managing uncertainty in agroforestry problems: applications of operation research models and ...

156 Pages·2016·3.05 MB·English

PONTIFICIAUNIVERSIDADCATOLICADECHILE
SCHOOLOFENGINEERING
MANAGING UNCERTAINTY IN AGROFORESTRY
PROBLEMS: APPLICATIONS OF OPERATION
RESEARCH MODELS AND METHODOLOGIES IN
THE WINE AND FORESTRY INDUSTRIES
´ ´
MAURICIO ANDRES VARAS VALDES
ThesissubmittedtotheOfficeofGraduateStudies
inpartialfulfillmentoftherequirementsforthedegreeof
DoctorinEngineeringSciences
Advisor:
SERGIOMATURANAVALDERRAMA
SantiagodeChile,January2016.
(cid:13)c MMXVI,MAURICIOANDRE´SVARASVALDE´S.
PONTIFICIAUNIVERSIDADCATOLICADECHILE
SCHOOLOFENGINEERING
MANAGING UNCERTAINTY IN AGROFORESTRY
PROBLEMS: APPLICATIONS OF OPERATION
RESEARCH MODELS AND METHODOLOGIES IN
THE WINE AND FORESTRY INDUSTRIES
´ ´
MAURICIO ANDRES VARAS VALDES
MembersoftheCommittee:
SERGIOMATURANAVALDERRAMA
ALEJANDROMACCAWLEYVERGARA
JORGEVERAANDREO
V´ICTORALBORNOZS.
SUSANCHOLETTE
CRISTIANVIALEDWARDS
ThesissubmittedtotheOfficeofGraduateStudies
inpartialfulfillmentoftherequirementsforthedegreeof
DoctorinEngineeringSciences
SantiagodeChile,January2016.
Toallthepeoplethat,inonewayor
another,madethisthesispossible.
ACKNOWLEDGEMENTS
To Professor Sergio Maturana, my Thesis Advisor, for giving me the honor of work-
ing with him. For all his kindness, his great enthusiasm in the development of this thesis,
for his unconditional academic support in all the fields of management sciences; but most
importantly,forteachingmehowtobearighteousman. Withoutbothhisacademicencour-
agementandrigorousness,thisresearchwouldhavebeenimpossibletobeaccomplished.
To Professor Jorge Vera, for helping me with all my mathematical inquiries and for
showing me the beauty of operations research. Also, I want to thank him for showing me
howthepassionforworktranslatesintoteachingexcellence.
To Professor Alejandro Mac Cawley, for giving me the chance to work with him as a
teacher assistant and learn from him the appeal of operations management. Besides, I also
want to thank him for his support and for encouraging me to finish my dissertation when I
thoughtitwasanimpossibletask.
To Jacqueline Lefin, secretary of the Industrial and Systems Engineering Department,
and Pilar Mart´ınez, administrative coordinator of the same Department, for all their kind-
ness and support since the undergraduate program. Also, I want to acknowledge Angela
Saba´ and Marcela Berr´ıos, secretaries of the Industrial Engineering Master Program at the
MII.
TomyfriendsfromboththeUndergraduateandGraduateProgram,whomademystay
at the engineering school and the doctoral program pleasant. Special thanks to Claudio
Araya, Pamela Carrillo, Alejandro Cataldo, Carolina Chamorro, Raimundo Elicer, Armin
Lu¨er, “Dino” Ortega, Walter Quintana, Raimundo Steidle, Ignacio Vargas and Cristian
Villalobos. Thanks for your friendship, your continuous support, and for sharing with me
yourincrediblewisdom.
And finally, to my family, for giving me hope in those moments when I thought I
was not capable of carrying out this research. Particularly, Ce´sar, my father, has been my
iv
exampleofbothresilienceandself-improvementallmylife. AllthatIamisbecauseofyou.
To my Mother Nancy, my brother Pablo, and my beloved sister Karina (R.I.P.) for giving
me their support and for always being there for me. To Katherine, my wife, who faced
the hard task of taking care of our son at the times when I was absent for the requirements
of the doctoral program. I will be forever grateful, Kath. And to Clemente, my firstborn;
everythingIdo,Idoitthinkingaboutyou.
