Optimal Distribution of City Sizes in a Region

1982 ◽  
Vol 14 (1) ◽  
pp. 21-32 ◽  
Author(s):  
T Tabuchi
Keyword(s):  
Population Distribution ◽  
Sufficient Conditions ◽  
Optimal Solution ◽  
Distribution Model ◽  
Tokyo Metropolitan Area ◽  
Congestion Cost ◽  
Spatial Distribution Model ◽  
Population Sizes ◽  
Optimal Population ◽  
Necessary And Sufficient

First, an optimal spatial distribution model is proposed of population sizes in a country. The objective function to be examined consists of the amount of interaction benefit which is formulated by means of accessibility, and the amount of intraaction congestion cost which is measured by means of population density. Second, the optimal population distribution is obtained by use of this optimization model, and the necessary and sufficient conditions for the optimal solution is given. Third, based upon the data analysis of population distribution in Japanese prefectures in 1975, it is shown that the Japanese population is undergoing suburbanization and that this leads to the optimal population distribution. Last, this model is used to obtain and analyze the optimal grid system population distribution of the Tokyo Metropolitan Area.

Fixation in bisexual models with variable population sizes

1997 ◽  
Vol 34 (02) ◽  
pp. 436-448 ◽  
Author(s):  
M. Möhle
Keyword(s):  
Main Part ◽  
Sufficient Conditions ◽  
Moran Model ◽  
Fisher Model ◽  
Population Sizes ◽  
Variable Population ◽  
Allelic Type ◽  
Ultimate Homozygosity ◽  
Necessary And Sufficient ◽  
Forward Process

A general exchangeable bisexual model with variable population sizes is introduced. First the forward process, i.e. the number of certain descending pairs, is studied. For the bisexual Wright-Fisher model fixation of the descendants occurs, i.e. their proportion tends to 0 or 1 almost surely. The main part of this article deals with necessary and sufficient conditions for ultimate homozygosity, i.e. the proportion of an arbitrarily chosen allelic type tends to 0 or 1 almost surely. The results are applied to a bisexual Wright-Fisher model and to a bisexual Moran model.

Optimal Spacecraft Trajectories

2018 ◽  
Author(s):  
John E. Prussing
Keyword(s):  
Conjugate Point ◽  
Sufficient Conditions ◽  
Optimal Solution ◽  
Order Conditions ◽  
Comprehensive Treatment ◽  
Reference Book ◽  
Graduate Level ◽  
Spacecraft Trajectories ◽  
Cooperative Rendezvous ◽  
Necessary And Sufficient

Optimal spacecraft trajectories are given a modern comprehensive treatment of the theory and important results. In most cases “optimal” means minimum propellant. Less propellant required results in more payload delivered to the destination. Both necessary and sufficient conditions for an optimal solution are analysed. Numerous illustrative examples are included and problems are provided at the ends of the chapters along with references. Newer topics such as cooperative rendezvous and second-order conditions are considered. Seven appendices are included to supplement the text, some with problems. Both classical results and newer research results are included. A new test for a conjugate point is demonstrated. The book is both a graduate-level textbook and a scholarly reference book.

Monge Properties, Optimal Greedy Policies, and Policy Improvement for the Dynamic Stochastic Transportation Problem

2020 ◽  
Author(s):  
Alexander S. Estes ◽  
Michael O. Ball
Keyword(s):  
Greedy Algorithm ◽  
Traffic Management ◽  
Transportation Problem ◽  
Sufficient Conditions ◽  
Optimal Solution ◽  
Necessary And Sufficient Conditions ◽  
Taxi Service ◽  
Dynamic Stochastic ◽  
Stochastic Transportation Problem ◽  
Necessary And Sufficient

We consider a dynamic, stochastic extension to the transportation problem. For the deterministic problem, there are known necessary and sufficient conditions under which a greedy algorithm achieves the optimal solution. We define a distribution-free type of optimality and provide analogous necessary and sufficient conditions under which a greedy policy achieves this type of optimality in the dynamic, stochastic setting. These results are used to prove that a greedy algorithm is optimal when planning a type of air-traffic management initiative. We also provide weaker conditions under which it is possible to strengthen an existing policy. These results can be applied to the problem of matching passengers with drivers in an on-demand taxi service. They specify conditions under which a passenger and driver should not be left unassigned.

scholarly journals On the closure of the sum of closed subspaces

2001 ◽  
Vol 26 (5) ◽  
pp. 257-267 ◽  
Author(s):  
Irwin E. Schochetman ◽  
Robert L. Smith ◽  
Sze-Kai Tsui
Keyword(s):  
Hilbert Space ◽  
Quadratic Programming ◽  
Programming Problem ◽  
Sufficient Conditions ◽  
Optimal Solution ◽  
The Other ◽  
Quadratic Programming Problem ◽  
Orthogonal Projections ◽  
The Cost ◽  
Necessary And Sufficient

We give necessary and sufficient conditions for the sum of closed subspaces of a Hilbert space to be closed. Specifically, we show that the sum will be closed if and only if the angle between the subspaces is not zero, or if and only if the projection of either space into the orthogonal complement of the other is closed. We also give sufficient conditions for the sum to be closed in terms of the relevant orthogonal projections. As a consequence, we obtain sufficient conditions for the existence of an optimal solution to an abstract quadratic programming problem in terms of the kernels of the cost and constraint operators.

