A Modification of the Modified Stollsteimer Location Moled

1975 ◽  
Vol 7 (1) ◽  
pp. 159-164 ◽  
Author(s):  
Stephen Fuller
Keyword(s):  
Cost Function ◽  
Optimal Solution ◽  
Computer Time ◽  
Solution Procedure ◽  
Plant Location ◽  
Model Parameters ◽  
Basic Model ◽  
Long Run ◽  
Large Numbers ◽  
Cost Parameters

The Stollsteimer plant location model is a normative tool appropriate for deterrmning least-cost number, size and location of a subindustry's marketing facilities. Several modification and extensions of the basic model have increased its value to the applied economist. Ladd and Halvorson developed a procedure to determine sensitivity of the optimal solution to variation in model parameters, i.e., the researcher may resolve how magnitude cost parameters are altered before the solution becomes non-optimal. The basic model's solution procedure prevented application where large numbers of potential plant sites were involved. A recent modification by Warrack and Fletcher effects a reduction in required computer time by approximating optimization, thus increasing size of plant location problems investigated. Polopolus extended the basic model to encompass multiple product plants and, in collaboration with Chern, modified the basic Stollsteimer model to permit substitution of a discontinuous, long-run plant cost function for the strategically assumed continuous linear form. Prior to the latter modification, the basic model accommodated only a long-run total plant cost function which was linear with a positive intercept.

The economic average cost Brownian control problem

2019 ◽  
Vol 51 (01) ◽  
pp. 300-337
Author(s):  
Melda Ormeci Matoglu ◽  
John H. Vande Vate ◽  
Haiyue Yu
Keyword(s):  
Control Problem ◽  
Average Cost ◽  
Drift Rate ◽  
Sufficient Conditions ◽  
Optimal Solution ◽  
Fixed Costs ◽  
Long Run ◽  
Brownian Control Problem ◽  
Cost Parameters ◽  
The Cost

AbstractIn this paper we introduce and solve a generalization of the classic average cost Brownian control problem in which a system manager dynamically controls the drift rate of a diffusion process X. At each instant, the system manager chooses the drift rate from a pair {u, v} of available rates and can invoke instantaneous controls either to keep X from falling or to keep it from rising. The objective is to minimize the long-run average cost consisting of holding or delay costs, processing costs, costs for invoking instantaneous controls, and fixed costs for changing the drift rate. We provide necessary and sufficient conditions on the cost parameters to ensure the problem admits a finite optimal solution. When it does, a simple control band policy specifying economic buffer sizes (α, Ω) and up to two switching points is optimal. The controller should invoke instantaneous controls to keep X in the interval (α, Ω). A policy with no switching points relies on a single drift rate exclusively. When there is no cost to change the drift rate, a policy with a single switching point s indicates that the controller should change to the slower drift rate when X exceeds s and use the faster drift rate otherwise. When there is a cost to change the drift rate, a policy with two switching points s < S indicates that the controller should maintain the faster drift rate until X exceeds S and maintain the slower drift rate until X falls below s.

Optimal Trajectories of Open-Chain Robot Systems: A New Solution Procedure Without Lagrange Multipliers

1998 ◽  
Vol 120 (1) ◽  
pp. 134-136 ◽  
Author(s):  
Sunil K. Agrawal ◽  
Pana Claewplodtook ◽  
Brian C. Fabien
Keyword(s):  
Differential Equations ◽  
Lagrange Multipliers ◽  
Nonlinear Differential Equations ◽  
Boundary Value ◽  
Optimal Solution ◽  
Solution Procedure ◽  
Optimal Trajectories ◽  
Point Boundary ◽  
Open Chain ◽  
Robot Systems

For an n d.o.f. robot system, optimal trajectories using Lagrange multipliers are characterized by 4n first-order nonlinear differential equations with 4n boundary conditions at the two end time. Numerical solution of such two-point boundary value problems with shooting techniques is hard since Lagrange multipliers can not be guessed. In this paper, a new procedure is proposed where the dynamic equations are embedded into the cost functional. It is shown that the optimal solution satisfies n fourth-order differential equations. Due to absence of Lagrange multipliers, the two-point boundary-value problem can be solved efficiently and accurately using classical weighted residual methods.

scholarly journals Managing cost uncertainties in transportation and assignment problems

1998 ◽  
Vol 2 (1) ◽  
pp. 65-104 ◽  
Author(s):  
V. Adlakha ◽  
H. Arsham
Keyword(s):  
Time Lag ◽  
Real Life ◽  
Optimal Solution ◽  
Global Market ◽  
Solution Algorithm ◽  
Assignment Problems ◽  
The Stability ◽  
Order Assignment ◽  
Cost Parameters ◽  
The Cost

