The article investigates the problem of task assignment of vehicles for a production company. The presented problem is a complex decision-making issue which has not been analyzed in the literature before. Two stages must be passed through in order to solve the task assignment problem of the vehicles for the production company. The first stage is to designate the tasks, the other one is to determine the number of the vehicles that is needed to perform these tasks. The task in the analyzed problem is defined as transporting the cargo from the suppliers to the warehouses and from the warehouses to the production company. The number of the tasks depends on the type of the vehicle which carries out a given task. In order to solve the presented problem, the mathematical model has been developed, i.e., decision variables, constraints, and criterion functions. There are three types of decision variables occurring in the model, which means that this problem is quite complex. The first type of the decision variables determines the volume of the cargo which flows among the facilities on a given working day, the second type of the decision variables determines the use of a given type of the vehicle in the task, and the third type of the decision variables determines the number of the vehicles which perform the task. The criterion functions take the following form: the fuel consumption costs, the transition costs of the cargo via the warehouses, the purchase costs of the cargo, and the task completion time. In order to solve the task assignment problem of the vehicles, a genetic algorithm has been developed. The proposed method of task assignment solution is unique due to the coding method of individuals and related recombination procedures. The construction stages of this algorithm are presented. The algorithm has been verified by the use of the real input data. The developed model and method of its solution are unique in the application to the service of manufacturing enterprises. Due to the high efficiency and multi-aspect approach, it can be applied in enterprises of various industries as support for decision-makers in the optimization of resources.

The article presents an approach to assessing the reliability of logistics processes implemented in supply chains in terms of time losses resulting from the selection of a variant of material flows in the supply chain. In order to define this indicator, a mathematical model of the supply chain has been developed, i.e. the parameters of the research problem, the decision variables, the constraints and the evaluation criteria. The method of evaluating the reliability of the system is presented in diagram form. The algorithm was verified based on experimental data. In order to evaluate the reliability of the logistic processes for the sample supply chain, a simulation model was developed that determines the time losses in the points and linear elements of the examined chain. Time losses are dictated by traffic delays resulting from traffic congestion on particular sections of the route and road junctions and delays in point elements in the supply chain.

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This paper presents the problem of the assessment of the supply chains in the context of their effectiveness. In this paper the concepts of a supply chain and effectiveness were characterized. The supply chain is a structure of entities which are connected with each other by the use of material and financial flows and functional, structural, technological, economic and information dependencies. Entities such as: suppliers, final recipients, entrepreneurs, warehouse facilities, supply centers, logistics operators, carriers, etc. perform material flows from suppliers to recipients. The concept of efficiency, in general terms, refers to economic rationality and means the relationship between the achieved or expected effects and the expenditures incurred. Additionally, indicators of measuring the effectiveness of the supply chain were described. In order to assess the effectiveness of the supply chain the decision model was developed. Optimization is crucial in decision support systems. The development of an appropriate model for mapping the behavior of a real object or system and formulating an optimization task is a necessary activity in effective management. This is even more important if we want to be competitive. Along with the development of decision support systems, as well as the development of systems for data acquisition on the system functioning, which feed optimization models in ever more detailed form, complex decision models are created that take into account many optimization criteria and require a large amount of data. It allows, however, to ensure the sustainable development of the system and simultaneous implementation of its basic tasks. The main aim of this paper is to present the stages and assumptions of the model for assessing the effectiveness of the supply chain. The main data input, constraints of the model, the criteria functions were determined.

The aim of the article was to develop a tool to support the process of planning and managing aircraft (ac) maintenance. Aircraft maintenance management has been presented for scheduled technical inspections resulting from manufacturers’ technical documentation for ac. The authors defined the problem under investigation in the form of a four-phase decisionmaking process taking into account assignment of aircraft to airports and maintenance stations, assignment of crew to maintenance points, setting the schedules, i.e. working days on which aircraft are directed to maintenance facilities. This approach to the planning and management of aircraft maintenance is a new approach, unprecedented in the literature. The authors have developed a mathematical model for aircraft maintenance planning and management in a multi-criteria approach and an optimisation tool based on the operation of a genetic algorithm. To solve the problem, a genetic algorithm was proposed. The individual steps of the algorithm construction were discussed and its effectiveness was verified using real data.