A Time-Stepping Scheme for Quasistatic Multibody Systems

2005 ◽  
Author(s):  
J. C. Trinkle ◽  
Stephen Berard ◽  
J. S. Pang
Keyword(s):  
Three Dimensional ◽  
Sufficient Conditions ◽  
Optimal Solution ◽  
Contact Forces ◽  
Global Optimal Solution ◽  
Convex Optimization Problem ◽  
Time Stepping ◽  
Global Optimal ◽  
Necessary And Sufficient ◽  
First Time

Two new instantaneous-time models for predicting the motion and contact forces of three-dimensional, quasistatic multi-rigid-body systems are developed; one linear and one nonlinear. The nonlinear characteristic is the result of retaining the usual quadratic friction cone in the model. Discrete-time versions of these models provide the first time-stepping methods for such systems. As a first step to understanding their usefulness in simulation and manipulation planning, a theorem defining the equivalence of solutions of a time-stepping method for the nonlinear model and a global optimal solution of a related convex optimization problem is given. In addition, a Proposition giving necessary and sufficient conditions for solution uniqueness of the nonlinear time-stepping method is given. Finally, a simple example is discussed to help develop intuition about quasistatic systems and to solidify the reader’s understanding of the theorem and proposition.

scholarly journals Optimal Replenishment Decisions under Two-Level Trade Credit with Partial Upstream Trade Credit Linked to Order Quantity and Limited Storage Capacity

2014 ◽  
Vol 2014 ◽  
pp. 1-14 ◽  
Author(s):  
Chih-Te Yang ◽  
Liang-Yuh Ouyang ◽  
Chang-Hsien Hsu ◽  
Kuo-Liang Lee
Keyword(s):  
Trade Credit ◽  
Storage Capacity ◽  
Sufficient Conditions ◽  
Real Life ◽  
Optimal Solution ◽  
Economic Order Quantity ◽  
Order Quantity ◽  
Eoq Models ◽  
Necessary And Sufficient ◽  
Theoretical Results

This paper extends the previous economic order quantity (EOQ) models under two-level trade credit such as Goyal (1985), Teng (2002), Huang (2003, 2007), Kreng and Tan (2010), Ouyang et al. (2013), and Teng et al. (2007) to reflect the real-life situations by incorporating the following concepts: (1) the storage capacity is limited, (2) the supplier offers the retailer a partially upstream trade credit linked to order quantity, and (3) both the dispensable assumptions that the upstream trade credit is longer than the downstream trade creditN<Mand the interest charged per dollar per year is larger than or equal to the interest earned per dollar per yearIc<Ieare relaxed. We then study the necessary and sufficient conditions for finding the optimal solution for various cases and establish a useful algorithm to obtain the solution. Finally, numerical examples are given to illustrate the theoretical results and provide the managerial insights.

Fixation in bisexual models with variable population sizes

1997 ◽  
Vol 34 (2) ◽  
pp. 436-448 ◽  
Author(s):  
M. Möhle
Keyword(s):  
Main Part ◽  
Sufficient Conditions ◽  
Moran Model ◽  
Fisher Model ◽  
Population Sizes ◽  
Variable Population ◽  
Allelic Type ◽  
Ultimate Homozygosity ◽  
Necessary And Sufficient ◽  
Forward Process

A general exchangeable bisexual model with variable population sizes is introduced. First the forward process, i.e. the number of certain descending pairs, is studied. For the bisexual Wright-Fisher model fixation of the descendants occurs, i.e. their proportion tends to 0 or 1 almost surely.The main part of this article deals with necessary and sufficient conditions for ultimate homozygosity, i.e. the proportion of an arbitrarily chosen allelic type tends to 0 or 1 almost surely. The results are applied to a bisexual Wright-Fisher model and to a bisexual Moran model.

Some Reconsiderations of Simon's City-Size Distribution Model

1977 ◽  
Vol 9 (9) ◽  
pp. 1043-1053 ◽  
Author(s):  
A Okabe
Keyword(s):  
Steady State ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
City Size ◽  
Distribution Model ◽  
Type Model ◽  
Size Distributions ◽  
City Size Distribution ◽  
Necessary And Sufficient ◽  
Over Time

In conjunction with the empirical findings that the form of city-size distributions is stable over time, this paper reexamines Simon's (1955) model and provides a better understanding of that model. First, a Simon-type model is proposed which is a generalization of Simon's model. Second, Simon's model is reexamined with respect to the ‘steady state’. Third, in the context of the Simon-type model, the necessary and sufficient conditions for the ‘steady state’ with the Yule (1924) city-size distributions are investigated. Last, the necessary and sufficient conditions for the ‘asymptotically steady state’ are obtained.

scholarly journals Solution of a bi-criteria problem of rating alternatives using tropical optimization

2019 ◽  
pp. 15-32
Author(s):  
Nikolai K. Krivulin ◽  
◽  
Margarita A. Tsobenko ◽  
Keyword(s):  
Pareto Front ◽  
Sufficient Conditions ◽  
Optimal Solution ◽  
Pairwise Comparisons ◽  
Logarithmic Scale ◽  
Third Order ◽  
Tropical Mathematics ◽  
All Solutions ◽  
Computational Procedures ◽  
Necessary And Sufficient

A problem is considered to evaluate scores (priorities, weights) of alternatives through the results of pairwise comparisons according to two criteria. A formal derivation and computational procedures of the solution to the problem are described, using methods of tropical mathematics, which studies algebraic systems with specially defined operations of addition and multiplication. The problem is reduced to simultaneous approximation of two matrices of pairwise comparisons by a common consistent matrix, in the Chebyshev metric in logarithmic scale. First, auxiliary variables are introduced to represent the minima of the objective functions, and a parameterized inequality is derived, which determines the set of solutions to the original optimization problem. The necessary and sufficient conditions for the existence of solutions of the inequality are used to evaluate the values of parameters, which correspond to the Pareto front of the problem. All solutions of the inequality under the obtained values are taken as a Pareto-optimal solution for the problem. To illustrate the computational procedures used, numerical examples of evaluating scores of alternatives are given for problems with matrices of the third order.

Sign in / Sign up

Export Citation Format

Share Document