisions need to be made cleverly in order to overcomethese pressures of SC Two major decision categories are temporaland functional There are five sub decisions such as sourcing, loca-tion, allocation, routing and inventory are involved in functionaldecision and three sub decisions such as strategic, tactical and opera-tional are involved in temporal decision The decision framework incomplex SC is detailed inFigure 1.3

There are various elements involved in the decisions and it ishighlighted in Figure 1.4 The elements are in two dimensions,namely modeling and entity dimensions In modeling dimensions,various elements such as inputs, constraints, outputs, logics, para-meters, etc are involved In entity dimension, various elements such

as product, mode, customer, supplier, plants, lines, warehouses, etc.are involved

Shortening product life cycles

Demanding customers and Resource Availability

New compliance Agenda (sustainable, environment

al and risk issues)

Performance Issues Rapid ROI Moving fixed cost to available Shared risk Better visibility Optimizing existing systems

Figure 1.2: Various Elements Driving Complexity of Supply Chain

Among various pressures indicated inFigure 1.2, resource ability is one of the key and recent pressures that drives the organi-zation, society, and the SC as well As indicated in Figure 1.3,Resource Allocation (RA) is one of the critical decisions that drivesthe organization in terms of cost and service level.

avail-With the scope of allocation decisions in mind, approximately

120 articles have been identified that were published in thelast decade, including a few papers that have appeared in 2011.Further screening yielded 98 articles from 19 journals that address

Supply Chain Decisions

Strategic

Sourcing Location Allocation Routing Inventory

Tactical Operational

Figure 1.3: Decision Framework for Supply Chain

Figure 1.4: Elements Involved in Decisions Required for Supply Chain

relevant aspects to our analysis Of these, 56 were published in

2004 or later, which clearly shows the recent progress thisresearch area is experiencing For example, compared to 2002, thenumber of publications doubled in 2007 (22 against 11) In parti-cular, the European Journal of Operational Research has been amajor forum for the presentation of new developments andresearch results (in total 44 articles were identified) Other jour-nals such as Computers & Operations Research (18 papers),Interfaces (six papers), Transportation Research (seven papers),and Omega and International Journal of Production Economics(each with six articles) have significantly contributed to this emer-ging researchfield

1.2 Resource Allocation Problems in

Supply Chain

RA involves the distribution and utilization of available resources

in the system Because resource availability is usually scarce andexpensive, it becomes important to find optimal solutions to suchproblems Thus, RA problems represent an important class of pro-blems faced by mathematical programmers Conventionally, such

RA problems have been modeled and solved for allocation insingle-echelon SC, single-objective allocation, allocation with cer-tainty of static input data, single-performance measure driven allo-cation, disintegrated allocation and routing both in strategic andoperational level Such models that consider the above assump-tions/constraints are nominal models, and their solutions aredenoted as nominal solutions However, in practice, these assump-tions are rarely, if ever, true, which raises questions regarding thepracticability and validity of the problems and solutions obtainedunder these assumptions The allocation problems focusing bi ormultiple objectives, dynamic allocation bases on dynamic inputdata and constraints, multiple-performance driven allocation andintegrated allocation and routing context are complex combinator-ial problems which demand high computational time and effortfor deriving compromised near-optimal/optimal solutions In fact,Mulvey (1981) and Ben-Tal and Nemirovski (2000) showed thatsuch nominal solutions shall become irrelevant in the presence ofreal-world uncertainty In this research, RA problems involvingflow of resources over a typically, large-scale multi-echelon SC net-work in an optimal manner is studied This research focuses onthe development of models and heuristics for six new and complexsub-classes of RA problems in SC network focusing bi-objectives,

dynamic input data, and multiple performance measures-basedallocation and integrated allocation, and routing with complexconstraints These sub-classes have some applications that are ofspecial interest, including those that arise in the areas of warehous-ing, transportation, logistics, and distribution These applicationdomains have important economic value, and high importance isattached to achieve efficient solutions The diagrammatic represen-tation of RA problem in SC is shown inFigure 1.5.

