Resource Allocation Problems in Supply Chains

197 Pages·2015·2.798 MB·English

by  K. Ganesh, R. A. Malairajan, Sanjay Mohapatra, M. Punniyamoorthy

Resource Allocation Problems in
Supply Chains
Thispageintentionallyleftblank
Resource Allocation
Problems in Supply Chains
By
K. Ganesh
McKinsey & Company, Inc., Chennai, India
R. A. Malairajan
Anna University, Tuticorin, India
Sanjay Mohapatra
Xavier Institute of Management, Mumbai, India
M. Punniyamoorthy
National Institute of Technology, Tiruchirappalli, India
UnitedKingdom(cid:1)NorthAmerica(cid:1)Japan
India(cid:1)Malaysia(cid:1)China
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Abstract
R
esourceAllocation(RA)involvesthedistributionandutiliza-
tion of available resources in the system. Because resource
availability is usually scarce and expensive, it becomes
importanttofindoptimalsolutionstosuchproblems.Thus,RApro-
blems representan importantclass ofproblemsfacedbymathemati-
cal programmers. Conventionally, such RA problems have been
modeled and solved for allocation in single-echelon Supply Chain
(SC), single-objective allocation, and allocation with certainty of
static input data, single-performance measure driven allocation, dis-
integrated allocation and routing both in strategic and operational
levels. Such models that consider the above assumptions/constraints
are nominal models and their solutions are denoted nominal
solutions. However, in practice, these assumptions are rarely, if
ever, true, which raises questions regarding the practicability and
validity ofthe problemsandsolutions 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 allocation
and routing context are complex combinatorial problems which
demand high computational time and effort for deriving compro-
mised near-optimal/optimal solutions. In this research, we study RA
problems involving flow of resources over a typically, large-scale
multi-echelonSCnetworkinanoptimalmanner.
This research focuses on development of models and heuristics
for six new and complex sub-classes of RA problems in SC network
focusing bi-objectives, dynamic input data, and multiple perfor-
mance measures based allocation and integrated allocation and
routing with complex constraints. This study considers six set of
variants of the RA problems normally encountered in practice but
have not been given attention to hitherto. These variants of the clas-
sical RA are complex and pertaining to both manufacturing and
service 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
SCnetwork,RAvariantinintegrateddecisionandupperbounddri-
ven capacitated multi echelon SC network, RA variant in integrated
decision and time driven capacitated multi echelon SC network, RA
v
vi ABSTRACT
variant in integrated decision, bound and time driven capacitated
multi echelon SC network are the new variants proposed in this
research. These variants have some applications that are of special
interest, including those that arise in the areas of warehousing,
transportation, logistics, and distribution. These application
domains have important economic value, and high importance is
attachedtoachieveefficientsolutions.
The Non-deterministic Polynomial (NP)-hardness of these pro-
blems mandates the use of heuristics/meta-heuristics as solution
methodology to solve these complex variants. Mathematical pro-
gramming model, genetic algorithms, simulated annealing, simula-
tion modeling, and decision-making models are used as solution
methodologiestoaddressthesevariants.Thesolutionmethodologies
are designed as unified methodology to solve the original or base
variant of the proposed variants. The proposed unified solution
methodologies are evaluated by comparing it with published results
using standard, derived, and randomly generated data sets. In cases
where benchmarks are not available, the published best results for
the simpler versions of RA are used as substitutes for the lower
bounds. The solution methodologies performed exceedingly well in
the evaluations, recording better or equally good results in compari-
sontotheexistingmethodologies.
Keywords:Resourceallocationproblems;supplychain;