Last, but not least, this thesis was supported by FONDECYT grants 1110367 and
1150882,andspeciallybyMECESUPgrantPUC0710.
v
TABLEOFCONTENTS
ACKNOWLEDGEMENTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iv
LISTOFTABLES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ix
LISTOFFIGURES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xi
1. INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1. Operationresearchmodelsinforestry . . . . . . . . . . . . . . . . . . . 1
1.1.1. Theforestproductionchainandtheroleofsawmills . . . . . . . . . . 3
1.1.2. Thesawmillproductionschedulingproblem . . . . . . . . . . . . . . 5
1.1.3. The impact of uncertainty on the development of feasible production
schedules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
1.1.4. Researchonthesawmillproductionproblemunderuncertainty . . . . 6
1.1.5. The scope of scheduling production for a sawmill: a robust optimization
approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
1.2. Operationresearchmodelsinagriculture . . . . . . . . . . . . . . . . . . 8
1.2.1. Theagri-foodsupplychainandthecaseofwine . . . . . . . . . . . . 11
1.2.2. ORmodelsappliedinthewineindustry . . . . . . . . . . . . . . . . 15
1.2.3. Theimpactofuncertaintiesinwineproductionactivities . . . . . . . 17
1.2.4. Themanagementofhigh-valuegoodsinthewineindustryunderuncertainty 19
1.2.5. Lot-sizing in an export-focused winery and the impact of postponement
practicesunderuncertainty . . . . . . . . . . . . . . . . . . . . 20
1.3. Objectiveandmainhypothesisofthisthesis . . . . . . . . . . . . . . . . 21
1.4. Theremainderofthisthesis . . . . . . . . . . . . . . . . . . . . . . . . . 21
2. SCHEDULINGPRODUCTIONFORASAWMILL:AROBUSTOPTIMIZATION
APPROACH. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
2.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
2.2. Robustoptimizationmethodology . . . . . . . . . . . . . . . . . . . . . 27
vi
2.3. Theschedulingproductionmodel . . . . . . . . . . . . . . . . . . . . . . 29
2.3.1. Problemdescription . . . . . . . . . . . . . . . . . . . . . . . . . . 30
2.3.2. Modelformulation . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
2.4. Robustreformulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
2.4.1. Uncertaintyinproductdemand . . . . . . . . . . . . . . . . . . . . . 32
2.4.2. Uncertaintyinsupplyofrawmaterials . . . . . . . . . . . . . . . . . 34
2.5. Computationalanalysisofthemodel . . . . . . . . . . . . . . . . . . . . 37
2.5.1. Uncertaintyindemandparameters . . . . . . . . . . . . . . . . . . . 37
2.5.2. Uncertaintyinsupplyparameters . . . . . . . . . . . . . . . . . . . 44
2.5.3. Uncertaintyinbothdemandandsupplyparameters . . . . . . . . . . 47
2.6. Concludingremarksandfutureresearch . . . . . . . . . . . . . . . . . . 54
Appendix2.A:thedata . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
3. MANAGING PREMIUM WINES UNDER UNCERTAINTY: A TWO-STAGE
HEURISTICTOSETTINGSTOCKLEVELS . . . . . . . . . . . . . . . . . . 58
3.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
3.1.1. Managing high-value goods in the wine industry under uncertainty:
preliminaryconsiderations . . . . . . . . . . . . . . . . . . . . . 58
3.2. Computing the mean delays of customer orders for an asymmetric cyclic
queuesystemunderanexhaustiveservicepolicy . . . . . . . . . . . . . . . . . 64
3.2.1. Winandsetal. approach . . . . . . . . . . . . . . . . . . . . . . . . 64
3.2.2. Anumericalexample . . . . . . . . . . . . . . . . . . . . . . . . . . 69
3.3. Settingheuristicallywinestocklevelsusingan(s-1,s)inventorycontrolpolicy 73
3.3.1. Theoptimizationproblem . . . . . . . . . . . . . . . . . . . . . . . 73
3.3.2. Solvingthewinestocksettingproblem . . . . . . . . . . . . . . . . 75
3.3.3. Anumericalexample(cont.) . . . . . . . . . . . . . . . . . . . . . . 81
3.4. Theheuristicaccuracy . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
3.4.1. Theheuristicaccuracyinourworkingexample . . . . . . . . . . . . 83
3.4.2. Thesymmetricalcase . . . . . . . . . . . . . . . . . . . . . . . . . 84
3.5. ConcludingRemarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
vii
