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Logistic tasks are aimed at the optimal distribution of material, energy, financial and human resources. This research has a narrow field aimed at optimal management of financial resources and their redistribution. Specifically, a reinvestment policy model is derived by maximizing the profit of a business entity. Reinvestment is done with risk-free assets, but they have different maturity periods. This makes it difficult to assess the optimal investment strategy, as reinvestment can be done at the end of the maturity period. This study develops a model for a dynamic control process, which leads to the formalization of a discrete integer time optimization problem. Its solution gives a sequence of investments and a total optimal return. The solution to the problem is illustrated in an EXCEL environment. The added value of this study stems from the formalization and quantification of the model for the reinvestment strategy in the optimization problem.

An investment policy is suggested about assets on real estate markets. Such analysis recommends investments in non-financial assets and optimization of the results from such decisions. The formalization of the investment policy is based on the portfolio theory for asset allocation. Two main criteria are applied for the decision making: return and risk. The decision support is based on Mean-Variance portfolio model. A dynamical and adaptive investment policy is derived for active portfolio management. Sliding procedure in time with definition and solution of a set of portfolio problems is applied. The decision defines the relative value of the investment to which real estates are to be allocated. The regional real estate markets of six Bulgarian towns, which identify the regions with potential for investments, are compared. The added value of the paper results in development of algorithm for a quantitative analysis of real estate markets, based on portfolio theory.

The urban traffic control optimization is a complex problem because of the interconnections among the junctions and the dynamical behavior of the traffic flows. Optimization with one control variable in the literature is presented. In this research optimization model consisting of two control variables is developed. Hierarchical bi-level methodology is proposed for realization of integrated optimal control. The urban traffic management is implemented by simultaneously control of traffic light cycles and green light durations of the traffic lights of urban network of crossroads.

The paper realizes inclusion of probabilistic measure for risk, VaR (Value at Risk), into a portfolio optimization problem. The formal analysis of the portfolio problem illustrates the evolution of the portfolio theory in sequentially inclusion of different market characteristics into the problem. They make modifications and complications of the portfolio problem by adding various constraints to consider requirements for taxes, boundaries for assets, cardinality constraints, and allocation of the investment resources. All these characteristics and parameters of the investment participate in the portfolio problem by analytical algebraic relations. The VaR definition of the portfolio risk is formalized in a probabilistic manner. The paper applies approximation of such probabilistic constraint in algebraic form. Geometrical interpretation is given for explaining the influence of the VaR constraint to the portfolio solution. Numerical simulation with data of the Bulgarian Stock Exchange illustrates the influence of the VaR constraint into the portfolio optimization problem.

The paper makes analytical overviews of the Markowitz portfolio and the Capital Asset Pricing models and motivates the advances of the Black-Litterman (BL) one. This overview implies that for a small set of assets the BL model needs the characteristics of a specific market point, which cannot be taken from a global market index. The paper derives analytic relations for the new specific market point with analytical approximation of the efficient frontier. The BL model insists also expert views, which influence the portfolio solution. The paper derives formalization of the expert views from the difference between the evaluated implied returns and historical mean assets returns. Such form of expert views makes modifications of the BL model. This allows comparisons between Markowitz (MV) and BL portfolio performance. Benefits of this research are demonstrated with market data and comparison of the MV and BL portfolio results.

The general contribution of this research is the implementation of new formal type of relative view, which has been added to the Black-Litterman Model (BLM) for asset management. It is well known that the BLM integrates both historical data about the assets’ returns and subjective views given by experts and investors. Such complicated model is expected to give more realistic assessment about the dynamical behavior of the stock exchanges. The BLM applies both absolute and relative views about the asset returns. The paper proves that the currently applied relative views with equal weights are equivalent to assess the risk of a virtual portfolio with these assets of the view which participate with equal weights. The paper extends this form of views, applying non-equal weights of the assets. This new formal description has been tested on a market, containing ten world known indices for a 10 years period. The calculations which have been provided give benefits to the suggested non-equal weighted form of subjective views. It gives more conservative results and decreases the portfolio risk supporting the same level of returns, provided by the average market behavior.

The increase of the utilization of public rail transportations is searched in directions for redistribution of the passenger travels between rail and bus transportation. The rail transport benefits by redistribution of the transportation flows on paths, predominantly supported by rails. The redistribution of the transportation is formalized by bi-level optimization problem. The upper level optimization estimates the maximal flow, which can be transported through a transportation network, supported both by bus and rail transports. The lower level optimization gives priority to the rail transport by decreasing the costs of flow distribution, using rail transport. This bi-level optimization problem was applied for the case of optimization of the rail exploitation in Bulgaria, defining priorities in transportation of the National transport scheme.

The Intelligent Transportation System (ITS) is used as a term for integrating requirements and functionalities towards transportation systems, which in urban environment raises complex exploitation and control problems. Important part of the ITS is the control which has to be applied for traffic flows. The control processes are strongly linked with requirements and targets for optimization of the transportation behavior. The paper applies new optimization formal description of control by bi-level optimization. Except the trivial traffic lights control, the bi-level formalization allows additional traffic characteristics to be defined like maximal/minimal values. The paper defines, solves and provides numerical simulations for minimization of the vehicle queues in front of the traffic lights. Such bi-level optimization problem is applied simultaneously for maximization the traffic flows on arterial and important directions of the urban transportation network. The formal description of the bi-level problem is provided. The results of the bi-level control have been compared with the cases of single optimization of the vehicles queues. The simulation results prove that the bi-level problem gives benefits satisfying an additional goal, which improves additional characteristic of the transport behavior. The bi-level optimization formalism can be used as a tool for implementation of integration of ITS control policies.

The paper defines and solves a Linear-Quadratic-Gaussian (LQG) optimization problem addressing real time control policy of Urban Transportation Network (UTN). The paper presents UTN model definition, analysis and LQG optimization problem definition, resulting in special problem structure. A real application for UTN situated in Sofia, Bulgaria along Yosif Gurko street was provided for testing this control policy.

This paper applies a bi-level formalism for the optimal control of an urban transportation network. The well known store-and-forward model in traffic control is utilized in order to increase the control space of the optimization problem. Mainly, the store-and-forward models apply the split as a control argument, assuming the traffic light cycle as a constant parameter. The paper shows that by using a bi-level formalism the control problem can be defined within increased control space comprising both the split and the cycle. Both are found as optimal solutions of a bi-level optimization problem.

The operation of a complex system like a transportation network is considered with respect to the opportunities to identify the application of autonomic properties. The autonomic features of self-properties are analyzed. A multilevel approach is suggested for the formalization of the transport operation. The integration of relevant optimization problems is also considered in the framework of a multilevel, hierarchical scheme of control. The application of bi-level formalism in the transportation systems gives quantitative assessment of the control processes in the traffic control system. The multilevel approach allows the increase of the solution space of a complex optimization problem with an additional traffic control variable, which in the classical optimal formalization participates with fixed parameters in the optimization problem. The benefit of the multilevel control approach is tested in a real network of crossroad sections.