Finding the Sequence of Largest Small n-Polygons by Numerical Optimization

LSP(n), the largest small polygon with n vertices, is the polygon of unit diameter that has maximal area A(n). It is known that for all odd values n≥3, LSP(n) is the regular n-polygon; however, this statement is not valid for even values of n. Finding the polygon LSP(n) and A(n) for even values n≥6 has … Read more

Packing Ovals In Optimized Regular Polygons

We present a model development framework and numerical solution approach to the general problem-class of packing convex objects into optimized convex containers. Specifically, here we discuss the problem of packing ovals (egg-shaped objects, defined here as generalized ellipses) into optimized regular polygons in R”. Our solution strategy is based on the use of embedded Lagrange … Read more

Globally Optimized Finite Packings of Arbitrary Size Spheres in R^d

This work discusses the following general packing problem-class: given a finite collection of d-dimensional spheres with arbitrarily chosen radii, find the smallest sphere in R^d that contains the entire collection of these spheres in a non-overlapping arrangement. Generally speaking, analytical solution approaches cannot be expected to apply to this general problem-type, except for very small … Read more

Optimized Ellipse Packings in Regular Polygons Using Embedded Lagrange Multipliers

In this work, we present model development and numerical solution approaches to the general problem of packing a collection of ellipses into an optimized regular polygon. Our modeling and solution strategy is based on the concept of embedded Lagrange multipliers. This concept is applicable to a wide range of optimization problems in which explicit analytical … Read more

General Ellipse Packings in an Optimized Circle Using Embedded Lagrange Multipliers

The general ellipse packing problem is to find a non-overlapping arrangement of 𝑛 ellipses with (in principle) arbitrary size and orientation parameters inside a given type of container set. Here we consider the general ellipse packing problem with respect to an optimized circle container with minimal radius. Following the review of selected topical literature, we … Read more

Socially optimal location of facilities with fixed servers, stochastic demand and congestion

We present two capacity choice scenarios for the socially optimal location of facilities with fixed servers, stochastic demand and congestion. Walk-in health clinics, motor vehicle inspection stations, automobile emissions testing stations, and internal service systems are motivating examples of such facilities. The choice of locations for such facilities influences not only distances for users traveling … Read more

Unit load and material handling considerations in facility layout design

The effectiveness of a layout design cannot be completely measured if the operational characteristics of the manufacturing system are ignored. There is, therefore, a need to develop integrated manufacturing system design models. In this paper, the integration of unit load and material handling considerations in facility layout design is presented. This integration is based on … Read more

An extended distance-based facility layout problem

The distance-based facility layout problem with unequal-area departments has been studied by many researchers for over 30 years. Still, current approaches require certain assumptions that limit the type of solutions obtained. In this paper, we consider manufacturing systems in which replicates of the same machine type may exist in the facility and propose an extended … Read more

Integrating design and production planning considerations in multi-bay manufacturing facility layout

This paper develops a new mathematical model that integrates layout design and production planning to prescribe efficient multi-bay manufacturing facilities. The model addresses the need to distribute department replicas throughout the facility and extends the use of product and process requirements as problem parameters in order to increase process routing flexibility. In addition, the model … Read more

A spring-embedding approach for the facility layout problem

The facility layout problem is concerned with finding the most efficient arrangement of a given number of departments with unequal area requirements within a facility. The facility layout problem is a hard problem, and therefore, exact solution methods are only feasible for small or greatly restricted problems. In this paper, we propose a spring-embedding approach … Read more