供应链中生产和运输协调调度问题初探

提出了解决供应链中生产和航空运输协调调度问题的理论框架.基于对生产调度和航空运输调度彼此制约关系的分析,协调调度问题被分解为两个子调度问题.建立了航空运输子调度问题的整数规划模型,并证明了该问题为NP完全问题.提出了基于倒排调度方法(backward scheduling method)的调度算法解单机生产调度子问题.     

Direct method of solution for general boundary value problem of the Laplace equation

A general boundary value problem for two-dimensional Laplace equation in the domain enclosed by a piecewise smooth curve is considered. The Dirichlet and the Neumann data are prescribed on respective parts of the boundary, while there is the second part of the boundary on which no boundary data are given. There is the third part of the boundary on which the Robin condition is prescribed. This problem of finding unknown values along the whole boundary is ill posed. In this sense we call our problem an inverse boundary value problem. In order for a solution to be identified the inverse problem is reformulated in terms of a variational problem, which is then recast into primary and adjoint boundary value problems of the Laplace equation in its conventional form. A direct method for numerical solution of the inverse boundary value problem using the boundary element method is presented. This method proposes a non-iterative and unified treatment of conventional boundary value problem, the Cauchy problem, and under- or over-determined problems.     

球约束凸二次规划的一个算法

针对球约束凸二次规划问题，利用Lagrange对偶将其转化为无约束优化问题，然后运用单纯形法对其求解，获得原问题的最优解。最后，对文中给出的算法给出了论证。     

基于TRIZ理论的套袋机套袋装置优化设计

目的解决现有套袋机套袋装置在套袋过程中薄膜内袋容易产生折角的问题。方法利用TRZI理论中功能模型及因果链分析对初始问题进行全面分析,找到根本问题后,再将根本问题转化为TRIZ问题模型,然后利用TRIZ中解决问题的工具找到多个解决方案模型,并对方案模型进行可用性评估。结果将评估所得的最优方案进行实施,薄膜内袋折角的问题被解决,双层袋合格率达到99.5%。结论利用TRIZ理论中的一系列工具对薄膜内袋折角问题进行转化,建立了解决方案模型,选取了最优方案进行实施,成功解决了薄膜内袋折角问题。     

Role of similarity measures in PCB grouping procedures

The problem of grouping printed circuit boards (PCBs) for simultaneous assembly on electronic assembly machines is an extension of the set-covering problem. A general approach based on cluster analysis and measure of similarity between PCBs is suggested as a basis of PCB grouping. The approach is independent of the specific similarity measure used. We show that, due to the analogy between this problem and the problem of machine cell formation in group technology, similarity measures developed for the second problem are useful as building blocks in a general framework that solves the PCB grouping problem.     

A review of one aspect of the thermal-explosion theory

The historical development of the thermal-explosion theory is examined and reviewed, It is shown that the original formulation of the problem by Semenov accurately defines the phenomenon and explains the reason for the explosion. He showed that, when the heat generation within the solid exceeds the heat dissipation to the surroundings, explosion occurs. Frank-Kamenetskii’s disapproval of Semenov’s logic theorized that the difference between the temperatures at the center of the solid and its surface is the cause of the explosion. His famous and ingenious small-temperature model and the solution to the differential equation that resulted from that distorted the problem and delayed the progress to a full understanding of the problem. He concluded that explosion occurs when no solution to the problem exists. The exact solution to the problem by Shouman, Donaldson and Tsao reaffirmed the validity of the Semenov formulation. Further examination of the effect of reactant consumption on the problem produced full understanding of the physics of the problem.     

Application of dynamic programming to the general inverse problem

The general inverse problem is one for which measurements are made on some of the state variables and it is desired to find the forcing functions. This problem is a natural one for the method of dynamic programming. The formulation and solution of the problem are presented in matrix form, together with two illustrative examples of an inverse heat conduction problem and an inverse structural dynamics problem.     

The discrete method of separation of variables for composite material problems

In this paper, we propose the discrete method of separation of variables for the numerical solutions of the composite material problems on a polygon. After a suitable transformation of coordinates, the original boundary value problem is reduced to a discontinuous coefficients problem on a semi-infinite strip. Then we get the semi-discrete approximation of the discontinuous coefficients problem which is equivalent to a boundary value problem of a system of ordinary differential equations (O.D.E's) with constant coefficients. After solving the boundary value problem of the system by a direct method, then the semi-discrete approximation of the original problem is obtained. Especially we can see that the semi-discrete approximation in form of separable variables naturally possesses the singularity of the original problem. Finally, the numerical examples show that our method is feasible and very effective for solving composite material problems numerically.     