The basic elements and position involved in RA problem withbasic formulation is detailed:

Set of elements (e.g., personnel, facilities, tasks):

A = {a1,…, ai,…, an}

Set of positions (e.g., locations, processors):

B = {b1,…, bj,…., bm}

(now letn = m)

Effectiveness of pairaiandbjis:c (ai,bj)

xij = 1 if ai is located into position bj and 0 otherwise

Positions (e.g., Locations, Sites etc.,)

Figure 1.5: Diagrammatic Representation of Resource Allocation in SupplyChain

The problem is : maxX

Semi-structured interview with 40 global manufacturing and service

SC executives was conducted to understand and explore the new,critical, and challenging constraints and variants of RA problems inthe current trend of SC network Based on the semi-structured inter-view, the pressing constraints and issues in RA problems are col-lected Keeping that as a base, a detailed business and researchliterature review is conducted and six critical RA variants in variousdimensions of SC are identified for the current research

1.3.1 RESOURCE ALLOCATION VARIANT IN BI-OBJECTIVE

CAPACITATED SUPPLY CHAIN NETWORK

Logistics quality is often measured by the logistics manager’s ability

to distribute products on specific time and on budget Thus, themain drive to improve logistics productivity is the enhancement ofcustomer services and asset utilization through a significant reduc-tion in order cycle time (lead time) and logistics costs Goal of redu-cing order cycle time often conflicts with the goal of reducinglogistics costs So, a compromised allocation solution is needed forlogistics manager But, at times, priority is dynamic for the objec-tives based on the situation and so the managers should need a set

of compromised and non-dominated solutions to choose the bestwhich suits the need (Zhou, Min, & Gen, 2003) The allocation ispurely based on the minimization of cost and time with equal vary-ing (equal and unequal) capacity and capacity restriction in thesource This RA variant is termed as Bi-Objective Resource

Allocation Problem with Varying Capacity (BORAPVC).Applications of BORAPVC are in automotive and process industry,which include warehouse allocation to customers in distribution,supplier allocation to manufacturing plant in sourcing, and distribu-tor allocation to retailer in delivery.

1.3.2 RESOURCE ALLOCATION VARIANT IN BI-OBJECTIVE BOUNDDRIVEN CAPACITATED SUPPLY CHAIN NETWORK

In the current competitive trend, organization running multiple ness units shall face extreme performance variations due to sub-optimal allocation of destination nodes to source nodes Many com-panies would like to have a balanced service for all the resources inorder to improve the asset utilization and cost reduction in terms ofhaving lower and upper bound service limit for each resource Thegoal of allocation of resources with bi-objective and bound condi-tions is a complex action Logistics manager is in the need of obtain-ing a compromised bound driven non-dominated allocation solution

busi-to balance the performance variations of resources (Teng, Yao, &

Hu, 2007) The allocation is purely based on the minimization oftwo objectives, namely cost and service level with varying andbounded capacity (equal and unequal) and capacity restriction inthe source This RA variant is termed as Bi-Objective Resource

(BORAPBVC) Applications of BORAPBVC are in automotive, cess, and health care industry which include customer allocation towarehouses and patient allocation to hospitals

pro-1.3.3 RESOURCE ALLOCATION VARIANT IN MULTIPLE

MEASURES DRIVEN CAPACITATED MULTI-ECHELON SUPPLY

CHAIN NETWORK

When properly designed and operated, the traditional SC hasoffered customers with three primary benefits
reduced cost, fasterdelivery, and improved quality But managers are increasingly recog-nizing that these advantages, while necessary, are not always suffi-cient in the modern business world A new paradigm is emerging of

a more sophisticated SC
one that also serves as a vehicle for oping and sustaining competitive advantage under a variety of per-formance measures (Melnyk et al., 2010) Allocation in old SC wasstrategically decoupled and price driven; the allocation in new SC isstrategically coupled and value driven with multiple performancemeasures The allocation is purely based on the multiple perfor-mance measures for multi-echelon SC with the consideration ofinventory and shortage This RA variant is termed as MultipleMeasures Resource Allocation Problem for Multi-echelon SC

devel-(MMRAPMSC) Applications of MMRAPMSC are in ing and process industry.

manufactur-1.3.4 RESOURCE ALLOCATION VARIANT IN INTEGRATED DECISION

AND UPPER BOUND DRIVEN CAPACITATED MULTI-ECHELON SUPPLY

CHAIN NETWORK

An SC is a system of facilities and activities that functions to cure, produce, allocate, and distribute goods to customers SCM isbasically a set of approaches utilized to efficiently integrate suppli-ers, manufacturers, warehouses, and end-customers, so that mer-chandise is produced and distributed at the right quantities, to theright locations, and at the right time, in order to minimize system-wide costs (or maximize profits) while satisfying service levelrequirements Although it would be ideal from a research standpoint

pro-to develop large-scale integrated models consisting of multiple ties with integrated decisions while trying to understand effective SCpractices, it is often very difficult to get any useful insights fromsuch large models because they are intractable When two logisticaldecisions of the SC, namely allocation (a tactical decision) and rout-ing (operational decision) are combined with the varying (equal andunequal) capacity from the source, demand from the destination andwith a upper bound on the service quantity or distance, the problem

