Approximation Algorithms for a New Truck Loading Problem in Urban Freight Transportation

2020 ◽  
Vol 54 (3) ◽  
pp. 690-702
Author(s):  
Jie Fan ◽  
Guoqing Wang ◽  
Matthias Thürer
Keyword(s):  
Approximation Algorithm ◽  
Bin Packing ◽  
Freight Transportation ◽  
Performance Ratio ◽  
Fixed Cost ◽  
Worst Case ◽  
Urban Freight ◽  
Truck Loading ◽  
Loading Problem ◽  
Urban Freight Transportation

Motivated by urban freight transportation practices in China, we study an optimal truck loading problem in which a fixed cost and an additional cost that depends on the number of unloading points are associated with each truck used. The truck loading problem is modeled as a one-dimensional bin packing problem, where the cost of each bin is a convex fixed-plus-linear function of the number of items in the bin. The objective is to minimize the total cost of bins used. We develop an asymptotic polynomial time approximation scheme and an efficient approximation algorithm with an asymptotic worst-case performance ratio of 1.5 to tackle the problem. Our computational experiments indicate that the approximation algorithm performs well for certain order patterns, and also reveal several important insights on using the freight charge scheme.

scholarly journals Analysis of an Approximation Algorithm for Scheduling Independent Parallel Tasks

1999 ◽  
Vol Vol. 3 no. 4 ◽  
Author(s):  
Keqin Li
Keyword(s):  
Approximation Algorithm ◽  
Bin Packing ◽  
Random Variables ◽  
Packing Problem ◽  
Performance Ratio ◽  
Worst Case ◽  
Average Case ◽  
Parallel Tasks ◽  
International Audience ◽  
Worst Case Performance Ratio

International audience In this paper, we consider the problem of scheduling independent parallel tasks in parallel systems with identical processors. The problem is NP-hard, since it includes the bin packing problem as a special case when all tasks have unit execution time. We propose and analyze a simple approximation algorithm called H_m, where m is a positive integer. Algorithm H_m has a moderate asymptotic worst-case performance ratio in the range [4/3 ... 31/18] for all m≥ 6; but the algorithm has a small asymptotic worst-case performance ratio in the range [1+1/(r+1)..1+1/r], when task sizes do not exceed 1/r of the total available processors, where r>1 is an integer. Furthermore, we show that if the task sizes are independent, identically distributed (i.i.d.) uniform random variables, and task execution times are i.i.d. random variables with finite mean and variance, then the average-case performance ratio of algorithm H_m is no larger than 1.2898680..., and for an exponential distribution of task sizes, it does not exceed 1.2898305.... As demonstrated by our analytical as well as numerical results, the average-case performance ratio improves significantly when tasks request for smaller numbers of processors.

scholarly journals DATA COLLECTION METHODOLOGIES IN URBAN FREIGHT TRANSPORTATION

2021 ◽  
Vol 2021 (1) ◽  
pp. 103-107
Author(s):  
Ol'ga Lebedeva
Keyword(s):  
Freight Transportation ◽  
Main Task ◽  
Reliable System ◽  
Traffic Demand ◽  
Urban Freight ◽  
Freight Traffic ◽  
Urban Freight Transport ◽  
Demand Assessment ◽  
Urban Freight Transportation ◽  
Adequate Data

The well-known approaches to the process of modeling the demand in urban freight transportation in conditions of limited availability of adequate data are considered. The main task is to select a model for creating a reliable system for analyzing urban freight traffic. Demand assessment models were chosen as input data because they are the most representative for assessing urban freight transport performance.

Electric vehicles in the last mile of urban freight transportation: A sustainability assessment of postal deliveries in Rio de Janeiro-Brazil

2019 ◽  
Vol 67 ◽  
pp. 491-502 ◽  
Author(s):  
Renata Albergaria de Mello Bandeira ◽  
George Vasconcelos Goes ◽  
Daniel Neves Schmitz Gonçalves ◽  
Márcio de Almeida D'Agosto ◽  
Cíntia Machado de Oliveira
Keyword(s):  
Electric Vehicles ◽  
Rio De Janeiro ◽  
Sustainability Assessment ◽  
Freight Transportation ◽  
Urban Freight ◽  
Last Mile ◽  
Urban Freight Transportation

A fuzzy multi-criteria model for evaluating sustainable urban freight transportation operations

2018 ◽  
Vol 184 ◽  
pp. 727-739 ◽  
Author(s):  
Renata A.M. Bandeira ◽  
Marcio A. D'Agosto ◽  
Suzana K. Ribeiro ◽  
Adriano P.F. Bandeira ◽  
George V. Goes
Keyword(s):  
Freight Transportation ◽  
Urban Freight ◽  
Urban Freight Transportation

GENERALIZED FIRST-FIT ALGORITHMS IN TWO AND THREE DIMENSIONS

1990 ◽  
Vol 01 (02) ◽  
pp. 131-150 ◽  
Author(s):  
KEQIN LI ◽  
KAM-HOI CHENG
Keyword(s):  
Bin Packing ◽  
Three Dimensional ◽  
Packing Problem ◽  
Three Dimensions ◽  
Performance Ratio ◽  
Dimensional Case ◽  
Performance Bound ◽  
Worst Case ◽  
Packing Problems ◽  
The One

We investigate the two and three dimensional bin packing problems, i.e., packing a list of rectangles (boxes) into unit square (cube) bins so that the number of bins used is a minimum. A simple on-line packing algorithm for the one dimensional bin packing problem, the First-Fit algorithm, is generalized to two and three dimensions. We first give an algorithm for the two dimensional case and show that its asymptotic worse case performance ratio is [Formula: see text]. The algorithm is then generalized to the three dimensional case and its performance ratio [Formula: see text]. The second algorithm takes a parameter and we prove that by choosing the parameter properly, it has an asymptotic worst case performance bound which can be made as close as desired to 1.72=2.89 and 1.73=4.913 respectively in two and three dimensions.

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