An optimal ordering policy for situations with uncertainty in supply

A one-period inventory model where supply is a random variable with mean proportional to the quantity ordered has been considered. Under new better than used in expectation assumption on the supply variable, a strategy which maximizes a minimum profit has been suggested. An estimate for this maximin order quantity whenever the (customer) demand distribution is unknown has been proposed and almost sure convergence of this estimate to its true value with increasing sample size has been established.     

Note: On the greedy algorithm for optimal assembly

The greedy and balanced algorithms for the optimal assembly of arbitrary structure functions (not necessarily binary) are discussed. Conditions under which these algorithms yield optimal configurations are deduced. © 1992 John Wiley & Sons, Inc.     

An efficient algorithm for the location-allocation problem with rectangular regions

The location-allocation problem for existing facilities uniformly distributed over rectangular regions is treated for the case where the rectilinear norm is used. The new facilities are to be located such that the expected total weighted distance is minimized. Properties of the problem are discussed. A branch and bound algorithm is developed for the exact solution of the problem. Computational results are given for different sized problems.     

An integer programming algorithm for portfolio selection with fixed charges

A mean-variance portfolio selection model with limited diversification is formulated in which transaction and management costs are incorporated as the sum of a linear cost and a fixed cost. The problem is a fixed charge integer programming problem solved by hypersurface search using dynamic programming. Fathoming is performed in the forward pass of dynamic programming so that values of the state variable which correspond to infeasible solutions are eliminated from the tables. This logic permits the solution of problems with 20–30 possible investments.     

An advanced dual algorithm with constraint relaxation for all-integer programming

In this article we present an all-integer cutting plane algorithm called the Reduced Advanced Start Algorithm (RASA). The technique incorporates an infeasible advanced start based on the optimal solution to the LP relaxation, and initially discards nonbinding constraints in this solution. We discuss the results of computational testing on a set of standard problems and illustrate the operation of the algorithm with three small examples.     

An asymptotically optimal inspection policy

An inspection model in life testing situations is discussed. The system under study is assumed to consist on n independent components all of which fail independently in an exponential fashion. Failures can be discovered only through inspection. The experimenter is assumed to lack the knowledge of the parameter of the exponential distribution. A stochastic sequential inspection policy is suggested which uses the data collected through experimentation to estimate the unknown parameter. It is shown that this policy is asymptotically optimal. Some numerical demonstrations are included.     

An algorithm for the solution of a location problem with metric constraints

In many location problems, the solution is constrained to lie within a closed set. In this paper, optimal solutions to a special type of constrained location problem are characterized. In particular, the location problem with the solution constrained to be within a maximum distance of each demand point is considered, and an algorithm for its solution is developed and discussed.     

An iterative algorithm for the multifacility minimax location problem with euclidean distances

An iterative solution method is presented for solving the multifacility location problem with Euclidean distances under the minimax criterion. The iterative procedure is based on the transformation of the multifacility minimax problem into a sequence of squared Euclidean minisum problems which have analytical solutions. Computational experience with the new method is also presented.     

一种单平台的无源被动定位算法

提出了一种对匀速扫描雷达的单站被动定位方法 ,主要论述了该定位方法的数学模型 ,仿真分析结果表明该算法有较好的定位精度     

An algorithm for a class of loading problems

The loading problem we consinder is to assign a set of discrete objects, each having a weight, to a set of boxes, each of which has a capacity limit, in such a way that every object is assigned to a box and the number of boxes used is minimized. A characterization of the assignments is offered and used to develop a set of rules for generating nonredundant assignments. The rules are incorporated into an implicit enumeration algorithm. The algorithm is tested against a very good heuristic. Computational experience shows that the algorithm is highly efficient, solving problems of up to 3600 0-1 variables in a CPU second.     

An algorithm for 0-1 multiple-knapsack problems

The 0-1 multiple-knapsack problem is an extension of the well-known 0-1 knapsack problem. It is a problem of assigning m objects, each having a value and a weight, to n knapsacks in such a way that the total weight in each knapsack is less than its capacity limit and the total value in the knapsacks is maximized. A branch-and-bound algorithm for solving the problem is developed and tested. Branching rules that avoid the search of redundant partial solutions are used in the algorithm. Various bounding techniques, including Lagrangean and surrogate relaxations, are investigated and compared.     

一种纯方位跟踪中的在线式伪线性算法

针对伪线性参数估计不能进行实时状态跟踪的问题,讨论了一种新的在线式的伪线性跟踪算法.对算法的实现过程进行了推导,并应用于纯方位目标的跟踪问题中.仿真结果表明,与传统累积形式的伪线性跟踪算法相比,该算法在保证一定精度的同时,能够降低每个估计时刻的计算量,减少计算占用的资源,是一种有效的算法.     