enti-of integrated decision and upper bound driven capacitated echelon SC network is formed (Shen, 2007) The integrated alloca-tion and routing is purely based on the upper bound on servicequantity for a varying demand-oriented multi-echelon SC with theconsideration of limitation on the number of supply catalystresource This RA variant is termed as Integrated ResourceAllocation and Routing Problem with Upper Bound (IRARPUB).Applications of IRARPUB are in manufacturing and service industrywhich include refuse (waste) collection, urban solid waste manage-ment, winter gritting, postal distribution, meter reading, and schoolbus routing

multi-1.3.5 RESOURCE ALLOCATION VARIANT IN INTEGRATED DECISION

AND TIME DRIVEN CAPACITATED MULTI-ECHELON SUPPLY CHAIN

NETWORK

Time is of utmost importance in logistics Time can even be the sive factor for efficiency and effectiveness of the SC The Just inTime concept, for example, successfully streamlined the inboundlogistics for production companies Service lead times are anotherwell-known element in logistics Agreed service lead times can forcechoices in the SC processes which are not necessarily the most costeffective or environmentally friendly The integrated decision with

deci-allocation and routing in a time window driven scenario in the citated SC network is a challenging problem The integrated alloca-tion and routing is purely based on the time window for the service

capa-at the demanding node with the considercapa-ation of travel time of cle for a varying demand-oriented multi-echelon SC with the consid-eration of limitation on the number of supply catalyst resource(Ronald, 1999) This RA variant is termed as Integrated ResourceAllocation and Routing Problem with Time Window (IRARPTW).Applications of IRARPTW are in manufacturing and service indus-try which include urban solid waste management, taxi cab routing,postal distribution, and school bus routing

vehi-1.3.6 RESOURCE ALLOCATION VARIANT IN INTEGRATED DECISION,BOUND AND TIME DRIVEN CAPACITATED MULTI-ECHELON SUPPLYCHAIN NETWORK

Decisions at SC are driven by multiple constraints The expectation

on the service from the customer is multifold but the execution isdriven by various practical and real-life constraints The allocationdecision integrated with routing by considering the time constraints

of service and bound on the service limit is a challenging scenario inthe current trend of SC The integrated allocation and routing ispurely based on the time window for the service at the demandingnode with the contemplation of bound on the service for a multi-echelon SC with the consideration of limitation on the number ofsupply catalyst resource (Brauer & Backholer, 2009) This RAvariant is termed as Integrated Resource Allocation and RoutingProblem with Bound and Time Window (IRARPBTW) Applications

of IRARPBTW are in manufacturing and service industry whichinclude milk collection and distribution, blood collection and distri-bution, components collection and distribution, etc

1.4 Scope of the Present Study

The current study addresses six complex variants of RA problems inmulti-echelon SC with applications in manufacturing and serviceindustries The objective is to develop solution methodologies forthese variants of RA problems in SC

The aim of this research is to address various variants pertaining

to RA problems in the SC context and to develop comprehensivesolutions to solve the problem in a reasonable computation time.The objective of this research is to address all the below new

variants and to propose suitable comparative solution gies leveraging heuristics of meta-heuristics or combinationapproaches:

methodolo-• RA variant in bi-objective capacitated SC network

• RA variant in bi-objective bound driven capacitated SC network

• RA variant in multiple measures driven capacitated echelon SC network

multi-• RA variant in integrated decision and upper bound driven citated multi-echelon SC network

capa-• RA variant in integrated decision and time driven capacitatedmulti-echelon SC network

• RA variant in integrated decision, bound and time driven tated multi-echelon SC network

capaci-2 Literature Review

2.1 Resource Allocation Problem

RA involves the distribution and utilization of available resourcesacross the system Because resource availability is usually scarce andexpensive, it becomes important to find optimal or even “good”solutions to such problems Thus, RA problems represent an impor-tant class of problems faced by mathematical programmers

A conceptual framework for RA problems based on literaturereview is detailed inFigure 2.1

AP Number of

Products

No of Facility

& Stages

Linear Euclidean

Recti- Hattan

Man-Actual Distance

Distance Measures

Objectives Type

Elastic Single

Multiple

Deterministic Stochastic

Qualitative Quantitative Single Multiple

Plane/Continuous Network Location

Discrete Location (MIP)

MinSum MinMax In-Elastic

Figure 2.1: Conceptual Framework for Resource Allocation Problems

13

2.2 Review of the RA Variants

Addressed in Current Research

Literature on the RA variants addressed in this study is presented innext few paragraphs

