A robust optimization approach for the capacitated vehicle routing problem with demand uncertainty

Sungur, Ilgaz; Ordóñez, Fernando; Dessouky, Maged

doi:10.1080/07408170701745378

Cited by 190 publications

(120 citation statements)

References 35 publications

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“…The robust vehicle routing problem with time windows and uncertain travel times (T -V RP T W ) has been mentioned already in [21]. However, their modeling assumption leads to all travel times taking their maximum values, which is an over-conservative model.…”

Section: Introductionmentioning

confidence: 99%

“…Travel times belong here to a demand uncertainty polytope, which makes the problem harder to solve, yet tractable, than its deterministic counterpart. The retribution of the addition in complexity is that our model is more flexible than the one from [21] and leads to less conservative robust solutions.…”

Section: Introductionmentioning

confidence: 99%

“…However, their modeling assumption leads to all travel times taking their maximum values, which is an over-conservative model. In fact, [21] mainly focus on the robust capacitated vehicle routing problem, see also [17]. The literature on the stochastic version of the V RP T W is also scant, among which [7,18] which considers stochastic travel times.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Layered Formulation for the Robust Vehicle Routing Problem with Time Windows

Agra

Christiansen

Figueiredo

et al. 2012

Lecture Notes in Computer Science

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Abstract. This paper studies the vehicle routing problem with time windows where travel times are uncertain and belong to a predetermined polytope. The objective of the problem is to find a set of routes that services all nodes of the graph and that are feasible for all values of the travel times in the uncertainty polytope. The problem is motivated by maritime transportation where delays are frequent and must be taken into account. We present an extended formulation for the vehicle routing problem with time windows that allows us to apply the classical (static) robust programming approach to the problem. The formulation is based on a layered representation of the graph, which enables to track the position of each arc in its route. We test our formulation on a test bed composed of maritime transportation instances.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Layered Formulation for the Robust Vehicle Routing Problem with Time Windows

Agra

Christiansen

Figueiredo

et al. 2012

Lecture Notes in Computer Science

View full text Add to dashboard Cite

show abstract

“…Due to the recognized practical importance of incorporating uncertainty, the uncertain version of routing problems has also attracted increasing attention. Researchers have formulated various problems depending on the uncertainty under consideration; for example, uncertainty in customer presence (see for instance, Jaillet, 1988;Jaillet and Odoni, 1988;Campbell and Thomas, 2008), uncertainty in demand (see for instance, Bertsimas, 1992;Bertsimas and Simchi-Levi, 1996;Sungur et al, 2008;Gounaris et al, 2013), and uncertainty in travel time (see for instance, Russell and Urban, 2008;Chang et al, 2009;Li et al, 2010). A comprehensive overview can be found in Cordeau et al (2007), Häme and Hakula (2013).…”

Section: Related Workmentioning

confidence: 99%

Routing Optimization Under Uncertainty

Jaillet

Sim

2016

Operations Research

104

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We consider a class of routing optimization problems under uncertainty in which all decisions are made before the uncertainty is realized. The objective is to obtain optimal routing solutions that would, as much as possible, adhere to a set of specified requirements after the uncertainty is realized. These problems include finding an optimal routing solution to meet the soft time window requirements at a subset of nodes when the travel time is uncertain, and sending multiple capacitated vehicles to different nodes to meet the customers' uncertain demands. We introduce a precise mathematical framework for defining and solving such routing problems. In particular, we propose a new decision criterion, called the Requirements Violation (RV) Index, which quantifies the risk associated with the violation of requirements taking into account both the frequency of violations and their magnitudes whenever they occur. The criterion can handle instances when probability distributions are known, and ambiguity, when distributions are partially characterized through descriptive statistics such as moments information. We develop practically efficient algorithms involving Benders decomposition to find the exact optimal routing solution in which the RV Index criterion is minimized, and give numerical results from several computational studies that show the attractive performance of the solutions.

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“…The robust optimization approach, introduced by Ben-Tal and Nemirovski [2] and more recently extended to integer programming [8] and VRP [43], requires that the solution satisfy the constraints with uncertain parameters for all possible values in the uncertainty set U. That is, we rewrite constraint (8) and constraint (15) as follows:…”

Section: Stochastic Modelmentioning

confidence: 99%

The Stochastic Vehicle Routing Problem for Minimum Unmet Demand

Shen

Ordóñez

Dessouky

2009

Springer Optimization and Its Applications

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Summary. In this paper, we are interested in routing vehicles to minimize unmet demand with uncertain demand and travel time parameters. Such a problem arises in situations with large demand or tight deadlines, so that routes that satisfy all demand points are difficult or impossible to obtain. An important application is the distribution of medical supplies to respond to large-scale emergencies, such as natural disasters or terrorist attacks. We present a chance constrained formulation of the problem that is equivalent to a deterministic problem with modified demand and travel time parameters, under mild assumptions on the distribution of stochastic parameters; and relate it with a robust optimization approach. A tabu heuristic is proposed to solve this MIP and simulations are conducted to evaluate the quality of routes generated from both deterministic and chance constrained formulations. We observe that chance constrained routes can reduce the unmet demand by around 2%-6% for moderately tight deadline and total supply constraints.

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A robust optimization approach for the capacitated vehicle routing problem with demand uncertainty

Cited by 190 publications

References 35 publications

Layered Formulation for the Robust Vehicle Routing Problem with Time Windows

Layered Formulation for the Robust Vehicle Routing Problem with Time Windows

Routing Optimization Under Uncertainty

The Stochastic Vehicle Routing Problem for Minimum Unmet Demand

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