An algorithm for the discrete bilevel programming problem

The bilevel programming problem (BLPP) is an example of a two-stage, noncooperative game in which the first player can influence but not control the actions of the second. This article addresses the linear formulation and presents a new algorithm for solving the zero-one case. We begin by converting the leader's objective function into a parameterized constraint, and then attempt to solve the resultant problem. This produces a candidate solution that is used to find a point in the BLPP feasible reagion. Incremental improvements are sought, which ultimately lead to a global optimum. An example is presented to highlight the computations and to demonstrate some basic characteristics of the solution. Computational experience indicates that the algorithm is capable of solving problems with up to 50 variables in a reasonable amount of time.     

An improved algorithm for the dynamic lot-sizing problem with learning effect in setups

The dynamic lot-sizing problem with learning in setups is a variation of the Wagner-Whitin lot-sizing problem where the setup costs are a concave, nondecreasing function of the cumulative number of setups. This problem has been a subject of some recent research. We extend the previously studied model to include nonstationary production costs and present an O(T²) algorithm to solve this problem. The worst-case complexity of our algorithm improves the worst-case behavior of the algorithms presently known in the literature. © 1993 John Wiley & Sons, Inc.     

An algorithm for separable piecewise convex programming problems

We present a branch and bound algorithm to solve mathematical programming problems of the form: Find x =|(x₁,…x_n) to minimize Σ?_i0(x₁) subject to x?G, l≦x≦L and Σ?_i0(x₁)≦0, j=1,…,m. With l=(l₁,…,l_n) and L=(L₁,…,L_n), each ?_ij is assumed to be lower aemicontinuous and piecewise convex on the finite interval [l_i.L_i]. G is assumed to be a closed convex set. The algorithm solves a finite sequence of convex programming problems; these correspond to successive partitions of the set C={x|l ≦ x ≦L} on the bahis of the piecewise convexity of the problem functions ?_ij. Computational considerations are discussed, and an illustrative example is presented.     

An approximative algorithm for the fixed charge problem

This paper describes an approximate solution method for solving the fixed charge problem. This heuristic approach is applied to a set of test problems to explore the margin of error. The results indicate that the proposed fixed charge simplex algorithm is capable of finding optimal or near optimal solutions to moderate sized fixed charge problems. In the absence of an exact method, this heuristic should prove useful in solving this fundamental nonlinear programming problem.     

An exact algorithm for the maximal covering problem

This article develops a robust, exact algorithm for the maximal covering problem (MCP) using dual-based solution methods and greedy heuristics in branch and bound. Based on tests using randomly generated problems with problem parameters similar to those in the existing literature, the hybrid approach developed in this work appears to be effective over a wide range of MCP model parameters. The method is further validated on problems constructed from three real-world data sets. The extensive computational study compares the new method with other existing exact methods using problems that are as big, or larger than, those used in previous work on MCP. The results show that the proposed method is effective in most instances of MCP. In particular, it is shown that bounding schemes using Lagrangian relaxation are effective on MCP as a method of obtaining both exact and heuristic solutions. © 1996 John Wiley & Sons, Inc.     

An algorithm for maximizing target achievement in the stochastic knapsack problem with normal returns

We consider the stochastic linear knapsack problem in which costs are known with certainty but returns are independent, normally distributed random variables. The objective is to maximize the probability that the overall return equals or exceeds a specified target value. A previously proposed preference order dynamic programming-based algorithm has been shown to be potentially suboptimal. We offer an alternative hybrid DP/branch-and-bound algorithm that both guarantees optimality and significantly outperforms generating the set of Pareto optimal returns.© 1993 John Wiley & Sons, Inc.     

A two-echelon inventory model with purchases,dispositions, shipments,returns and transshipments

This paper presents a one-period two-echelon inventory model with one warehouse in the first echelon and n warehouses in the second echelon. At the beginning of the period the stock levels at all facilities are adjusted by purchasing or disposing of items at the first echelon, returning or shipping items between the echelons and transshipping items within the second echelon. During the period, demands (which may be negative) are placed on all warehouses in the second echelon and an attempt is made to satisfy shortages either by an expedited shipment from the first echelon to the second echelon or an expedited transshipment within the second echelon. The decision problem is to choose an initial stock level at the first echelon (by a purchase or a disposition) and an initial allocation so as to minimize the initial stock movement costs during the period plus inventory carrying costs and system shortage costs at the end of the period. It is shown that the objective function takes on one of four forms, depending on the relative magnitudes of the various shipping costs. All four forms of the objective function are derived and proven to be convex. Several applications of this general model are considered. We also consider multi-period extensions of the general model and an important special case is solved explicitly.     

一种离焦模糊图像的约束复原方法

针对离焦模糊图像,提出了一种基于图像质量的约束复原算法.该算法基于平滑约束最小二秉,采用正则化技术以减少高频噪声的放大.使用人类视觉系统(HVS)特性中的对比敏感度函数(CSF)对图像功率谱加权来评价图像质量,通过搜索图像质量的最大值实现对正则参数的自适应选择,使复原结果更符合人的视觉感受.实验结果表明:该算法不需要估计降质图像的噪声水平,却能获得和平滑最小二秉复原方法相当甚至更好的复原结果.