A dual-based optimization procedure for the two-echelon uncapacitated facility location problem

The two-echelon uncapacitated facility location problem (TUFLP) is a generalization of the uncapacitated facility location problem (UFLP) and multiactivity facility location problem (MAFLP). In TUFLP there are two echelons of facilities through which products may flow in route to final customers. The objective is to determine the least-cost number and locations of facilities at each echelon in the system, the flow of product between facilities, and the assignment of customers to supplying facilities. We propose a new dual-based solution procedure for TUFLP that can be used as a heuristic or incorporated into branch-and-bound procedures to obtain optimal solutions to TUFLP. The algorithm is an extension of the dual ascent and adjustment procedures developed by Erlenkotter for UFLP. We report computational experience gained by solving over 420 test problems. The largest problems solved have 25 possible facility locations at each echelon and 35 customer zones, implying 650 integer variables and 21,875 continuous variables.     

基于高斯和-容积Kalman滤波的高轨双星辐射源跟踪

高轨双星系统可通过测量辐射源信号的到达时差、频差和到达高轨卫星的多普勒频移,跟踪沿地球表面巡航且载频固定、已知的运动辐射源。针对辐射源运动方程和观测方程的强非线性,提出了基于高斯和框架与5阶容积Kalman滤波的运动辐射源跟踪算法GS-5CKF。算法将起始时刻的时差观测量所确定的处于地球表面的时差线按辐射源经度等间隔划分,初始化多个并行的5阶容积Kalman滤波器,线性组合各滤波器每个时刻的输出以获得辐射源运动状态的估计。针对5阶容积Kalman滤波器,提出了相应的非线性测度并引入滤波器分裂与合并,以提高跟踪精度并保持GS-5CKF算法计算复杂度基本不变。仿真表明,相对仅使用单个5阶容积Kalman滤波器和基于高斯和框架但使用3阶容积Kalman滤波器的GS-3CKF等算法,提出的跟踪算法具有更高的估计精度。     

单星定向原理及GPS仿真试验

介绍了一种新的卫星定向方法,该方法仅利用一颗地球静止轨道卫星完成定向;介绍了利用GPS卫星进行单星定向原理验证试验的方法、条件和结果。试验结果表明,对于3m长基线,单星定向精度可达0.05°。从而说明利用一颗地球静止轨道卫星进行定向,在原理上是正确可行的。     

Duality in constrained multi‐facility location models

We consider the ??_p‐norm multi‐facility minisum location problem with linear and distance constraints, and develop the Lagrangian dual formulation for this problem. The model that we consider represents the most general location model in which the dual formulation is not found in the literature. We find that, because of its linear objective function and less number of variables, the Lagrangian dual is more useful. Additionally, the dual formulation eliminates the differentiability problem in the primal formulation. We also provide the Lagrangian dual formulation of the multi‐facility minisum location problem with the ??_pb‐norm. Finally, we provide a numerical example for solving the Lagrangian dual formulation and obtaining the optimum facility locations from the solution of the dual formulation. © 2002 Wiley Periodicals, Inc. Naval Research Logistics 49: 410–421, 2002; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/nav.10010     

Optimal search for a moving target with the option to wait

We investigate the problem in which an agent has to find an object that moves between two locations according to a discrete Markov process (Pollock, Operat Res 18 (1970) 883–903). At every period, the agent has three options: searching left, searching right, and waiting. We assume that waiting is costless whereas searching is costly. Moreover, when the agent searches the location that contains the object, he finds it with probability 1 (i.e. there is no overlooking). Waiting can be useful because it could induce a more favorable probability distribution over the two locations next period. We find an essentially unique (nearly) optimal strategy, and prove that it is characterized by two thresholds (as conjectured by Weber, J Appl Probab 23 (1986) 708–717). We show, moreover, that it can never be optimal to search the location with the lower probability of containing the object. The latter result is far from obvious and is in clear contrast with the example in Ross (1983) for the model without waiting. © 2009 Wiley Periodicals, Inc. Naval Research Logistics 2009     

