The value of the stochastic solution in multistage problems

Escudero, Laureano F.; Garín, Araceli; Maestre, María Merino; Pérez, Gloria

doi:10.1007/s11750-007-0005-4

Cited by 99 publications

(74 citation statements)

References 9 publications

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“…To calculate EEV for the proposed three-stage stochastic model, we use an approach introduced by Escudero et al (2007). In this approach we take into account that the deterministic model should be able to make decisions at the second stage based on the new information revealed at this stage, i.e.…”

Section: Computational Setupmentioning

confidence: 99%

A stochastic fleet size and mix model for maintenance operations at offshore wind farms

Gundegjerde

Halvorsen

Halvorsen-Weare

et al. 2015

Transportation Research Part C: Emerging Technologies

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Section: Computational Setupmentioning

confidence: 99%

A stochastic fleet size and mix model for maintenance operations at offshore wind farms

Gundegjerde

Halvorsen

Halvorsen-Weare

et al. 2015

Transportation Research Part C: Emerging Technologies

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“…The expected network will therefore be represented by the initial network of stage 1. Escudero et al (2007) describe a method for computing EEV that fits multi-stage problems which we will follow: A deterministic expected value scenario problem is solved in the first step of the procedure. The resulting optimal first stage variables are saved, and for the following stage in the scenario tree, an expected value scenario problem is solved for each scenario tree node leading up to the final stage.…”

Section: Value Of Using a Stochastic Modelmentioning

confidence: 99%

A three-stage stochastic facility routing model for disaster response planning

Rennemo

Rø

Hvattum

et al. 2014

Transportation Research Part E: Logistics and Transportation Re

168

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This paper presents a humanitarian logistics decision model to be used in the event of a disaster. The operations under consideration span from opening of local distribution facilities and initial allocation of supplies, to last mile distribution of aid. A mathematical model is developed aiming to enable efficient decision making, maximizing the utility of distribution of aid amongst beneficiaries. This model is formulated as a three-stage mixed-integer stochastic programming model to account for the difficulty in predicting the outcome of a disaster.Accessibility of new information implies initiation of distinct operations in the humanitarian supply chain, be it facility location and supply allocation, or last mile distribution planning and execution. The realized level of demand, in addition to the transportation resources available to the decision maker for execution of last mile aid distribution and the state of the infrastructure, are parameters treated as random due to uncertainty.An assessment of the applicability and validity of the stochastic program is made through extensive computational testing based on several test instances. The results show that instances of considerable size are challenging to solve due to the complexity of the stochastic programming model but, still, optimal solutions may be found within a reasonable time frame. Moreover, findings prove the value of the stochastic programming model to be significant as compared with a deterministic expected value approach. Finally, the model is also applied to a case study based on the earthquake that hit Haiti in January of 2010, showing how it could be used in a realistic operation framework.

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“…In order to evaluate the effectiveness of these approaches, two wellknown measures of uncertainty effects, the expected value of perfect information (EVPI) and the value of the stochastic solution (VSS), are considered in this paper. For details about these measures, see Birge and Louveaux (1997), Kall and Wallace (1994), Madansky (1960), Avriel and Williams (1970), Escudero et al (2007), and Bard et al (2007), among others.…”

Section: The Value Of the Information And Stochastic Solutionmentioning

confidence: 99%

“…The VSS measure combines RP and EEV and compares the here-and-now and expected value approaches. A general procedure to obtain VSS is presented in Escudero et al (2007).…”

Section: The Value Of the Stochastic Solutionmentioning

confidence: 99%

On the cutting stock problem under stochastic demand

et al. 2008

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This paper addresses the one-dimensional cutting stock problem when demand is a random variable. The problem is formulated as a two-stage stochastic nonlinear program with recourse. The first stage decision variables are the number of objects to be cut according to a cutting pattern. The second stage decision variables are the number of holding or backordering items due to the decisions made in the first stage. The problem's objective is to minimize the total expected cost incurred in both stages, due to waste and holding or backordering penalties. A Simplex-based method with column generation is proposed for solving a linear relaxation of the resulting optimization problem. The proposed method is evaluated by using two well-known measures of uncertainty effects in stochastic programming: the value of stochastic solution-VSS-and the expected value of perfect information-EVPI. The optimal two-stage solution is shown to be more effective than the alternative wait-andsee and expected value approaches, even under small variations in the parameters of the problem.In the one-dimensional cutting stock problem, a stock of available objects, such as bars, bobbins and reels must be cut into smaller items in order to exactly meet the demand, while at-

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The value of the stochastic solution in multistage problems

Abstract: Stochastic programming, Scenario tree, Complete recourse, Deterministic equivalent model, 60H35, 65C20, 68Q25,

Cited by 99 publications

References 9 publications

A stochastic fleet size and mix model for maintenance operations at offshore wind farms

A stochastic fleet size and mix model for maintenance operations at offshore wind farms

A three-stage stochastic facility routing model for disaster response planning

On the cutting stock problem under stochastic demand

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