2.2.1 BI-OBJECTIVE GENERALIZED ASSIGNMENT PROBLEM

Literature pertaining to bi-objective/multi-objective GeneralizedAssignment Problem (GAP) is very limited Hajri Gabouj (2003)investigated a fuzzy genetic multi-objective optimization algorithmfor a multi-level GAP, an application encountered in clothing indus-try.Zhou et al (2003) explored a Genetic Algorithm (GA) approachfor Bi-Objective Generalized Assignment Problem (BGAP), an appli-cation of allocation of customers to warehouses From the literaturereview, it was inferred that the BGAP was addressed less in the lit-erature and also there would be a lot of opportunity to explore sev-eral solution approaches to solve BGAP to find Pareto optimalsolutions It is also evident that none of the researchers proposedSimulated Annealing (SA) to solve BGAP

A well-known search heuristic that has been used to solve avariety of combinatorial optimization problem is SA (Golden &Skiscim, 1986; Kirkpatrick, Gelatt, & Vecchi, 1983) SA is inspiredfrom the physical annealing process emanating in statisticalmechanics It is a local search meta-heuristic, in the sense that it con-ducts local search while guiding the overall exploration processintelligently, offering the possibility of accepting, in a controlledmanner, solutions that do not descend along the path of search.This feature allows SA to escape from a low-quality local optimum.More precisely, at each iteration of SA, a neighbor s0 Є N(s) ofthe current solution s is generated stochastically and a decision ismade concerning the replacement or not ofs by s0 If s0 is a bettersolution thans, that is, B = c(s)−c(s0)<0 for a minimization problem

or B = c(s)−c(s0)>0 for a maximization problem, the search movesfroms to s0; otherwise, the search moves tos0with a probability ofe(−B)/T This probability depends on the degree of degradation (thesmaller the value of B, the greater the accepting probability) and acontrol parameterT called temperature (higher temperatures lead tohigher accepting probabilities and vice versa); the evolution of thetemperature is governed by a cooling schedule specifying the stepsfor progressive reduction of temperature Introducing terms such as

“cooling schedule” and “temperature” essentially searches for bettersolutions in a discrete solution space with a provision to accommo-date inferior solutions at intermediate stages in order to avoid beingtrapped at local optima Typically, SA stops when afixed number of

non-improving iterations is realized with a single temperature orwhen a pre-specified number of iterations is reached.

The SA method is known to be a compact and robust technique,providing excellent solutions to single-objective optimization pro-blems with a substantial reduction in computational cost Later, thismethod has been adapted for the multi-objective framework.Balram(2005)detailed the literature pertaining to the application of SA tomulti-objective combinatorial optimization problems Given the pro-ven success of SA to multi-objective combinatorial optimization pro-blems, it is believed that SA is suitable for solving BGAP

2.2.2 MULTI-COMMODITY NETWORK FLOW PROBLEM

There are various studies on network optimization techniques Themodels were formulated for the various scenarios and worked out.Significant work has been carried out for the various connotations

of Multi-Commodity Network Flow (MCNF) Here are some dies mentioned, which are considered to be significant

stu-One of the earlier studies on MCNF in an alternate derivation

of the dual condition (called the severance-value condition) posed byOnaga and Kakusho (1971)is deemed to mention here

pro-Geoffrion and Graves (1974) formulated MCNF as a mixedinteger linear program They developed, implemented, and success-fully applied a solution technique based on Benders Decomposition

to a major foodfirm with 17 commodity classes, 14 plants, 45 ble distribution center sites, and 121 customer zones.Panagiotakopoulos (1976)presented a network model for the analy-sis of waste management systems He formulated this MCNF pro-blem as a linear program where each column in the constraintmatrix corresponds to a chain in the network and used a column-generation scheme based on a shortest route algorithm to obtain thesolution

possi-Minoux (1981)described an algorithm based on generalization

of the max-flow min-cut theorem to solve the MCNF He also duced a generic model through MCNF to the CommunicationNetworks (Minoux, 2001) Rees, Clayton, and Taylor (1987) sug-gested that MCNF can serve as an effective distribution planningtool wherein cost minimization is not always the sole objective of afirm involved in distributing commodity items through a network ofoutlets, retail centers, etc Typically, many firms have objectivessuch as meeting preferred customer demand in order to establishgood will or to reduce inventory levels at a particular store

intro-Leighton et al (1991)described the first polynomial-time binatorial algorithms for approximately solving the multi-commodity flow problem Gabrel and Minoux (1997) focused onthe development of relaxations for MCNF problems in order to

com-derive lower bounds They proposed an alternative relaxation of theproblem in terms of a large-scale linear programming (LP) model,which can be solved by a generalized LP approach.