A numerical example of optimal bang-bang controls

Summary The problem of computing optimal bang-bang controls for a nonlinear control system is discussed. It is shown that the method of replacing the optimal bang-bang control problem by a parameter optimization problem leads to an efficient algorithm. The problem of bringing a rotating rigid body to rest in minimum time is used to illustrate the theory. In this example, the parameter optimization problem reduces to a one-dimensional search.     

An Algorithm for a Class of Three-Dimensional Assignment Problems Arising in Scheduling Applications

A scheduling problem often arising in trade shows and conventions is modeled as a planar three-dimensional assignment problem having a special cost structure. A polynomial-time algorithm for solving this case of the planar assignment problem is presented. The algorithm can also be used to solve heuristically a variation of the m-traveling salesman problem which arises as a secondary problem in the original scheduling application. Computational experience with data from a tourism industry convention scheduling problem is given.     

Optimum Design of Discrete-Time Differentiators via Semi-Infinite Programming Approach

In this paper, a general optimum full-band, high-order discrete-time differentiator design problem is formulated as a peak-constrained least squares optimization problem. That is, the objective of the optimization problem is to minimize the total weighted square error of the magnitude response subject to the peak constraint of the weighted error function. This problem formulation provides great flexibility for the tradeoff between the ripple energy and the ripple magnitude of the discrete-time differentiator. The optimization problem is actually a semi-infinite programming problem. Our recently developed dual parameterization algorithm is applied to solve the problem. The main advantages of employing the dual parameterization algorithm to solve the problem are as follows: 1) the guarantee of the convergence of the algorithm and 2) the obtained solution being the global optimal solution that satisfies the corresponding continuous constraints. Moreover, the computational cost of the algorithm is lower than that of algorithms that are implementing the semidefinite programming approach.      

Conceptual design optimization of rectilinear building frames: A knapsack problem approach

This article presents an automated technique for preliminary layout (conceptual design) optimization of rectilinear, orthogonal building frames in which the shape of the building plan, the number of bays and the size of unsupported spans are variables. It adopts the knapsack problem as the applied combinatorial optimization problem, and describes how the conceptual design optimization problem can be generally modelled as the unbounded multi-constraint multiple knapsack problem. It discusses some special cases, which can be modelled more efficiently as the single knapsack problem, the multiple-choice knapsack problem or the multiple knapsack problem. A knapsack contains sub-rectangles that define the floor plan and the location of columns. Particular conditions or preferences for the conceptual design can be incorporated as constraints on the knapsacks and/or sub-rectangles. A bi-objective knapsack problem is defined with the aim of obtaining a conceptual design having minimum cost and maximum plan regularity (minimum structural eccentricity). A multi-objective ant colony algorithm is formulated to solve the combinatorial optimization problem. A numerical example is included to demonstrate the application of the present method and the robustness of the algorithm.     

An improved approach for determination of index positions on CNC magazines with cutting tool duplications by integrating shortest path algorithm

Optimisation of automatic tool changer (ATC) indexing problem, where cutting tools are allocated to the stations on a turret magazine of a CNC machine, is one of the challenging problems in machining. The aim of the problem is to minimise the total indexing time of ATC. This problem becomes even more challenging if duplication of cutting tools is allowed and a bidirectional ATC is used. The problem has a unique feature which has not been stressed yet by other researchers, that is, although ATC indexing (master problem) is the main optimisation problem, objective function evaluation of this problem is a standalone optimisation problem (sub problem) indeed. Although an approximation algorithm does not guarantee optimality for the master problem, the subproblem must be solved optimally; otherwise, deficiencies arising from ill-defined objective function might be encountered. Considering this interesting future, a novel methodology, which employs a shortest path algorithm, is developed. Thus, the subproblem of this complicated problem can be optimally solved. Moreover, two metaheuristics, based on threshold accepting and descent first improvement greedy methodologies, are proposed for generating efficient solutions. Finally, several benchmarking instances are generated and solved to test the proposed algorithms.     

