George Otieno Orwa


In this thesis, Vehicle Routing Problems (VRPs) subject to time restrictions andtime dependent congestions are discussed into adequate depth. Time dependentcongestion increases the complications of the problems and makes it challengingeven to find feasible solutions,Y & R. (1987) Y. & Gershwin (1991). This meansthat it becomes difficult to develop a routing procedure that will lead to shortestdelays. Said otherwise, it becomes very difficult to find the routes that would leadto the Feasibilty Routes. It also attempts to incorporate other factors that havebeen known to affect passenger transport in developing a model that can be usedin decision making regarding the management of a fleet of vehicles that herein,are assumed to be registered in a company.It is of concern that problems in which other variables that affect passenger Vehicle-Routing and Scheduling other than Time Restrictions and a mention of time dependentcongestions have not been looked at by Operational Researchers, M.B.M.(1988),Courant (1964),T & Z (1987) and Adan & Wal (1989). With this void inmind, in the first part of this thesis we identify a very robust property, which wechoose to refer to as the monotone property of the arrival times. This propertydoes allow for the simplification of the said complications arising as a result ofintroducing the aspect of Time-Dependent Congestions in the VRPs.It also enhances the performance of existing heuristics, by creating an enablingenvironment for the introduction of three Feasibility Conditions that are demonstratedin this thesis. These Feasibility Conditions greatly reduces the computationalburden involved in the development of proposed procedures. This is one ofthe contributions of this thesis to the field of Operational Research. In the secondpart of the thesis, insights into what causes congestion, what determines the timeand locations of traffic flow breakdown, and even how the congestion propagatesthrough the network, are the essential issues considered.In this context, we have in the thesis proposed a method of considering mostof these factors that determine the existence of passenger queues at the varioustermini in order to come up with a traffic flow model that will ease congestion.The proposal is tested using the Weibull distribution since it is an extreme valuedistribution and hence provides an allowance for proper extrapolation of resultsand further, it has allowance for many parameters, atleast three, allowing for theincorporation of other variables. For exact financial implications of how thesefactors affect the transport system, we have borrowed some concepts from FinancialMathematics, especially that of the Net Present Value (NPV), and used itin derivation of the model that incorporates other factors that affect passengertransport.Finally, in the thesis, empirical evidence of better performance for the proposedmodels in comparison to existing methods of addressing similar problems is provided.A conclusion that entails opening windows for future research in the VehicleRouting Problems is given


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