Thesis (MSc)--Stellenbosch University, 2015. / ENGLISH ABSTRACT: INTRODUCTION The Western Cape Government (WCG) uses Vehicle Operating Cost (VOC) as part of their Road Management System since 1992. VOC is used in the process of prioritisation of maintenance projects as well as for the identification of economically viable maintenance strategies and is thus an integral part of the system. In 2001 changes to the VOC calculation methodology in the system to Highway Development and Management (HDM-4) system methodology occurred. The reasons were twofold – to bring the calculation method in line with world trends and due to lack of updated cost factors used in the previous methodology. In October 2001 a model was implemented with riding quality (IRI) as independent variable. This model was partly based on regression table data. As no geometric/topography data, defined as Terrain data, was available at this stage, Terrain was ignored. In 2006 WCG Systems were updated with Global Positioning System (GPS) data and a process to classify or categorise Terrain was initiated, thus providing the opportunity to include Terrain. As part of the redevelopment to include Terrain, it was decided to re-evaluate the vehicle fleet. METHODOLOGY Various alternative methods to develop the Modified Simplification equations were available and evaluated, e.g. regression or direct mathematical substitution. HDM-4 requires the input of Vehicle Type dependent cost parameters that is based on real vehicles. The WCG required that changes to these dependent parameters is feasible, so that they can be updated periodically. A set of equations therefore needed to be developed, allowing the input of Vehicle Type dependent parameters and the subsequent calculation of VOC with riding quality (IRI) as independent variable. This renders the use of regression analysis untenable. Composition of the vehicle fleet on each road section is required to utilise HDM-4 for analyses. In order to simplify calculations, different traffic strata was defined, i.e. Business, Commuter, Rural and General. In the evaluation of the Vehicle it is this strata and data from permanent counting stations that is used to compile a Vehicle fleet. MODEL DEVELOPMENT The Modified Simplification to include Terrain results in 48 combinations of Vehicle Type, Surface Type and Terrain Type for the basic equation of VOC. VOC = TCav + PARTSCOST + LABOURCOST +DEPCSTav ( )´ Length of road segment 1000 +(FuelCostav +OilCostav )´ Length of road segment av TC -Tyre Cost PARTSCOST -Parts Cost LABOURCOST - Labour Cost av DEPCST - Depreciation Cost av FuelCost -Fuel Cost av OilCost - Oil Cost The variables in VOC are defined by a couple of equations. For explanatory purposes a numeric example is presented. CONCLUSION AND RECOMMENDATION The implementation of this Modified Simplification has assisted not only the WCG, but also other entities, that also use the VOC (published annually) based on these principles. Interested parties have the option to include Terrain in their implementation. Caution should be taken when using the Modified Simplification, as it is important that the principles used to simplify HDM-4 apply to the implementation and the business rules of the Management system of the user. The current development will not require a redevelopment due to any vehicle fleet change in future as the decision to simplify all defined Vehicle Types in HDM-4 allows the new fleet to be updated. Recommendation for further research and development include: • Standalone function that is already considered by the WCG • Investigating Published Vehicle data • Economic vehicle data for use in specific applications / AFRIKAANSE OPSOMMING: INLEIDING Sedert 1992 gebruik die Wes-Kaapse Regering (WCG) voertuiggebruikskoste (VOC) as deel van hul Plaveisel Bestuurstelsels. VOC word gebruik in die proses van prioritisering van die instandhoudingprojekte sowel as vir die identifisering van ekonomies-vatbare instandhouding-strategieë en is dus 'n integrale deel van die stelsel. In 2001 is daar besluit om oor te skakel na die berekeningsmetode van Highway Development and Management (HDM-4). Die redes was tweeledig – om die berekeningsmetode in lyn met die wêreld tendense te bring; en as gevolg van 'n gebrek aan opgedateerde koste-faktore in die voorheen-gebruikte metode. In Oktober 2001 is 'n VOC-model, met rygehalte (IRI) as onafhanklike veranderlike geïmplementeer. Hierdie model was gedeeltelik gebaseer op regressie tabel data. Aangesien daar geen geometriese/topografiese data (gedefiniëer as terreindata) beskikbaar was nie, is die terrein geïgnoreer. In 2006 is WCG Stelsels opgedateer met Globale Positionering Stelsel (GPS) data en 'n proses om terrein te klassifiseer is van stapel gestuur. Deur die verandering in beskikbare data, is die geleentheid om terrein in te sluit in die VOC model geskep. As deel van die insluiting van herontwikkeling om terrein in te sluit, is daar besluit om die voertuigvloot te her-evalueer. METODOLOGIE Verskeie alternatiewe metodes om die Gewysigde Vereenvoudiging-vergelykings te ontwikkel was beskikbaar en is geëvalueer, bv. regressie of direkte wiskundige vervanging en vereenvoudiging. HDM-4 se voertuigafhanklike koste-parameters is op werklike voertuie gebaseer. Die WCG het vereis dat hierdie afhanklike parameters veranderbaar moet wees, sodat hulle dit van tyd tot tyd kan opdateer. Dit was dus nodig om 'n stel vergelykings te ontwikkel met die tipe voertuigkosteafhanklike parameters as insette. Verder moes alle vergelykings weer in terme van rygehalte wees. Dit maak die gebruik van