Aggregating courier deliveries

We consider the problem of efficiently scheduling deliveries by an uncapacitated courier from a central location under online arrivals. We consider both adversary‐controlled and Poisson arrival processes. In the adversarial setting we provide a randomized (3βΔ/2δ ? 1) ‐competitive algorithm, where β is the approximation ratio of the traveling salesman problem, δ is the minimum distance between the central location and any customer, and Δ is the length of the optimal traveling salesman tour overall customer locations and the central location. We provide instances showing that this analysis is tight. We also prove a 1 + 0.271Δ/δ lower‐bound on the competitive ratio of any algorithm in this setting. In the Poisson setting, we relax our assumption of deterministic travel times by assuming that travel times are distributed with a mean equal to the excursion length. We prove that optimal policies in this setting follow a threshold structure and describe this structure. For the half‐line metric space we bound the performance of the randomized algorithm in the Poisson setting, and show through numerical experiments that the performance of the algorithm is often much better than this bound.     

An efficient heuristic procedure for the uncapacitated warehouse location problem

This paper introduces an efficient heuristic procedure for a special class of mixed integer programming problems called the uncapacitated warehouse (plant) location problem. This procedure is derived from the branching decision rules proposed for the branch and bound algorithm by the author in an earlier paper. It can be viewed as tracing a single path of the branch and bound tree (from the initial node to the terminal node), the path being determined by the particular branching decision rule used. Unlike branch and bound the computational efficiency of this procedure is substantially less than linearly related to the number of potential warehouse locations (integer variables) in the problem. Its computational efficiency is tested on problems found in the literature.     

Optimal location of a facility relative to area demands

This paper deals with the Weber single-facility location problem where the demands are not only points but may be areas as well. It provides an iterative procedure for solving the problem with l^p distances when p > 1 (a method of obtaining the exact solution when p = 1 and distances are thus rectangular already exists). The special case where the weight densities in the areas are uniform and the areas are rectangles or circles results in a modified iterative process that is computationally much faster. This method can be extended to the simultaneous location of several facilities.     

Cyclical job sequencing on multiple sets of identical machines

The problem posed in this paper is to sequence or route n jobs, each originating at a particular location or machine, undergoing r?1 operations or repairs, and terminating at the location or machine from which it originated. The problem is formulated as a 0-1 integer program, with block diagonal structure, comprised of r assignment subproblems; and a joint set of constraints to insure cyclical squences. To obtain integer results the solutions to each subproblem are ranked as required and combinations thereof are implicitly enumerated. The procedure may be terminated at any step to obtain an approximate solution. Some limited computational results are presented.     

OPTIMAL FACILITY LOCATION UNDER RANDOM DEMAND WITH GENERAL COST STRUCTURE

This paper investigates the problem of determining the optimal location of plants, and their respective production and distribution levels, in order to meet demand at a finite number of centers. The possible locations of plants are restricted to a finite set of sites, and the demands are allowed to be random. The cost structure of operating a plant is dependent on its location and is assumed to be a piecewise linear function of the production level, though not necessarily concave or convex. The paper is organized in three parts. In the first part, a branch and bound procedure for the general piecewise linear cost problem is presented, assuming that the demand is known. In the second part, a solution procedure is presented for the case when the demand is random, assuming a linear cost of production. Finally, in the third part, a solution procedure is presented for the general problem utilizing the results of the earlier parts. Certain extensions, such as capacity expansion or reduction at existing plants, and geopolitical configuration constraints can be easily incorporated within this framework.     

(2015GIS)北斗静止轨道卫星信号盲区快速并行解算方法

北斗系统静止轨道卫星信号盲区解算方法复杂、串行计算耗费时间长,需在并行环境下利用更多的计算资源进行北斗盲区的快速解算。本文在分析北斗盲区解算原理与算法并行特征基础上,提出了基于动态盲区影响域的并行解算方法,并以栅格单元为并行粒度进行任务划分,实现了北斗盲区的高效并行解算。基于全国范围59景数字高程模型数据,利用8进程进行盲区并行解算,耗费时间约为5小时。实验测试结果表明：算法的并行效率随着进程数的增加有所衰减,但稳定在96%以上。基于本文方法实现的程序中间件已集成应用于高性能地理信息平台中,应用效果良好。     

Sensitivity analysis of the optimal location of a facility

We perform a sensitivity analysis of the Euclidean, single-facility minisum problem, which is also known as the Weber problem. We find the sensitivity of the optimal site of the new facility to changes in the locations and weights of the demand points. We apply these results to get the optimal site if some of the parameters in the problem are changed. We also get approximate formulas for the set of all possible optimal sites if demand points are restricted to given areas, and weights must be within given ranges, which is a location problem under conditions of uncertainty.     