McBride (1998) used MCNF for solving extremely large tics problems with more than 600,000 constraints and 7,000,000variables in the food industry Yan and Chen (2002) modeled thebus movements and passengerflow to find the optimal bus routes/schedules and passenger transportation plans Mathematically, themodel is formulated as a mixed integer multiple commodity networkflow problem which contains a fleet of 320 buses with 23,652 pro-jected daily trips, betweenfive cities.Gabrel, Knippel, and Minoux(1999)described an exact solution procedure, based on the use ofstandard LP software, for MCNF with general discontinuous step-increasing cost functions They proposed an improved implementa-tion of the constraint generation principle to solve it Gabrel,Knippel, and Minoux (2003)presented and compared approximatesolution algorithms for discrete cost MCNF, namely extensions ofclassical greedy heuristics, based on link-rerouting andflow rerout-ing heuristics and a new approximate solution algorithm, whichbasically consists of a heuristic implementation of the exact Benders-type cutting plane generation method

logis-Ozdaglar and Bertsekas (2003)proposed new integer LP lations for the Optical Networks that tend to have integer optimalsolutions even when the integrality constraints are relaxed, therebyallowing the problem to be solved optimally by fast and highly effi-cient linear (not integer) programming methods

formu-Belotti (2005)investigated three problems, arising in thefield oftelecommunication, networks design with survivability constraints,and solved them through different approaches on a number of real-world network topologies with up to 40 nodes Teng et al (2007)discussed MCNF with random demand using the equilibrium theoryand the method of variational inequality They also analyzed thebehavior of the various decision makers as well as the effect of theirinteraction in different levels.Agarwal and Ergun (2008) studied acollaborative multi-commodityflow game where individual playersown capacity on the edges of the network and share the capacity todeliver commodities They presented membership mechanisms, byadopting a rationality-based approach using notions from game the-ory and inverse optimization, to allocate benefits among the players

in such a game Calitz (2008) applied MCNF for waste collectionvehicles to ensure quality-efficient service at minimum cost by redu-cing the total distance traveled by the collection vehicles within eachday Fayazbakhsh and Razzazi (2008) claim that MCNF might be

an appropriate tool to help the decision makers, which results in theminimization of the whole SC cost

Li, Chu, and Prins (2009) extended their classical capacitatedplant location problem by introducing a multi-commodityflow pro-blem in the distribution issue They proposed a Lagrangean-basedmethod, including a Lagrangean relaxation, a Lagrangean heuristic,and a subgradient optimization, to provide lower and upper bounds

of the model They also employed a Tabu search to further improveupper bounds provided by the Lagrangean procedure Ghatee andHashemi (2009)utilized fuzzy shortest paths andK  shortest paths

to generate preferred paths to solve the MCNF Frangioni andGendron (2009) studied 01 reformulations of the multi-commodity capacitated network design problem, which is usuallymodeled with general integer variables to represent design decisions

on the number of facilities to install on each arc of the network.They compared two cutting plane algorithms to compute the samelower bound on the optimal value of the problem: one based on thegeneration of residual capacity inequalities within the model withgeneral integer variables and the other based on the addition ofextended linking inequalities to the 01 reformulation To furtherimprove the computational results of the latter approach, they devel-oped a column-and-row generation approach Gamst, Jensen,Pisinger, and Plum (2010)solved multi-commodityk-splittable flowproblem through branch-and-price

Moreover, survey papers on multi-commodity network flowproblem (MNFP) by Assad (1978), Kennington (1978), Crainic,Frangioni, and Gendron (2001), and Minoux (2001) illustrate thewide variety of applications of the problem for a longer period.Nevertheless, the gap in the literature is evident that the application

of the meta-heuristics for the MCNF is few And also the literatureclearly explains the implication of MCNF for the optimization inthe patient distribution system

Liu and Zhang (2008)developed the optimal decision of nel selection for the manufacturer by using a three-stage dynamicgame model Yadav, Ghorpade, Mahajan, Tiwari, and Shankar(2009) presented a robust optimization technique, viz.Endosymbiotic Evolutionary Algorithm (EEA) for a multi-stage,multi-period logistics system Min, Ko, and Lim (2009) proposed

chan-an Analytic Hierarchy Process (AHP)-based Decision SupportSystem (DSS) to help multi-national firms tackle the problem ofdetermining the optimal transportation route to inland destinations

in land-locked countries Xanthopoulos and lakovou (2010)described the optimal configuration of efficient reverse logisticsnetworks, and an application of the optimization model is demon-strated, while obtained managerial insights are discussed Min andGuo (2010) proposed an equilibrium model combining game the-ory with GA to promote a compromise between the conflicting