Appendix3.A:Proposition3.2 . . . . . . . . . . . . . . . . . . . . . . . . . . 86
Appendix3.B:Lemma3.2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
4. A ROLLING HORIZON APPROACH TO ANALYZE THE EFFECTS OF
POSTPONEMENT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
4.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
4.2. Overviewofwineryproductionoperations . . . . . . . . . . . . . . . . . 91
4.3. Modelsforwineproductionplanning . . . . . . . . . . . . . . . . . . . . 94
4.3.1. Modelwithpostponementinthelabelingprocess . . . . . . . . . . . 95
4.3.2. Abenchmarkmodelwithoutpostponementinthelabelingprocess . . 98
4.4. Experimentalanalysis . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
4.4.1. Aframeworkfordecisionmakingandtheexperimentalscope . . . . . 101
4.4.2. Sets and instance parameters, rolling horizon setup and performance
measures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
4.4.3. Capacitytightnessandcertaindemanddatageneration . . . . . . . . 105
4.4.4. Error-pronedemandforecasting . . . . . . . . . . . . . . . . . . . . 106
4.4.5. Experimentalresults . . . . . . . . . . . . . . . . . . . . . . . . . . 107
4.5. Concludingremarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112
5. CONCLUSIONSANDFUTURERESEARCH . . . . . . . . . . . . . . . . . 114
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118
APPENDIXA. ANOTEONTHENEWSVENDORPROBLEMUNDERPOISSON
DEMAND . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131
A.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131
A.2. Settingtheoptimalorderquantityandbounds . . . . . . . . . . . . . . . 132
A.3. Behavioroftheoptimalsolutions∗(λ) . . . . . . . . . . . . . . . . . . 135
A.4. Behavioroftheoptimalvalueh∗(λ) . . . . . . . . . . . . . . . . . . . . 138
A.5. ConcludingRemarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140
viii
LISTOFTABLES
1.1 Taxonomyforcitedpapers. . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.1 SetsusedintheSchedulingProductionModel . . . . . . . . . . . . . . . . . 30
2.2 VariablesusedintheSchedulingProductionModel . . . . . . . . . . . . . . 30
2.3 ParametersusedintheSchedulingProductionModel . . . . . . . . . . . . . 31
2.4 GeneralLot-SizingandSchedulingProblemNotation . . . . . . . . . . . . . 31
2.5 Average operationalcosts forselected values ofraw materialsupply and product
demandconservatismparameters. . . . . . . . . . . . . . . . . . . . . . . . 54
3.1 Notation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
3.2 Optimalsolutionsandvalues. . . . . . . . . . . . . . . . . . . . . . . . . . 83
3.3 Stationary distribution estimation of the number of order waiting or being
processed. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
3.4 Heuristicinventorypositionforeachqueueinthesymmetriccase. . . . . . . 85
3.5 Estimationofthestationarydistributionatthesymmetricalcaseafterareplication
lengthof10,000,000hours. . . . . . . . . . . . . . . . . . . . . . . . . . . 85
3.6 Comparisonbetweentheheuristicandtheoptimalsolution. . . . . . . . . . . 85
4.1 Setsandparameterinstancevalues . . . . . . . . . . . . . . . . . . . . . . 103
4.2 Computation of the performance measures (average per period) for the model
whichallowspostponement. . . . . . . . . . . . . . . . . . . . . . . . . . . 105
4.3 Computation of the performance measures (average per period) for the model
withoutpostponement. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
4.4 Averageperperiodperformanceofimplementeddecisionsforγ =0.1 . . . . 108
4.5 Statisticalanalysisforthedifferenceswithγ =0.1 . . . . . . . . . . . . . . 108
4.6 Averageperperiodperformanceofimplementeddecisionsforγ =0.5 . . . . 109
ix
4.7 Statisticalanalysisforthedifferencesatγ =0.5 . . . . . . . . . . . . . . . . 109
4.8 Averageperperiodperformanceofimplementeddecisionsforγ =1.0 . . . . 109
4.9 Statisticalanalysisforthedifferencesatγ =1.0 . . . . . . . . . . . . . . . . 109
A.1 Rootsofthetranscendentalequations(A.19)forl ∈ {0..10}. . . . . . . . . . 137
(cid:16) (cid:17)
A.2 Slopeofthelinearinterpolants m = h∗(λl)−h∗(λl−1) joiningconsecutivepoints
l λ−λ
l l−1
ofsetP = {(λ ,h∗(λ )) : l ∈ Z+ ∪{−1}},for(cid:15) = {3, 1}. . . . . . . . . . . 139
l l 4 4
x