A robust approach to the chance-constrained knapsack problem

Klopfenstein, Olivier; Nace, Dritan

doi:10.1016/j.orl.2008.03.006

Cited by 50 publications

(49 citation statements)

References 12 publications

(27 reference statements)

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“…We show that when C 2 Z, problem CO C can be solved in Oðn 1=2 sÞ, improving over the solution time of OðnsÞ from Bertsimas and Sim (2003). Hence, our result extends to a large class of dynamic programming algorithms the ideas proposed by Klopfenstein and Nace (2008) and Monaci, Pferschy, and Serafini (2013) for the robust knapsack problem, by using a more general description of dynamic programming. In Section 5, we present a numerical comparison of models CO C and CO c on the shortest path problem and on the hop-constrained path diversified network design problem.…”

Section: Contributions and Structure Of The Papermentioning

confidence: 63%

Robust combinatorial optimization with variable cost uncertainty

Poss

2014

European Journal of Operational Research

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a b s t r a c tWe present in this paper a new model for robust combinatorial optimization with cost uncertainty that generalizes the classical budgeted uncertainty set. We suppose here that the budget of uncertainty is given by a function of the problem variables, yielding an uncertainty multifunction. The new model is less conservative than the classical model and approximates better Value-at-Risk objective functions, especially for vectors with few non-zero components. An example of budget function is constructed from the probabilistic bounds computed by Bertsimas and Sim. We provide an asymptotically tight bound for the cost reduction obtained with the new model. We turn then to the tractability of the resulting optimization problems. We show that when the budget function is affine, the resulting optimization problems can be solved by solving n þ 1 deterministic problems. We propose combinatorial algorithms to handle problems with more general budget functions. We also adapt existing dynamic programming algorithms to solve faster the robust counterparts of optimization problems, which can be applied both to the traditional budgeted uncertainty model and to our new model. We evaluate numerically the reduction in the price of robustness obtained with the new model on the shortest path problem and on a survivable network design problem.

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Section: Contributions and Structure Of The Papermentioning

confidence: 63%

Robust combinatorial optimization with variable cost uncertainty

Poss

2014

European Journal of Operational Research

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“…Recently, different groups of researchers are interested in develop more elaborated uncertainty sets in order to address the issue of over-conservative in worst case models while maintaining the computational tractability. Also several works have established the link between the chance-constrained technique and robust optimization [32,12,19,14]. In our work, the only difference between the deterministic counterpart of the robust model and the CCP model are the different safety factors used by each model.…”

Section: Solution and Analysis II -The Role Of The Safety Factormentioning

confidence: 98%

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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“…If the above problem is infeasible for Γ = 0 there is no solution to problem (15) either. The problem RKP(Γ) can be solved using a dynamic programming algorithm as indicated in Klopfenstein & Nace (2008). The main difficulty in these approximations is that for many Γ the RKP(Γ) problem may be infeasible.…”

Section: Then X Is Feasible For the Canonical Problem On Constraint Imentioning

confidence: 99%