Joint decision of condition-based maintenance and production scheduling for multi-component systems

In this study, system maintenance and production scheduling are jointly decided to solve the problems of resource idleness and time cost increase due to system maintenance in the processing of production scheduling. Based on the previous research on the integration of scheduling and maintenance of single machine and multi machine, considering the deterioration and economic dependence of each component in the system, a joint strategy of multi component condition-based maintenance combined with production scheduling is formulated. All the maintenance combinations and probability calculation formulas in the production scheduling process are developed using the deterioration state space partition method, and the probability density function and its numerical solution method are derived. A joint decision model is established to minimize the total weighted expected completion time. Finally, taking the KS5 adjustable multi axis tapping machine as an example, numerical experiments were conducted to verify the correctness of the proposed strategy and the established model.

Offensive, Defensive, and Generic Advertising Strategies in a Dynamic Oligopolistic Market

In today’s highly competitive business environment, advertisement plays an influential role in attracting customers and increasing market share. Companies adopt different advertising strategies in a competitive market, such as offensive, defensive, and generic, to keep and increase their market share. Researchers have generally modeled this problem using a dynamic differential game. All previous research studies have focused on finding these strategies in a duopoly market. Also, to simultaneously determine the optimal equilibrium strategy for these three strategies, the model is designed as a symmetric game due to the ease of solving. In contrast with the previous researches, the purpose of this paper is to present and solve an asymmetric game model to determine the optimal offensive, defensive, and generic advertising strategies in an oligopoly market. The proposed model’s objective is to obtain the maximum equilibrium profit for each company at any moment regarding the market share of each company and those of competitors. A numerical solution method based on the Pontryagin’s maximum principle is developed to solve the model. Then, the proposed model is solved for a triopoly market. Also, the sensitivity of the results to changes in model parameters has been investigated. The obtained results denote that in markets with more than two players under the asymmetric game, the proposed model can prescribe the optimal type of offensive, defensive, and generic advertising strategies.

A solution framework for linear PDE-constrained mixed-integer problems

We present a general numerical solution method for control problems with state variables defined by a linear PDE over a finite set of binary or continuous control variables. We show empirically that a naive approach that applies a numerical discretization scheme to the PDEs to derive constraints for a mixed-integer linear program (MILP) leads to systems that are too large to be solved with state-of-the-art solvers for MILPs, especially if we desire an accurate approximation of the state variables. Our framework comprises two techniques to mitigate the rise of computation times with increasing discretization level: First, the linear system is solved for a basis of the control space in a preprocessing step. Second, certain constraints are just imposed on demand via the IBM ILOG CPLEX feature of a lazy constraint callback. These techniques are compared with an approach where the relations obtained by the discretization of the continuous constraints are directly included in the MILP. We demonstrate our approach on two examples: modeling of the spread of wildfire and the mitigation of water contamination. In both examples the computational results demonstrate that the solution time is significantly reduced by our methods. In particular, the dependence of the computation time on the size of the spatial discretization of the PDE is significantly reduced.

Efficient Planning and Solving Algorithm of S -Shape Acceleration and Deceleration

S -shape acceleration and deceleration are the most widely used flexible acceleration and deceleration method in the current CNC system, but its velocity solution equation contains irrational terms, which create a more complicated solution process. When analyzing the solution process of the S -shape acceleration and deceleration directly, using a traditional numerical solution method, the phenomenon of “solving the interval jump” arises, which is the main reason for low efficiency and poor stability of the solution. According to the S -curve profile and solution, the concept of separating the curve profile recognition from the velocity solution was proposed, and a method of quickly identifying the interval of the solution location was introduced. Through the method mentioned above, the complete acceleration and deceleration curve parameters can be obtained through a one-time plan and a one-time solution, and the solution efficiency and stability are guaranteed; solving the Newton problem depends too much on the initial value of Newton velocity, which not only retains the speed advantage of the Newton method but also uses the downhill factor to ensure its convergence. Through the simulation comparison and analysis, the efficiency, stability, and universality of the method are verified.

Calculation of deflection of a composite wire by the numerical method of point masses with computer simulation

При увеличении скорости и глубины траления необходимо учитывать силы гидродинамического сопротивления ваеров, так как они при этих параметрах достигают значительных величин. Композитные ваера применяются на современных рыбопромысловых судах. В отличие от твердых тел гибкий композитный ваер меняет свою форму в процессе эксплуатации и обладает всеми свойствами канатно-веревочных изделий. В статье рассмотрен метод расчета формы и напряжений в ваере рыболовного трала под действием внешних сил с учетом изгибной жесткости. В отличие от метода расчета без учета изгибной жесткости, при расчете с учетом изгибной жесткости для каждого узла расчетной схемы вводится дополнительная связь и решается система дифференциальных уравнений при заданных начальных и граничных условиях. Рассмотрены численный метод решения, алгоритм которого состоит из двух вложенных циклов, и условия выхода из циклов. Приведен сравнительный анализ результатов численных и натурных экспериментов на предмет выявления погрешностей вычислений. With an increase in the speed and depth of trawling, it is necessary to take into account the forces of the hydrodynamic resistance of the wires, since they reach significant values with these parameters. Composite wires are used with modern fishing vessels. In contrast to solids, a flexible composite wire changes its shape during operation and has all the properties of rope products. The article discusses a method for calculating the shape and stresses in a fishing trawl wire under the action of external forces, taking into account bending stiffness. In contrast to the calculation method without taking into account the bending stiffness, when calculating with an account of the bending stiffness, an additional connection is introduced for each node of the calculation scheme and a system of differential equations is solved for given initial and boundary conditions. A numerical solution method has been reviewed, the algorithm of which consists of two embedded cycles, and the conditions for exiting the cycles. A comparative analysis of the results of numerical and full-scale experiments for the identification of calculation errors has been given.