The asymptotic joint distribution of the state occupancy times in an alternating renewal process

An alternating renewal process starts at time zero and visits states 1,2,…,r, 1,2, …,r 1,2, …,r, … in sucession. The time spent in state i during any cycle has cumulative distribution function F_i, and the sojourn times in each state are mutually independent, positive and nondegenerate random variables. In the fixed time interval [0,T], let U_i(T) denote the total amount of time spent in state i. In this note, a central limit theorem is proved for the random vector (U_i(T), 1 ≤ i ≤ r) (properly normed and centered) as T → ∞.     

A lagrangean relaxation algorithm for the constrained matrix problem

We present variants of a convergent Lagrangean relaxation algorithm for minimizing a strictly convex separable quadratic function over a transportation polytope. The algorithm alternately solves two “subproblems,” each of which has an objective function that is defined by using Lagrange multipliers derived from the other. Motivated by the natural separation of the subproblems into independent and very easily solved “subsubproblems,” the algorithm can be interpreted as the cyclic coordinate ascent method applied to the dual problem. We exhibit our computational results for different implementations of the algorithm applied to a set of large constrained matrix problems.     

Optimal replacement for fault-tolerant systems

We consider the optimal replacement problem for a fault tolerant system comprised of N components. The components are distingushable, and the state of the system is given by knowing exactly which components are operationl and which have failed. The individual component failure rates depend on the state of the entire system. We assume that the rate at which the system produces income decreases as the system deteriorates and the system replacement cost rises. Individual components cannot be replaced. We give a greedy-type algorithm that produces the replacement policy that maximizes the long-run net system income per unit time.     

复杂形状薄壁零件加工的综合质量控制

首先分析了加工时零件表面热量场和加工参数、余量场之间的关系;利用数字扫描及滤波的方法建立起复杂形面零件的数学模型;以此为基础,在加工过程中,对零件的几何质量和表面层质量进行了综合控制。研究表明,该方法是提高飞行器发动机中高负载复杂形状薄壁零件可靠性和寿命的有效新途径。     

The traveling salesman problem: An update of research

During the course of the last few years, attacks on the traveling salesman problem have resulted in a variety of often innovative and rather powerful computational procedures. In this article, we present a review of these results for problems defined on weighted and unweighted graphs. Some account of computational behavior for exact algorithms is provided; however, the primary coverage deals with the strategy of particular procedures. In addition, we include some aspects of nonexact algorithms with major interest confined to the establishment of worst-case bounds.     

A bounded dual (all-integer) integer programming algorithm with an objective cut

In this article, we describe a new algorithm for solving all-integer, integer programming problems. We generate upper bounds on the decision variables, and use these bounds to create an advanced starting point for a dual all-integer cutting plane algorithm. In addition, we use a constraint derived from the objective function to speed progress toward the optimal solution. Our basic vehicle is the dual all-integer algorithm of Gomory, but we incorporate certain row- and column-selection criteria which partially avoid the problem of dual-degenerate iterations. We present the results of computational testing.