regressie-analise ononderhoubaar. Samestelling van die voertuigvloot op elke padseksie is 'n vereiste om HDM-4 aan te wend vir ontledingsdoeleindes. Ten einde berekeninge te vereenvoudig is verskillende verkeerstrata gedefinieer, naamlik Besigheid, Pendel, Landelik en Algemeen. In die evaluering van die Voertuig is dit hierdie strata en data uit permanente telstasies wat gebruik word om 'n voertuigvloot saam te stel. MODELONTWIKKELING Die Gemodifiseerde Vereenvoudiging, insluitend terrein, het 48 kombinasies van tipe voertuig, oppervlak en terrein vir die basiese vergelyking van VOC: VOC = TCav + PARTSCOST + LABOURCOST +DEPCSTav ( )´ Length of road segment 1000 +(FuelCostav +OilCostav )´ Length of road segment TCav - Bandkoste; PARTSCOST - Onderdele-koste; LABOURCOST - Arbeidskoste; av FuelCost - Brandstofkoste; av DEPCST - Waardeverminderingskoste; av OilCost - Oliekoste Die veranderlikes in VOC word gedefinieer deur 'n paar vergelykings. Vir verduidelikende doeleindes word 'n numeriese voorbeeld ingesluit. GEVOLGTREKKING EN AANBEVELING Die implementering van hierdie Gewysigde Vereenvoudiging het nie net die WCG nie, maar ook ander entiteite wat ook die VOC (jaarliks gepubliseer) gebruik, bygestaan. Belangstellendes het die opsie om die terrein in hul implementering in te sluit. Dit is belangrik om ag te slaan op die beginsels wat gebruik is om HDM-4 te vereenvoudig tesame met die besigheidsreëls van die Gewysigde Vereenvoudiging, indien dit gebruik word. Die huidige model vereis nie 'n herontwikkeling as gevolg van enige voertuigvloot verandering in die toekoms nie. As gevolg van die besluit om alle gedefinieerde tipes voertuig te vereenvoudig, kan die voertuigvloot keuse net in die stelsel opgedateer word. Aanbeveling vir verdere navorsing en ontwikkeling sluit in: • Alleenstaande funksie wat reeds deur die WCG beskou word • Ondersoek Gepubliseerde Voertuig data • Gebruik van Ekonomiese voertuigdata vir sekere toepassings

While decision-making under uncertainty is a major universal problem, its implications in the field of transportation systems are especially enormous; where the benefits of right decisions are tremendous, the consequences of wrong ones are potentially disastrous. In the realm of highway systems, decisions related to the highway configuration (number of lanes, right of way, etc.) need to incorporate both the traffic demand and land price uncertainties. In the literature, these uncertainties have generally been modeled using the Geometric Brownian Motion (GBM) process, which has been used extensively in modeling many other real life phenomena. But few scholars, including those who used the GBM in highway configuration decisions, have offered any rigorous justification for the use of this model. This thesis attempts to offer a detailed analysis of various aspects of transportation systems in relation to decision-making. It reveals some general insights as well as a new concept that extends the notion of opportunity cost to situations where wrong decisions could be made. Claiming deficiency of the GBM model, it also introduces a new formulation that utilizes a large and flexible parametric family of jump models (i.e., Lévy processes). To validate this claim, data related to traffic demand and land prices were collected and analyzed to reveal that their distributions, heavy-tailed and asymmetric, do not match well with the GBM model. As a remedy, this research used the Merton, Kou, and negative inverse Gaussian Lévy processes as possible alternatives. Though the results show indifference in relation to final decisions among the models, mathematically, they improve the precision of uncertainty models and the decision-making process. This furthers the quest for optimality in highway projects and beyond.

While decision-making under uncertainty is a major universal problem, its implications in the field of transportation systems are especially enormous; where the benefits of right decisions are tremendous, the consequences of wrong ones are potentially disastrous. In the realm of highway systems, decisions related to the highway configuration (number of lanes, right of way, etc.) need to incorporate both the traffic demand and land price uncertainties. In the literature, these uncertainties have generally been modeled using the Geometric Brownian Motion (GBM) process, which has been used extensively in modeling many other real life phenomena. But few scholars, including those who used the GBM in highway configuration decisions, have offered any rigorous justification for the use of this model. This thesis attempts to offer a detailed analysis of various aspects of transportation systems in relation to decision-making. It reveals some general insights as well as a new concept that extends the notion of opportunity cost to situations where wrong decisions could be made. Claiming deficiency of the GBM model, it also introduces a new formulation that utilizes a large and flexible parametric family of jump models (i.e., Lévy processes). To validate this claim, data related to traffic demand and land prices were collected and analyzed to reveal that their distributions, heavy-tailed and asymmetric, do not match well with the GBM model. As a remedy, this research used the Merton, Kou, and negative inverse Gaussian Lévy processes as possible alternatives. Though the results show indifference in relation to final decisions among the models, mathematically, they improve the precision of uncertainty models and the decision-making process. This furthers the quest for optimality in highway projects and beyond.