In a fast changing global market, a manager is concerned with cost uncertainties of the cost matrix in transportation problems (TP) and assignment problems (AP).A time lag between the development and application of the model could cause cost parameters to assume different values when an optimal assignment is implemented. The manager might wish to determine the responsiveness of the current optimal solution to such uncertainties. A desirable tool is to construct a perturbation set (PS) of cost coeffcients which ensures the stability of an optimal solution under such uncertainties.The widely-used methods of solving the TP and AP are the stepping-stone (SS) method and the Hungarian method, respectively. Both methods fail to provide direct information to construct the needed PS. An added difficulty is that these problems might be highly pivotal degenerate. Therefore, the sensitivity results obtained via the available linear programming (LP) software might be misleading.We propose a unified pivotal solution algorithm for both TP and AP. The algorithm is free of pivotal degeneracy, which may cause cycling, and does not require any extra variables such as slack, surplus, or artificial variables used in dual and primal simplex. The algorithm permits higher-order assignment problems and side-constraints. Computational results comparing the proposed algorithm to the closely-related pivotal solution algorithm, the simplex, via the widely-used pack-age Lindo, are provided. The proposed algorithm has the advantage of being computationally practical, being easy to understand, and providing useful information for managers. The results empower the manager to assess and monitor various types of cost uncertainties encountered in real-life situations. Some illustrative numerical examples are also presented.

HIERARCHICAL GENETIC ALGORITHM FOR NEAR-OPTIMAL FEEDFORWARD NEURAL NETWORK DESIGN

2002 ◽  
Vol 12 (01) ◽  
pp. 31-43 ◽  
Author(s):  
GARY YEN ◽  
HAIMING LU
Keyword(s):  
Neural Network ◽  
Genetic Algorithm ◽  
Neural Networks ◽  
Cost Function ◽  
Design Procedure ◽  
Optimal Solution ◽  
Traditional Learning ◽  
Feed Forward Neural Network ◽  
Optimal Solution Set ◽  
Hierarchical Genetic Algorithm

In this paper, we propose a genetic algorithm based design procedure for a multi-layer feed-forward neural network. A hierarchical genetic algorithm is used to evolve both the neural network's topology and weighting parameters. Compared with traditional genetic algorithm based designs for neural networks, the hierarchical approach addresses several deficiencies, including a feasibility check highlighted in literature. A multi-objective cost function is used herein to optimize the performance and topology of the evolved neural network simultaneously. In the prediction of Mackey–Glass chaotic time series, the networks designed by the proposed approach prove to be competitive, or even superior, to traditional learning algorithms for the multi-layer Perceptron networks and radial-basis function networks. Based upon the chosen cost function, a linear weight combination decision-making approach has been applied to derive an approximated Pareto-optimal solution set. Therefore, designing a set of neural networks can be considered as solving a two-objective optimization problem.

scholarly journals A Fuzzy EPQ Model for Non-Instantaneous Deteriorating Items where Production Depends on Demand which is Proportional to Population, Selling Price as well as Advertisement

2019 ◽  
Vol 10 (5) ◽  
pp. 1679 ◽  
Author(s):  
Abhishek Kanti Biswas ◽  
Sahidul Islam
Keyword(s):  
Optimal Solution ◽  
Inventory Level ◽  
Selling Price ◽  
Distance Method ◽  
Defective Items ◽  
Holding Cost ◽  
Epq Model ◽  
Optimal Inventory Level ◽  
Cost Parameters ◽  
Total Average

The inventory system has been drawing more intrigue because this system deals with the decision that minimizes the total average cost or maximizes the total average profit. For any farm, the demand for any items depends upon population, selling price and frequency of advertisement etc. Most of the model, it is assumed that deterioration of any item in inventory starts from the beginning of their production. But in reality, many goods are maintaining their good quality or original condition for some time. So, price discount is availed for defective items. Our target is to calculate the total optimal cost and the optimal inventory level for this inventory model in a crisp and fuzzy environment. Here Holding cost taken as constant and no-shortages are allowed. The cost parameters are considered as Triangular Fuzzy Numbers and to defuzzify the model Signed Distance Method is applied. A numerical example of the optimal solution is given to clarify the model. The changes of different parameters effect on the optimal total cost are presented and sensitivity analysis is given.JEL Classification: C44, Y80, C61Mathematics Subject Classification: 90B05

scholarly journals ESTIMATING PROFIT , COST FUNCTION AND TECHNICAL EFFICIENCIES OF RICE PRODUCTION IN NEJAF FOR SEASON 2016*

2019 ◽  
Vol 50 (5) ◽  
Author(s):  
Al-Mashhdani & Mahmood
Keyword(s):  
Cost Function ◽  
Output Level ◽  
Average Output ◽  
Optimal Output ◽  
Long Run ◽  
Actual Output ◽  
Short Run ◽  
Profit Maximizing ◽  
Economic Price ◽  
The Cost

The aim of this study was to estimate the profit and cost functions as well as economic, price, cost, and technical efficiencies beside the other economic indices at actual, optimal and profit-maximizing output of rice. A random sample of 240 rice  farms in Nejaf province was used during the agricultural season 2016. From efficiency scales of profit function, it was shown that the output quantity had the greatest impact on the profit compared to other variables (average output costs and price). According to the cost function, the optimum output level and the profit- maximizing output  level for the short run were 64.84 tons and 117.4 tons respectively. The lowest price that the farmer can accept was 194.83 thousand dinars / ton. At this price, the producer loss all fixed costs in the short run, hoping that the price of rice will improve in the long run. Net profit was estimated on the basis of actual output, cost minimizing output (optimal) and profit-maximizing output, which amounted to 8084.32, 30852.65 and 45547.5 thousand dinars, respectively. The of technical efficiency were 34%. and the cost efficiency was 0.52. We conclude from the study that economic resources have not been exploited optimally, indicating that actual output is far from optimal output. The study recommends a output policy aimed at increasing economic efficiency and optimizing the use of available resources.

