Determination of optimal values for the technical characteristics of construction machinery unit with application of fractional linear programming

Paper covers issues connected to the determination of the technical characteristics of construction machinery unit performing a certain category of work. On the basis of the results of the review and analysis of scientific works concerning the problem under consideration the key disadvantages have been identified for the existing techniques. Optimization model for determination of the technical characteristics of construction machinery unit has been created. Initial form of the model is not linear toward unknown variables but it can be transformed to the linear form that allows application of simplex method for efficient solution of the problem. The created model has been implemented on a practical case – the obtained results indicated the adequacy of the developed tool.

Tropical Lexicographic Optimization: Synchronizing Timed Event Graphs

Tropical Algebra is used to model the dynamics of Timed Event Graphs (TEG), a particular class of Timed Discrete-Event System (TDES) in which we are interested only in synchronization and delay phenomena. Whenever this TEG has control inputs, we can use them to control the synchronization of the system to achieve some objective. Thus, this paper formulates a framework based on tropical algebra and lexicographic optimization to synchronize a TEG when dealing with many synchronization objectives that are ranked in previous priority order. We call this kind of problem the Tropical Lexicographic Synchronization Optimization (TLSO). This work develops a solution to this problem, based on Tropical Fractional Linear Programming (TFLP) and lexicographic optimization concepts. In this way, the basics of tropical algebra are determined, including essential terms to this paper, such as left and right residuations, and the following stages of the solution to the TLSO problem are explained. Therefore, this work presents a general framework based on structured algebraic models with application to TEG synchronization. By synchronization, we mean balancing and organizing events chronologically in order to achieve the desired goal. So, we are dealing with concepts closely related to symmetry ones. An illustrative numerical example is presented, which demonstrates the implementation of the proposed algorithms. The acquired results confirm the efficiency of the proposed methodology. Codes used for implementing the algorithms are listed in the appendix section of the article.

An Approach for Solving Linear Fractional Programming Problems

Linear fractional programming problems are useful tools in production planning, financial and corporate planning, health care and hospital planning and as such have attracted considerable research interest. The paper presents a new approach for solving a fractional linear programming problem in which the objective function is a linear fractional function, while the constraint functions are in the form of linear inequalities. The approach adopted is based mainly upon solving the problem algebraically using the concept of duality and partial fractions and an example is given to clarify the developed method.