Set partitioning based heuristics for interactive routing

Cullen, Frank H.; Jarvis, John J.; Ratliff, H. Donald

doi:10.1002/net.3230110206

Cited by 123 publications

(33 citation statements)

References 5 publications

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“…It offers the broad modeling flexibility inherent in set-covering formulations and is able to accommodate essentially arbitrarily complex routing constraints. Moreover, set-covering formulations are used frequently in many practical implementations of routing algorithms (see for example Balinsky and Quandt 1964, Ceria et al 1995, Cullen et al 1981, Desrochers et al 1992, so our results fit naturally within the current state of practice. Similarly, we are able to capture a wide array of distribution policies.…”

Section: Conclusion and Practical Implicationssupporting

confidence: 74%

Dynamic Vehicle Dispatching: Optimal Heavy Traffic Performance and Practical Insights

Gans

Ryzin

1999

Operations Research

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We analyze a general model of dynamic vehicle dispatching systems in which congestion is the primary measure of performance. In the model, a finite collection of tours are dynamically dispatched to deliver loads that arrive randomly over time. A load waits in queue until it is assigned to a tour. This representation, which is analogous to classical set-covering models, can be used to study a variety of dynamic routing and load consolidation problems. We characterize the optimal work in the system in heavy traffic using a lower bound from our earlier work (Gans and van Ryzin 1997) and an upper bound which is based on a simple batching policy. These results give considerable insight into how various parameters of the problem affect system congestion. In addition, our analysis suggests a practical heuristic which, in simulation experiments, significantly outperforms more conventional dispatching policies. The heuristic uses a few simple principles to control congestion, principles which can be easily incorporated within classical, static routing algorithms.

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Section: Conclusion and Practical Implicationssupporting

confidence: 74%

Dynamic Vehicle Dispatching: Optimal Heavy Traffic Performance and Practical Insights

Gans

Ryzin

1999

Operations Research

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“…These objectives refer to the minimization of user inconvenience. Although there exists an abundant body of literature on the DARP, a major part focuses exclusively on the minimization of routing costs based on the distance traveled by the different vehicles used [6,8,14,45]. In case, the objective of minimum user inconvenience is also treated, this is either done by applying it instead of the minimum cost objective or by means of a weighted sum objective function.…”

Section: Related Workmentioning

confidence: 99%

A heuristic two‐phase solution approach for the multi‐objective dial‐a‐ride problem

et al. 2009

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International audienceIn this article, we develop a heuristic two-phase solution procedure for the dial-a-ride problem with two objectives. Besides the minimum cost objective a client centered objective has been defined. Phase one consists of an iterated variable neighborhood search-based heuristic, generating approximate weighted sum solutions; phase two is a path relinking module, computing additional efficient solutions. Results for two sets of benchmark instances are reported. For the smaller instances, exact efficient sets are generated by means of the e-constraint method. Comparison shows that the proposed two-phase method is able to generate high-quality approximations of the true Pareto frontier

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“…Cullen, Jarvis and Ratliff [28] have proposed and tested a two-pronged heuristic combining a procedure similar to that just described with an approximate solution procedure for solving the set covering problem. The first phase solves an approximation to (11) with the cluster points chosen by a dispatcher or an analyst and with qiv set equal to the Euclidean distance between demand point i and cluster point v. After solving the generalized assignment problem t , though, the authors then redefine the location of each cluster point v so as to minimize the total distance from this point to all of the demand points assigned to it (this is convex optimization problem for each v).…”

Section: Optimization-based Heuristicsmentioning

confidence: 99%

“…Fisher and Jaikumar [43] have recently found that other approaches to solving the set covering problem can also be effective. Cullen, Jarvis and Ratliff [28] have also discovered that interactive heuristics stimulated by graphical display of tentative solutions can further enhance this solution approach. Another special network structure, the space-time diagram, emerges from scheduling considerations.…”

Section: Optimization-based Heuristicsmentioning

confidence: 99%

Combinatorial optimization and vehicle fleet planning: Perspectives and prospects

Magnanti¹

1981

Networks

125

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As a well‐structured and costly activity that pervades industries in both the public and private sector, vehicle fleet management would appear to be a splendid candidate for model‐based planning and optimization. And yet, until recently the combinatorial intricacies of vehicle routing and of vehicle scheduling have precluded the widespread use of optimization (exact) methods for this problem class. Our discussion in this paper identifies the extent and nature of these problem complexities and draws contrasts with other applications of combinatorial optimization. It also summarizes a number of successful uses of optimization for vehicle fleet planning and highlights potentially fruitful avenues for algorithmic development. In particular, we describe several alternative models and novel algorithms for the vehicle routing problem, show how various modeling approaches for this problem are intimately related, and illustrate the interplay between model formulations and the algorithms that they suggest. This discussion shows that prospects for applying exact methods, possibly in conjunction with heuristics, are far from fully realized and points to vehicle fleet planning as a tempting target of opportunity for further investigation.

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Set partitioning based heuristics for interactive routing

Cited by 123 publications

References 5 publications

Dynamic Vehicle Dispatching: Optimal Heavy Traffic Performance and Practical Insights

Dynamic Vehicle Dispatching: Optimal Heavy Traffic Performance and Practical Insights

A heuristic two‐phase solution approach for the multi‐objective dial‐a‐ride problem

Combinatorial optimization and vehicle fleet planning: Perspectives and prospects

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