Multicriteria fractional programming — an approach by means of conjugate functions

This paper deals with multicriteria fractional problems. Since this problems in general are not convex, the basic problem will be transformed into a convex optimization problem by using an extension of the conception of Dinkelbach to vector optimization. It will be formulated a dual problem to the transformed optimization problem, where conjugate functions are used. There will be proved strong and converse duality theorems with conclusions to basic fractional problem.     

Optimal Design of Trusses Under a Nonconvex Global Buckling Constraint

We propose a novel formulation of a truss design problem involving a constraint on the global stability of the structure due to the linear buckling phenomenon. The optimization problem is modelled as a nonconvex semidefinite programming problem. We propose two techniques for the numerical solution of the problem and apply them to a series of numerical examples.     

武器维修器材分层装箱算法研究

武器维修器材装箱问题是一个复杂的多约束组合优化问题。在考虑实际约束条件下,分析了武器维修器材装箱问题,采用空间分割、分层装载和最优选择等策略,提出了一种基于启发式的武器维修器材装箱算法,较好地解决了武器维修器材的优化装载问题。     

Temperature modulations in a circuit model of microwave heating

The problem of temperature-induced modulations on the electric field during microwave heating can be modelled as the problem of a voltage response to a periodically excited resonant circuit with a thermistor. However, even this simplified model is formulated in terms of partial differential equations. Asymptotic methods are used to reduce the problem to a phase-plane problem for the temperature profile coupled to the envelope equation for the voltage. It is shown how relaxation oscillations arise where the temperature modulates the voltage response. This strongly suggests the possibility of wave modulation in the problem of microwave heating.     

Maximization of System Reliability with a Choice of Redundancy Strategies

Optimal solutions to the redundancy allocation problem are determined when either active or cold-standby redundancy can be selectively chosen for individual subsystems. This problem involves the selection of components and redundancy levels to maximize system reliability. Previously, solutions to the problem could only be found if analysts were restricted to a predetermined redundancy strategy for the complete system. Generally, it had been assumed that active redundancy was to be used. However, in practice both active and cold-standby redundancy may be used within a particular system design and the choice of redundancy strategy becomes an additional decision variable. Available optimization algorithms are inadequate for these design problems and better alternatives are required. The methodology presented here is specifically developed to accommodate the case where there is a choice of redundancy strategy. The problem is formulated with imperfect sensing and switching of cold-standby redundant components and k -Erlang distributed time-to-failure. Optimal solutions to the problem are found by an equivalent problem formulation and integer programming. The methodology is demonstrated on a well-known test problem with interesting results. The optimal system design is distinctly different from the corresponding design obtained with only active redundancy. The availability of this tool can result in more reliable and cost-effective engineering designs.     

On the uncoupled problem of stress-assisted diffusion through a linear elastic solid

Summary In this paper, the uncoupled version of Aifantis bilinear stress-assisted theory of diffusion through a linear elastic solid is considered. In analogy to thermoelasticity the basic equations and certain special represertations of the general problem are presented. The general three-dimensional problem is reduced to a problem of body and surface forces and the reciprocal diffuso-elastic theorem is established. Analytical solutions of particular diffusion problems are derived and a complex formulation of the two-dimensional clastodiffusion problem is given. A crack elastodiffusion problem is considered as an application of the complex representation.     

A review of the research methodology for the re-entrant scheduling problem

This paper considers the re-entrant scheduling problem, wherein the most remarkable character is that the jobs enter the processing lines more than once. The objective is to provide a comprehensive review which gives the researchers and practitioners an overview of the applicability of techniques in re-entrant scheduling. Few published reviews dealt with this particular kind of problem and only some research regards the re-entrant character as a hypotaxis of their main problems. This paper is the first paper that gives a full picture of the re-entrant scheduling problem. Considered as a NP-hard problem, a growing number of researchers have employed various methods to solve this complex problem. A survey has been conducted from the recently published literature on the re-entrant problem. This paper has summarised the problem and the relative research methodologies have been studied. Mathematical methods and meta-heuristics, especially Petri net, dispatching rules and genetic algorithm, emerge as the most frequently used methods in recent years, which are presented in detail. Moreover, future research implications have been identified and are suggested. It may help to bring in more awareness of the problem and new techniques to solve it.