The network redesign problem for access telecommunications networks

The network redesign problem attempts to design an optimal network that serves both existing and new demands. In addition to using spare capacity on existing network facilities and deploying new facilities, the model allows for rearrangement of existing demand units. As rearrangements mean reassigning existing demand units, at a cost, to different facilities, they may lead to disconnecting of uneconomical existing facilities, resulting in significant savings. The model is applied to an access network, where the demands from many sources need to be routed to a single destination, using either low‐capacity or high‐capacity facilities. Demand from any location can be routed to the destination either directly or through one other demand location. Low‐capacity facilities can be used between any pair of locations, whereas high‐capacity facilities are used only between demand locations and the destination. We present a new modeling approach to such problems. The model is described as a network flow problem, where each demand location is represented by multiple nodes associated with demands, low‐capacity and high‐capacity facilities, and rearrangements. Each link has a capacity and a cost per unit flow parameters. Some of the links also have a fixed‐charge cost. The resulting network flow model is formulated as a mixed integer program, and solved by a heuristic and a commercially available software. © 1999 John Wiley & Sons, Inc. Naval Research Logistics 46: 487–506, 1999     

Properties of a multifacility location problem involving euclidian distances

This paper considers a problem of locating new facilities in the plane with respect to existing facilities, the locations of which are known. The problem consists of finding locations of new facilities which will minimize a total cost function which consists of a sum of costs directly proportional to the Euclidian distances among the new facilities, and costs directly proportional to the Euclidian distances between new and existing facilities. It is established that the total cost function has a minimum; necessary conditions for a mimumum are obtained; necessary and sufficient conditions are obtained for the function to be strictly convex (it is always convex); when the problem is “well structured,” it is established that for a minimum cost solution the locations of the new facilities will lie in the convex hull of the locations of the existing facilities. Also, a dual to the problem is obtained and interpreted; necessary and sufficient conditions for optimum solutions to the problem, and to its dual, are developed, as well as complementary slackness conditions. Many of the properties to be presented are motivated by, based on, and extend the results of Kuhn's study of the location problem known as the General Fermat Problem.     

One-facility location with rectilinear tour distances

This article concerns the location of a facility among n points where the points are serviced by “tours” taken from the facility. Tours include m points at a time and each group of m points may become active (may need a tour) with some known probability. Distances are assumed to be rectilinear. For m ≤ 3, it is proved that the objective function is separable in each dimension and an exact solution method is given that involves finding the median of numbers appropriately generated from the problem data. It is shown that the objective function becomes multimodal when some tours pass through four or more points. A bounded heuristic procedure is suggested for this latter case. This heuristic involves solving an auxiliary three-point tour location problem.     

Exploiting self‐canceling demand point aggregation error for some planar rectilinear median location problems

When solving location problems in practice it is quite common to aggregate demand points into centroids. Solving a location problem with aggregated demand data is computationally easier, but the aggregation process introduces error. We develop theory and algorithms for certain types of centroid aggregations for rectilinear 1‐median problems. The objective is to construct an aggregation that minimizes the maximum aggregation error. We focus on row‐column aggregations, and make use of aggregation results for 1‐median problems on the line to do aggregation for 1‐median problems in the plane. The aggregations developed for the 1‐median problem are then used to construct approximate n‐median problems. We test the theory computationally on n‐median problems (n ≥ 1) using both randomly generated, as well as real, data. Every error measure we consider can be well approximated by some power function in the number of aggregate demand points. Each such function exhibits decreasing returns to scale. © 2003 Wiley Periodicals, Inc. Naval Research Logistics 50: 614–637, 2003.     