Memory as National Values

2021 ◽  
pp. 120-148
Author(s):  
Kathrin Bachleitner
Keyword(s):  
Collective Memory ◽  
Refugee Crisis ◽  
Collective Memories ◽  
Course Of Action ◽  
Long Run ◽  
Large Numbers ◽  
National Values ◽  
Conscious Choice ◽  
The Relationship

This chapter places collective memory at the source of a country’s values. In that regard, it enquires into the nature of normative obligations arising from memory. Based on moral-philosophical considerations, it finds normativity in the ‘processes surrounding memory’ described in the temporal security concept. Over time, the relationship between collective memory, identity, and behaviour generates a ‘duty to act’ for countries in the sense of ‘ought’. This last and most diffuse impact of collective memory unfolds and persists into the long run. Through it, collective memory, entirely outside the realm of conscious choice, channels behaviour towards one good course of action. To illustrate this, the empirical study picks up the case countries, Germany and Austria, at a late point in time. In 2015, large numbers of refugees arrived at their borders during what became known as the ‘European refugee crisis’. In this ‘critical situation’, both countries were required to react and thus position themselves vis-à-vis the highly normative issue of asylum. With the help of a content analysis of official speeches, the case study demonstrates how German and Austrian politicians came to identify different versions of what a good response entails based on their country’s diverse collective memories.

On the optimality of stationary replacement strategies

1980 ◽  
Vol 17 (01) ◽  
pp. 178-186 ◽  
Author(s):  
Bo Bergman
Keyword(s):  
Large Class ◽  
Law Of Large Numbers ◽  
Martingale Differences ◽  
Long Run ◽  
Large Numbers ◽  
The Law

In this paper it is shown that for a large class of replacement problems the class of stationary replacement strategies is complete, i.e. in order to minimize the average long run cost per unit time it suffices to consider replacement rules which are equal for each new unit irrespectively of what has been observed from earlier units. The main result is based on a version of the law of large numbers for martingale differences proved in the appendix.

scholarly journals A grid-based distributed flood forecasting model for use with weather radar data: Part 1. Formulation

1998 ◽  
Vol 2 (2/3) ◽  
pp. 265-281 ◽  
Author(s):  
V. A. Bell ◽  
R. J. Moore
Keyword(s):  
Real Time ◽  
Weather Radar ◽  
Radar Data ◽  
Flood Forecasting ◽  
Absorption Capacity ◽  
Model Parameters ◽  
Grid Model ◽  
Basic Model ◽  
Digital Terrain ◽  
Runoff Production

Abstract. A practical methodology for distributed rainfall-runoff modelling using grid square weather radar data is developed for use in real-time flood forecasting. The model, called the Grid Model, is configured so as to share the same grid as used by the weather radar, thereby exploiting the distributed rainfall estimates to the full. Each grid square in the catchment is conceptualised as a storage which receives water as precipitation and generates water by overflow and drainage. This water is routed across the catchment using isochrone pathways. These are derived from a digital terrain model assuming two fixed velocities of travel for land and river pathways which are regarded as model parameters to be optimised. Translation of water between isochrones is achieved using a discrete kinematic routing procedure, parameterised through a single dimensionless wave speed parameter, which advects the water and incorporates diffusion effects through the discrete space-time formulation. The basic model routes overflow and drainage separately through a parallel system of kinematic routing reaches, characterised by different wave speeds but using the same isochrone-based space discretisation; these represent fast and slow pathways to the basin outlet, respectively. A variant allows the slow pathway to have separate isochrones calculated using Darcy velocities controlled by the hydraulic gradient as estimated by the local gradient of the terrain. Runoff production within a grid square is controlled by its absorption capacity which is parameterised through a simple linkage function to the mean gradient in the square, as calculated from digital terrain data. This allows absorption capacity to be specified differently for every grid square in the catchment through the use of only two regional parameters and a DTM measurement of mean gradient for each square. An extension of this basic idea to consider the distribution of gradient within the square leads analytically to a Pareto distribution of absorption capacity, given a power distribution of gradient within the square. The probability-distributed model theory (Moore, 1985) can then be used directly to obtain the integrated runoff production for the square for routing to the catchment outlet. justification for the simple linkage function is in part sought through consideration of variants on the basic model where (i) runoff production is based on a topographic index control on saturation and (ii) absorption capacity is related to the Integrated Air Capacity of the soil, as obtained from soil survey. An impervious area fraction is also introduced based on the use of Landsat classified urban areas. The Grid Model and its variants are assessed in Part 2 (Bell and Moore, 1998), first as simulation models and then as forecasting models, following the development of updating procedures to accommodate recent observations of flow so as to improve forecast performance in a real-time context.

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