Packing 16, 17 of 18 circles in an equilateral triangle

We present new, efficient packings for 16, 17 and 18 congruent circles in an equilateral triangle. The results have been found by the use of simulated annealing and a quasi-Newton optimization technique, supplemented with some human intelligence

Improved coverings of a square with six and eight equal circles

In a recent article, Tarnai and Gáspár used computer simulations to find thin coverings of a square with up to ten equal circles. We will give improved coverings with six and eight circles and a new, thin covering with eleven circles, found by the use of simulated annealing. Furthermore, we present a combinatorial method for constructing lower bounds for the optimal covering radius

Mixed policies for recovery and disposal of multiple-type consumer products

New European government policies aim at the closure of material flows as part of integrated chain management (ICM). One of the main implementation instruments is extended producer responsibility, which makes original equipment manufacturers (OEMs) formally responsible for take-back, recovery, and reuse of discarded products. One of the key problems for OEMs is to determine a recovery strategy, i.e., determine to what extent return products must be disassembled and which recovery and disposal (RD) options should be applied. On a tactical management level, this involves anticipation of problems such as meeting legislation, limited volumes of secondary end markets, bad quality of return products, and facility investments in recycling infrastructure. In this paper, a model is presented that can be used to determine a recovery strategy for multiple-type consumer products. The objective function incorporates technical, ecological, and commercial decision criteria and optimization occurs using a two-level optimization procedure. First, a set of potential product recovery and disposal (PRD) strategies is generated for each separate product type. Secondly, optimal PRD strategies are assigned to the products within a coherent multiproduct or product group policy. The aim is to find an optimal balance between maximizing net profit and meeting constraints like recovery targets, limited market volumes, and processing capacities. A TV case is worked out to illustrate the working of the model. Also, the managerial use of the model is discussed in view of establishing an economically and ecologically sound base for achieving ICM

Mixed policies for recovery and disposal of multiple type assembly products : commercial exploitation of compulsory return flows

New government policies aim at the closure of material flows as part of Integrated Chain Management (ICM). One of the main implementation instruments is extended producer responsibility, which makes Original Equipment Manufacturers (OEMs) formally responsible for take-back, recovery and reuse of discarded products. One of the key problems for OEMs is to determine to what extent return products must be disassembled and which Recovery and Disposal (RD-) options should be applied. On a tactical management level, this involves anticipation to problems like meeting legislation, limited volumes of secondary end markets, bad quality of return products and facility investments in recycling infrastructure. In this paper a model is described that can be used to find such a Recovery and Disposal Policy for multiple product types. The objective function incorporates technical, ecological and commercial decision criteria and optimisation occurs using a rwo-level optimisation procedure. First, a set of potential Product Recovery and Disposal Strategies is generated for each separate product type. Secondly, optimal PRD-strategies are assigned to the products within the context of a coherent product group. The aim is to find an optimal balance berween maximising net profit and meeting constraints like recovery targets, limited market volumes and processing capacities, A TV-case is worked out to illustrate the working of the model

A variable depth approach for the single-vehicle pickup and delivery problem with time windows

Consider a single depot and a set of customers with known demands, each of which must be picked up and delivered at specified locations and has two time windows in which the pickup and delivery must take place. We seek a route and a schedule for a single vehicle with known capacity, which minimizes the route duration, i.e., the difference between the arrival time and the departure time at the depot. In this paper we present a local search method for this problem based on a variable depth approach, similar to the Lin-Kernighan algorithm for the traveling salesman problem. The method consists of two phases. In the first phase a feasible route is constructed. In the second phase this solution is iteratively improved. In both phases we use a variable depth search built up out of seven basic types of arc-exchange procedures. When tested on real-life problems the method is shown to produce near-optimal solutions in a reasonable amount of computation time. Despite this practical evidence, there is the theoretical possibility that the method may end up with a poor or even infeasible solution. As a safeguard against such an emergency, we have developed an alternative algorithm based on simulated annealing. As a rule, it finds high quality solutions in a relatively large computation time. Keywords: dial-a-ride, pickup and delivery, routing, scheduling, local search, variable depth, simulated annealing

Allocating service parts in two-echelon networks at a utility company

We study a multi-item, two-echelon, continuous-review inventory problem at a Dutch utility company, Liander. We develop a model that optimizes the quantities of service parts and their allocation in the two-echelon network under an aggregate waiting time restriction. Specific aspects that we address are emergency shipments in case of stockout, and batching for regular replenishment orders at the central warehouse. We use column generation as a basic technique to solve this problem, and use various building blocks for single-item models as columns. Further, we study options to derive simple classification rules from the solution of our multi-item, two-echelon service part optimization problem using statistical techniques. Application of our models at Liander yields a solution that reduces costs by 15% and decreases the impact of waiting time for service parts by 52%

Stochastic optimization methods for extracting cosmological parameters from CMBR power spectra

The reconstruction of the CMBR power spectrum from a map represents a major computational challenge to which much effort has been applied. However, once the power spectrum has been recovered there still remains the problem of extracting cosmological parameters from it. Doing this involves optimizing a complicated function in a many dimensional parameter space. Therefore efficient algorithms are necessary in order to make this feasible. We have tested several different types of algorithms and found that the technique known as simulated annealing is very effective for this purpose. It is shown that simulated annealing is able to extract the correct cosmological parameters from a set of simulated power spectra, but even with such fast optimization algorithms, a substantial computational effort is needed.Comment: 7 pages revtex, 3 figures, to appear in PR