Unternehmensforschung

Let $$T \, =\, \{T_1, T_2, \ldots, T_n\}$$ be a set of n independent tasks and $$\mathcal{P}=\{P_1, P_2,\ldots, P_m\}$$ a set of m processors. During each time instant, each processor can be used by a single task at most. A schedule is for each task an allocation of one or more time intervals to one or more processors. A schedule is said to be optimal if it minimizes the maximum completion time. We say a schedule S has the machine saturation property (MS property) if, at any time instant of task execution, all the machines are simultaneously busy. In this paper, we analyze the conditions under which a parallel scheduling system allows a schedule with the MS property. While for some simple models the analytical conditions can be easily stated, a graph model approach is required when conflicts of processor usage are present. For this reason, we define the class of saturated graphs that correspond to scheduling systems with the MS property. We present efficient graph recognition algorithms to verify the MS property directly on some classes of saturated graphs

In this paper, the feasible type SQP method is improved. A new algorithm is proposed to solve nonlinear inequality constrained problem, in which a new modified method is presented to decrease the computational complexity. It is required to solve only one QP subproblem with only a subset of the constraints estimated as active per single iteration. Moreover, a direction is generated to avoid the Maratos effect by solving a system of linear equations. The theoretical analysis shows that the algorithm has global and superlinear convergence under some suitable conditions. In the end, numerical experiments are given to show that the method in this paper is effective.

Chúng tôi giới thiệu một cơ chế lọc để đảm bảo sự hội tụ cho các phương pháp Lagrange mở rộng trong lập trình phi tuyến. Ngược lại với các phương pháp Lagrange mở rộng truyền thống, cách tiếp cận của chúng tôi không yêu cầu sử dụng các chuỗi buộc phải cung cấp để đưa sai số bậc nhất về zero. Thay vào đó, chúng tôi sử dụng một bộ lọc để đưa các thước đo tối ưu về zero. Thuật toán của chúng tôi linh hoạt theo nghĩa cho phép các bước lập trình bậc hai có ràng buộc bằng nhau để tăng tốc độ hội tụ cục bộ. Chúng tôi cũng bao gồm một giai đoạn khôi phục tính khả thi cho phép phát hiện nhanh các vấn đề không khả thi. Chúng tôi cung cấp một bằng chứng hội tụ cho thấy thuật toán của chúng tôi hội tụ đến các điểm tĩnh bậc nhất. Chúng tôi cũng cung cấp các kết quả số sơ bộ cho thấy hiệu quả của phương pháp mà chúng tôi đề xuất.

The allocation problem of rewards/costs is a basic question for players, namely, individuals and companies that are planning cooperation under uncertainty. The involvement of uncertainty in cooperative game theory is motivated by the real world in which noise in observation and experimental design, incomplete information and vagueness in preference structures and decision-making play an important role. In this study, a new class of cooperative games, namely, the cooperative bubbly games, where the worth of each coalition is a bubble instead of a real number, is presented. Furthermore, a new solution concept, the bubbly core, is defined. Finally, the properties and the conditions for the non-emptiness of the bubbly core are given. The paper ends with a conclusion and an outlook to related and future studies.

Bin packing problems are at the core of many well-known combinatorial optimization problems and several practical applications alike. In this work we introduce a novel variant of an abstract bin packing problem which is subject to a chaining constraint among items. The problem stems from an application of container handling in rail freight terminals, but is also of relevance in other fields, such as project scheduling. The paper provides a structural analysis which establishes computational complexity of several problem versions and develops (pseudo-)polynomial algorithms for specific subproblems. We further propose and evaluate simple and fast heuristics for optimization versions of the problem.

Stochastic single-machine scheduling problems with special tree-like GERT precedence constraints and expected weighted flow time or maximum expected lateness as objective functions are considered. To obtain polynomial algorithms for these problems, Smith's ratio rule and Lawler's rule for the deterministic problems 1¦outtree¦Σw v C v and 1¦prec¦f max , respectively, are generalized.

Ermittlung des günstigsten Bestellzeitpunktes, wenn die Zeitspanne zwischen der Bestellung und der Lieferung eine Zufallsveränderliche mit bekannter Verteilung ist.

Numerical evaluation of compound distributions is an important task in insurance mathematics and quantitative risk management. In practice, both recursive methods as well as transform based techniques are widely used. We give a survey of these tools, point out the respective merits and provide some numerical examples.

After providing minimax strategy in simple and composite hypothesis testing for optimal simple inspection plan design, this paper examines Bernoulli', Gauss' and Poisson' approximations.