适用于北斗混合星座的相对定位随机模型建模策略

为提高模糊度解算成功率和基线解精度,提出适用于北斗的相对定位随机模型建模策略,即混合随机建模策略。采用最小二乘方差分量估计方法对北斗单差观测量方差进行估计。对处于不同高度的三轨道卫星观测量方差分别建模:对地球静止轨道卫星观测量方差采用载噪比模型建模,对倾斜地球同步轨道卫星和中地球轨道卫星观测量方差均采用仰角模型建模。根据不同模型实时组建观测量的随机模型。试验结果表明:相比于采用传统简化模型和单一的仰角或载噪比模型,混合随机模型能更加真实地反映不同卫星观测量的随机噪声特性,模糊度解算成功率和相对定位精度均有提高,总体性能最优,因而能更好地适用于北斗系统。     

Multi-item service constrained (s,S) policies for spare parts logistics systems

Many organizations providing service support for products or families of products must allocate inventory investment among the parts (or, identically, items) that make up those products or families. The allocation decision is crucial in today's competitive environment in which rapid response and low levels of inventory are both required for providing competitive levels of customer service in marketing a firm's products. This is particularly important in high-tech industries, such as computers, military equipment, and consumer appliances. Such rapid response typically implies regional and local distribution points for final products and for spare parts for repairs. In this article we fix attention on a given product or product family at a single location. This single-location problem is the basic building block of multi-echelon inventory systems based on level-by-level decomposition, and our modeling approach is developed with this application in mind. The product consists of field-replaceable units (i.e., parts), which are to be stocked as spares for field service repair. We assume that each part will be stocked at each location according to an (s, S) stocking policy. Moreover, we distinguish two classes of demand at each location: customer (or emergency) demand and normal replenishment demand from lower levels in the multiechelon system. The basic problem of interest is to determine the appropriate policies (s_i S_i) for each part i in the product under consideration. We formulate an approximate cost function and service level constraint, and we present a greedy heuristic algorithm for solving the resulting approximate constrained optimization problem. We present experimental results showing that the heuristics developed have good cost performance relative to optimal. We also discuss extensions to the multiproduct component commonality problem.     

The dynamic transshipment problem

We investigate the strategy of transshipments in a dynamic deterministic demand environment over a finite planning horizon. This is the first time that transshipments are examined in a dynamic or deterministic setting. We consider a system of two locations which replenish their stock from a single supplier, and where transshipments between the locations are possible. Our model includes fixed (possibly joint) and variable replenishment costs, fixed and variable transshipment costs, as well as holding costs for each location and transshipment costs between locations. The problem is to determine how much to replenish and how much to transship each period; thus this work can be viewed as a synthesis of transshipment problems in a static stochastic setting and multilocation dynamic deterministic lot sizing problems. We provide interesting structural properties of optimal policies which enhance our understanding of the important issues which motivate transshipments and allow us to develop an efficient polynomial time algorithm for obtaining the optimal strategy. By exploring the reasons for using transshipments, we enable practitioners to envision the sources of savings from using this strategy and therefore motivate them to incorporate it into their replenishment strategies. © 2001 John Wiley & Sons, Inc. Naval Research Logistics 48:386–408, 2001     

An analysis of single item inventory systems with returns

Inventory systems with returns are systems in which there are units returned in a repairable state, as well as demands for units in a serviceable state, where the return and demand processes are independent. We begin by examining the control of a single item at a single location in which the stationary return rate is less than the stationary demand rate. This necessitates an occasional procurement of units from an outside source. We present a cost model of this system, which we assume is managed under a continuous review procurement policy, and develop a solution method for finding the policy parameter values. The key to the analysis is the use of a normally distributed random variable to approximate the steady-state distribution of net inventory. Next, we study a single item, two echelon system in which a warehouse (the upper echelon) supports N(N ? 1) retailers (the lower echelon). In this case, customers return units in a repairable state as well as demand units in a serviceable state at the retailer level only. We assume the constant system return rate is less than the constant system demand rate so that a procurement is required at certain times from an outside supplier. We develop a cost model of this two echelon system assuming that each location follows a continuous review procurement policy. We also present an algorithm for finding the policy parameter values at each location that is based on the method used to solve the single location problem.