A distribution-free TSP tour length estimation model for random graphs

Çavdar, Bahar; Sokol, Joel

doi:10.1016/j.ejor.2014.12.020

Cited by 37 publications

(15 citation statements)

References 18 publications

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“…The results indicated that the formula by Beardwood et al (1959) could be improved by using a different functional form, however, this new result was not generalized for other sizes and shapes of areas. More recently, Çavdar and Sokol (2015) tested several existing tour length approximations, including those of Beardwood et al (1959) and Chien (1992) , and introduced a new model incorporating the standard deviation of the horizontal and vertical customer coordinates. The tested instances have different node dispersions and the areas in which the customers are located have different shapes.…”

Section: Discussionmentioning

confidence: 99%

The Dynamic-Demand Joint Replenishment Problem with Approximated Transportation Costs

Baller

Dabia

Dullaert

et al. 2019

European Journal of Operational Research

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Section: Discussionmentioning

confidence: 99%

The Dynamic-Demand Joint Replenishment Problem with Approximated Transportation Costs

Baller

Dabia

Dullaert

et al. 2019

European Journal of Operational Research

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“…In this case, two K-means algorithms are used to partition the area and create candidate territories, which are then combined with a mathematical model based on formulations of a set covering model, which seeks to minimize the number of territories needed to perform the distribution service. It is important to mention that in this research, the level of service is represented, approximating the time it takes for the distribution service with the formula proposed in [40] since it allows an approximation with differently shaped territories without assuming a distribution of the customers in the zone.…”

Section: Literature Reviewmentioning

confidence: 99%

“…Generally, this step would correspond to the resolution of a traveling salesman problem (TSP) in case of knowing the specific customers that must be served. Given that the exact customers of each workday are unknown and the TSP is a complex problem in itself [50], it is decided to estimate the tour length using a "distributionfree" approximation as proposed in [40] and then multiply the length of the route by the average speed of travel observed within the urban center, which we denote as s w .…”

Section: Problem Descriptionmentioning

confidence: 99%

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A Districting Application with a Quality of Service Objective

Álvarez-Miranda

Pereira

2021

Mathematics

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E-commerce sales have led to a considerable increase in the demand for last-mile delivery companies, revealing several problems in their logistics processes. Among these problems, are not meeting delivery deadlines. For example, in Chile, the national consumer service (SERNAC) indicated that in 2018, late deliveries represented 23% of complaints in retail online sales and were the second most common reason for complaints. Some of the causes are incorrectly designed delivery zones because in many cases, these delivery zones do not account for the demographic growth of cities. The result is an imbalanced workload between different zones, which leads to some resources being idle while others fail to meet their workload in satisfactory conditions. The present work proposes a hybrid method for designing delivery zones with an objective based on improving the quality of express delivery services. The proposed method combines a preprocess based on the grouping of demand in areas according to the structure of the territory, a heuristic that generates multiple candidates for the distribution zones, and a mathematical model that combines the different distribution zones generated to obtain a final territorial design. To verify the applicability of the proposed method, a case study is considered based on the real situation of a Chilean courier company with low service fulfillment in its express deliveries. The results obtained from the computational experiments show the applicability of the method, highlighting the validity of the aggregation procedure and improvements in the results obtained using the hybrid method compared to the initial heuristic. The final solution improves the ability to meet the conditions associated with express deliveries, compared with the current situation, by 12 percentage points. The results also allow an indicative sample of the critical service factors of a company to be obtained, identifying the effects of possible changes in demand or service conditions.

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“…One of the earliest papers by Beardwood et al [1] developed analytically derived formulas for the TSP. Christofides and Eilon [2], Hindle and Worthington [3], and Cavdar and Sokol [4] improved these formulas by using empirically estimated parameters. Golden and Alt [5] constructed interval estimates of the optimal solution value.…”

Section: Introductionmentioning

confidence: 99%

Estimating the Tour Length for the Close Enough Traveling Salesman Problem

et al. 2021

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We construct empirically based regression models for estimating the tour length in the Close Enough Traveling Salesman Problem (CETSP). In the CETSP, a customer is considered visited when the salesman visits any point in the customer’s service region. We build our models using as many as 14 independent variables on a set of 780 benchmark instances of the CETSP and compare the estimated tour lengths to the results from a Steiner zone heuristic. We validate our results on a new set of 234 instances that are similar to the 780 benchmark instances. We also generate results for a new set of 72 larger instances. Overall, our models fit the data well and do a very good job of estimating the tour length. In addition, we show that our modeling approach can be used to accurately estimate the optimal tour lengths for the CETSP.

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A distribution-free TSP tour length estimation model for random graphs

Cited by 37 publications

References 18 publications

The Dynamic-Demand Joint Replenishment Problem with Approximated Transportation Costs

The Dynamic-Demand Joint Replenishment Problem with Approximated Transportation Costs

A Districting Application with a Quality of Service Objective

Estimating the Tour Length for the Close Enough Traveling Salesman Problem

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