mathematicalprogrammingmodel;heuristic;meta-heuristic;
geneticalgorithms;simulatedannealing;simulatedmodeling
Contents
ListofTables xi
ListofFigures xiii
ListofSymbolsandAbbreviations xv
AbouttheAuthors xxi
SECTION1 Introduction 1
1.1. SupplyChainManagement 1
1.2. ResourceAllocationProblemsinSupplyChain 5
1.3. MotivationofResourceAllocationProblems 7
1.3.1. ResourceAllocationVariantinBi-Objective
CapacitatedSupplyChainNetwork 7
1.3.2. ResourceAllocationVariantinBi-ObjectiveBound
DrivenCapacitatedSupplyChainNetwork 8
1.3.3. ResourceAllocationVariantinMultipleMeasures
DrivenCapacitatedMulti-EchelonSupplyChain
Network 8
1.3.4. ResourceAllocationVariantinIntegratedDecisionand
UpperBoundDrivenCapacitatedMulti-EchelonSupply
ChainNetwork 9
1.3.5. ResourceAllocationVariantinIntegratedDecisionand
TimeDrivenCapacitatedMulti-EchelonSupplyChain
Network 9
1.3.6. ResourceAllocationVariantinIntegratedDecision,
BoundandTimeDrivenCapacitatedMulti-Echelon
SupplyChainNetwork 10
1.4. ScopeofthePresentStudy 10
SECTION2 Literature Review 13
2.1. ResourceAllocationProblem 13
2.2. ReviewoftheRAVariantsAddressedinCurrentResearch 14
2.2.1. Bi-ObjectiveGeneralizedAssignmentProblem 14
2.2.2. Multi-CommodityNetworkFlowProblem 15
2.2.3. MultipleMeasuresResourceAllocationProblem 21
vii
viii CONTENTS
2.2.4. MixedCapacitatedArcRoutingProblem 24
2.2.5. EmployeeRoutingProblem 26
2.2.6. VehicleRoutingProblemwithBackhaulswithTime
Windows 30
2.3. ObservationsandResearchGap 35
2.4. Summary 36
SECTION3 Bi-Objective Capacitated Supply Chain Network 37
3.1. Bi-ObjectiveResourceAllocationProblemwithVarying
Capacity 37
3.2. SolutionMethodologytoSolveBORAPVC 39
3.2.1. MathematicalProgrammingModelfor
BORAPVC 39
3.2.2. SimulatedAnnealingwithPopulationSizeInitialization
throughNeighborhoodGenerationforGAPand
BORAPVC 40
3.3. ComputationalExperimentsandResults 43
3.4. Conclusion 47
SECTION4 Bi-Objective Bound Driven Capacitated
Supply Chain Network 49
4.1. Bi-ObjectiveResourceAllocationProblemwithBoundand
VaryingCapacity 49
4.2. SolutionMethodologytoSolveIRARPUB 54
4.2.1. RecursiveFunctionInherentGeneticAlgorithm
(REFING)forMCNFandBORAPBVC 54
4.3. ComputationalExperimentsandResults 58
4.3.1. PerformanceofSolutionMethodology 58
4.4. CaseStudyDemonstration 59
4.4.1. ProblemIdentificationandDiscussion 62
4.4.2. FormulationoftheProblem 66
4.4.3. ModelTesting 68
4.4.4. AnalysisofResultsandDiscussion 72
4.4.5. ManagerialImplications 72
4.4.6. SummaryforCaseStudy 72
4.5. Conclusion 73
SECTION5 Multiple Measures Driven Capacitated
Multi-Echelon Supply Chain Network 75
5.1. MultipleMeasuresResourceAllocationProblemfor
Multi-EchelonSupply 75
5.2. SolutionMethodologyforMMRAPMSC 76
Contents ix
5.2.1. SimulationModelingwithMultiplePerformances
Measures(SIMMUM)forMMRAPMSC 76
5.2.2. ModelDescriptions 77
5.2.3. SIMMUMModelAssumptions 78
5.2.4. DecisionVariablesinSIMMUM 79
5.2.5. MultiplePerformanceMeasuresofMulti-Echelon
SupplyChain 80
5.2.6. SIMMUMModelInitialization 81
5.2.7. SIMMUMModelExecution 81
5.2.8. OutputofSIMMUMModel 82
5.2.9. SIMMUMModelImplementation 85
5.3. SimulationModelExperimentationsandResults 86
5.4. CaseStudyforInventoryandPurchasingPolicy 90
5.4.1. ProcurementPolicyforall“A”ClassItems 91
5.4.2. InventoryPolicyforall“A”ClassItems 92
5.4.3. ProcurementandInventoryPolicyforall“B”“C”
ClassItems 93
5.5. Conclusion 94
SECTION6 Integrated Decision and Upper Bound Driven
Capacitated Multi-Echelon Supply Chain Network 97
6.1. IntegratedResourceAllocationandRoutingProblemwith
UpperBound 97
6.1.1. Constraints 99
6.1.2. AssumptionsofIRARPUBProblem 99
6.2. SolutionMethodologytoSolveIRARPUB 100
6.2.1. Dijkstra’sAlgorithmandLocalSearchInherent
GeneticAlgorithm(DIALING)forMCARPand
IRARPUB 100
6.2.2. ParameterSettingsforDIALING 108
6.3. ComputationalExperimentsandResults 108
6.3.1. PerformanceofSolutionMethodology 109
6.4. CaseStudyforIRARPUB 111
6.5. Conclusion 113
SECTION7 Integrated Decision and Time Driven Capacitated
Multi-Echelon Supply Chain Network 115
7.1. IntegratedResourceAllocationandRoutingProblemwith
TimeWindow 115
7.2. SolutionMethodologytoSolveIRARPTW 116
7.2.1. ClusteringInherentGeneticAlgorithm(CLING)for
VRPTWandIRARPTW 117