A note on the allocation of queuing facilities using a minisum criterion

This paper suggests a formulation and a solution procedure for resource allocation problems which consider a central planner, m static queuing facilities providing a homogeneous service at their locations, and a known set of demand points or customers. It is assumed that upon a request for service the customer is routed to a facility by a probabilistic assignment. The objective is to determine how to allocate a limited number of servers to the facilities, and to specify demand rates from customers to facilities in order to minimize a weighted sum of response times. This sum measures the total time lost in the system due to two sources: travel time from customer to facility locations and waiting time for service at the facilities. The setting does not allow for cooperation between the facilities.     

Modelling ship operational reliability over a mission under regular inspections

A ship is required to operate for a fixed mission period. Should a critical item of equipment fail at sea, the ship is subject to a costly event with potentially high risk to ship and crew. Given warning of a pending defect, the ship can try to return to port under its own power and thus attempt to avoid an at sea failure. Defects which lead to a failure are detected by inspection, and the task is to select the appropriate frequency of inspection to balance the number of occasions that a ship fails at sea and the number of preventive inspection based returns to port during a mission to correct a defect. The modelling entails using the delay time concept. Expressions are established for the expected number of preventive and failure returns over a mission, and an example given of a cost based balance to select an optimal inspection period. Although addressing ship reliability, the model has relevance to the mission reliability of any repairable equipment with remote main repair facilities.     

Improving the computational efficiency of metric-based spares algorithms

We propose a new heuristic algorithm to improve the computational efficiency of the general class of Multi-Echelon Technique for Recoverable Item Control (METRIC) problems. The objective of a METRIC-based decision problem is to systematically determine the location and quantity of spares that either maximizes the operational availability of a system subject to a budget constraint or minimizes its cost subject to an operational availability target. This type of sparing analysis has proven essential when analyzing the sustainment policies of large-scale, complex repairable systems such as those prevalent in the defense and aerospace industries. Additionally, the frequency of these sparing studies has recently increased as the adoption of performance-based logistics (PBL) has increased. PBL represents a class of business strategies that converts the recurring cost associated with maintenance, repair, and overhaul (MRO) into cost avoidance streams. Central to a PBL contract is a requirement to perform a business case analysis (BCA) and central to a BCA is the frequent need to use METRIC-based approaches to evaluate how a supplier and customer will engage in a performance based logistics arrangement where spares decisions are critical. Due to the size and frequency of the problem there exists a need to improve the efficiency of the computationally intensive METRIC-based solutions. We develop and validate a practical algorithm for improving the computational efficiency of a METRIC-based approach. The accuracy and effectiveness of the proposed algorithm are analyzed through a numerical study. The algorithm shows a 94% improvement in computational efficiency while maintaining 99.9% accuracy.     

On a Mathematical Comparison between Hierarchy and Network with a Classification of Coordination Structures

This paper proposes a mathematical model to compare a network organization with a hierarchical organization. In order to formulate the model, we define a three-dimensional framework of the coordination structure of a network and of other typical coordination structures. In the framework, we can define a network structure by contrasting it with a hierarchy, in terms of the distribution of decision making, which is one of the main features of information processing. Based on this definition, we have developed a mathematical model for evaluating coordination structures. Using this model, we can derive two boundary conditions among the coordination structures with respect to the optimal coordination structure. The boundary conditions help us to understand why an organization changes its coordination structure from a hierarchy to a network and what factors cause this change. They enable us, for example, to find points of structural change where the optimal coordination structure shifts from a hierarchy to a hierarchy with delegation or from a hierarchy with delegation to a network, when the nature of the task changes from routine to non-routine. In conclusion, our framework and model may provide a basis for discussing the processes that occur when coordination structures change between a hierarchy and a network.     

The existence of monotonic solutions of a nonlinear car-following equation

A leader-follower pair of cars whose motion is subject to a nonlinear car-following equation are travelling with the same positive constant velocity when the leader begins to change his velocity in a monotonic way to a different non-negative value. Conditions are found for the headway between leader and follower to tend monotonically to a positive value. The results are extended to a system of a leader and two followers.     

On Martingale Approximation of Adapted Processes

We show that the existence of a martingale approximation of a stationary process depends on the choice of the filtration. There exists a stationary linear process which has a martingale approximation with respect to the natural filtration, but no approximation with respect to a larger filtration with respect to which it is adapted and regular. There exists a stationary process adapted, regular, and having a martingale approximation with respect to a given filtration but not (regular and having a martingale approximation) with respect to the natural filtration.     

Persistence Terrace for Topological Inference of Point Cloud Data

Topological data analysis (TDA) is a rapidly developing collection of methods for studying the shape of point cloud and other data types. One popular approach, designed to be robust to noise and outliers, is to first use a smoothing function to convert the point cloud into a manifold and then apply persistent homology to a Morse filtration. A significant challenge is that this smoothing process involves the choice of a parameter and persistent homology is highly sensitive to that choice; moreover, important scale information is lost. We propose a novel topological summary plot, called a persistence terrace, that incorporates a wide range of smoothing parameters and is robust, multi-scale, and parameter-free. This plot allows one to isolate distinct topological signals that may have merged for any fixed value of the smoothing parameter, and it also allows one to infer the size and point density of the topological features. We illustrate our method in some simple settings where noise is a serious issue for existing frameworks and then we apply it to a real dataset by counting muscle fibers in a cross-sectional image. Supplementary material for this article is available online.     

带交货期的工件族生产与配送的排序问题

本文考虑了多个客户订购不同种类的工件,工件生产完后需要运输到客户的单机供应链排序问题.由于工件属于不同的种类,在加工不同种类工件前要有一个准备时间.每个客户分布在不同位置,客户的每个工件都有一个交货期,工件是分批配送的,每一批配送需要花费一定的时间及费用.考虑了两个与交货期有关的目标函数,分别给出了它们的最优算法.     

A multidimensional tropical optimization problem with a non-linear objective function and linear constraints

We examine a multidimensional optimization problem in the tropical mathematics setting. The problem involves the minimization of a non-linear function defined on a finite-dimensional semimodule over an idempotent semifield subject to linear inequality constraints. We start with an overview of known tropical optimization problems with linear and non-linear objective functions. A short introduction to tropical algebra is provided to offer a formal framework for solving the problem under study. As a preliminary result, a solution to a linear inequality with an arbitrary matrix is presented. We describe an example optimization problem drawn from project scheduling and then offer a general representation of the problem. To solve the problem, we introduce an additional variable and reduce the problem to the solving of a linear inequality, in which the variable plays the role of a parameter. A necessary and sufficient condition for the inequality to hold is used to evaluate the parameter, whereas the solution to the inequality is considered a solution to the problem. Based on this approach, a complete direct solution in a compact vector form is derived for the optimization problem under fairly general conditions. Numerical and graphical examples for two-dimensional problems are given to illustrate the obtained results.     

Moufang sets and jordan division algebras

We give a simple criterion which determines when a permutation group U and one additional permutation give rise to a Moufang set. We apply this criterion to show that every Jordan division algebra gives rise in a very natural way to a Moufang set, to provide sufficient conditions for a Moufang set to arise from a Jordan division algebra and to give a characterization of the projective Moufang sets over a commutative field of characteristic different from 2. The first author is a Postdoctoral Fellow of the Research Foundation – Flanders (Belgium) (FWO-Vlaanderen).