Error bound comparisons for aggregation/disaggregation techniques applied to the transportation problem

Norman, Susan K.; Rogers, David F.; Levy, Martin S.

doi:10.1016/s0305-0548(99)00025-8

Cited by 6 publications

(5 citation statements)

References 5 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The objective of the study is to compare the performance of the proposed error bounds regarding the difference from the actual error and the correlation with it. Our numerical study is based on the study design presented in Norman, Rogers, and Levy (1999). To analyze the results we used the Pearson Correlation Coefficient, descriptive statistics and the hypothesis test for the mean of two independent samples (t-test) (Montgomery, 2001).…”

Section: Numerical Studymentioning

confidence: 99%

“…The second area is much less investigated. To our knowledge the first comprehensive study in this direction has been made recently in Norman, Rogers, and Levy (1999) for the classical transportation problem (TP) where they explored, among others, the following question: r If a model is aggregated using different methods to create several different smaller models and an error bound (a priori and/or a posteriori) is calculated for each aggregated model, does the model with the tightest error bound(s) give the closest approximation of the objective function value?…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Using error bounds to compare aggregated generalized transportation models

Litvinchev

Rangel

2006

Ann Oper Res

View full text Add to dashboard Cite

A comparative study of aggregation error bounds for the generalized transportation problem is presented. A priori and a posteriori error bounds were derived and a computational study was performed to (a) test the correlation between the a priori, the a posteriori, and the actual error and (b) quantify the difference of the error bounds from the actual error. Based on the results we conclude that calculating the a priori error bound can be considered as a useful strategy to select the appropriate aggregation level. The a posteriori error bound provides a good quantitative measure of the actual error.

show abstract

Section: Numerical Studymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Using error bounds to compare aggregated generalized transportation models

Litvinchev

Rangel

2006

Ann Oper Res

View full text Add to dashboard Cite

show abstract

“…Our work stands in contrast to past research in spatial aggregation effects and optimal zoning (see Masser and Brown 1975;Openshaw 1977;Chang, Khatlib, and Ou 2002) which has focused on small zones rather than the individual entities utilized here. Furthermore, the aggregation procedure is endogenous to the HAP, which typically is not the case when aggregation examined in the context of spatial modeling (see Murray and Gottsegen 1997;Norman, Rogers, and Levy 1999;Chang, Khatlib, and Ou 2002;Horner and Murray 2002). Lastly, it should be pointed out that the HAP avoids two major error sources of error in location modeling.…”

Section: Model Developmentmentioning

confidence: 99%

“…Previous literature, to the extent that it has examined aggregation issues, has taken several tracks. First, aggregation in location problems has been viewed as a means of reducing problem size (see Orlin and Stein 1993;Norman, Rogers, and Levy 1999). Geoffrion's (1977) article is an exemplar of this theme as it shows how aggregation can make otherwise unmanageable procurement models feasible, with quantifiable amounts of error.…”

Section: Introductionmentioning

confidence: 99%

“…Aggregation is a well-studied problem in location theory but most often from the point of view of the error introduced by misrepresenting spatial entities or using improper zones in a given problem (see Murray and Gottsegen 1997;Norman, Rogers, and Levy 1999;Chang, Khatlib, and Ou 2002;Horner and Murray 2002). In contrast, we seek an objective way to cluster, concentrate, or batch geographical units in pursuit of solving an optimization problem such that intermediate representations between fully aggregate and fully disaggregate interactions are available.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

A Combined Cluster and Interaction Model: The Hierarchical Assignment Problem

Horner

O’Kelly

2005

Geographical Analysis

View full text Add to dashboard Cite

This article presents a new spatial modeling approach that deals with interactions between individual geographic entities. The developed model represents a generalization of the transportation problem and the classical assignment problem and is termed the hierarchical assignment problem (HAP). The HAP optimizes the spatial flow pattern between individual origin and destination locations, given that some grouping, or aggregation of individual origins and destinations is permitted to occur. The level of aggregation is user specified, and the aggregation step is endogenous to the model itself. This allows for the direct accounting of aggregation costs in pursuit of optimal problem solutions. The HAP is formulated and solved with several sample data sets using commercial optimization software. Trials illustrate how HAP solutions respond to changes in levels of aggregation, as well as reveal the diverse network designs and allocation schemes obtainable with the HAP. Connections between the HAP and the literature on the p-median problem, cluster analysis, and hub-and-spoke networks are discussed and suggestions for future research are made. IntroductionThe transportation problem (TP) is a widely used spatial optimization procedure that minimizes interaction costs between origin and destination locations subject to capacity constraints (Hitchcock 1941;Taaffe, Gauthier, and O'Kelly 1996). Applications of the TP are quite varied including its use in the wood processing industry, agriculture, school district delineation, and in modeling aspects of journey to work travel (White 1988;Taaffe, Gauthier, and O'Kelly 1996). The classical assignment problem (AP) is a similar optimization procedure also entailing matching resources or assets [supply] with tasks [demand] such that costs are minimized (Kuhn 1955). Management scientists utilize the AP to assign workers to tasks (Ross and Soland 1975). Similarly, industrial engineers employ the AP to pair production machinery A major feature separating these two interaction models is that the TP often deals with aggregates of entities at origin and destination locations, while the AP is concerned with individual entities at separate origin and destination locations. In a typical TP application, agricultural production and consumption patterns are estimated by zone, and then flows between zones are optimized (Auburn 1988). The AP, in contrast, would be used in a situation to optimize assignments between individual farmers and warehouses. Researchers interested in these problems must choose between using exogenously generated aggregates input into the TP, or using totally disaggregate geographic entities input into the AP. Ideally, the level and configuration of aggregation would be a choice in such an interaction problem, rather than an exogenous input as is the case with the TP.Previous literature, to the extent that it has examined aggregation issues, has taken several tracks. First, aggregation in location problems has been viewed as a means of reducing problem size (see Orlin an...

show abstract

Aggregated Problem and Bounds for Aggregation

Litvinchev

Цурков

2003

Aggregation in Large-Scale Optimization

View full text Add to dashboard Cite

Error bound comparisons for aggregation/disaggregation techniques applied to the transportation problem

Cited by 6 publications

References 5 publications

Using error bounds to compare aggregated generalized transportation models

Using error bounds to compare aggregated generalized transportation models

A Combined Cluster and Interaction Model: The Hierarchical Assignment Problem

Aggregated Problem and Bounds for Aggregation

Contact Info

Product

Resources

About