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(Max,+) model for alignment selection and schedule optimization in a flow network

Abstract:

The following work presents an algebraic optimization model for the problem of scheduling operations in an oil seaport with the purpose of simultaneously minimizing costs due to late client service, as well as selecting the pipeline alignments (i.e. paths) in order to serve each client. The model is based on (max, +) algebra, and alignment selection constraints are easily incorporated into a generic constraint modeling several phenomena in the system. The main contribution of this work is the mathematical formulation of a concise (max, +) model which covers several phenomena, such as conflict, time dependencies and resource assignment, through one constraint structure. Moreover, this structure is quite flexible and intuitive for the modeler. The results can be adapted to a wide spectrum of optimization problems.