Building a stochastic programming model from scratch: a harvesting management example

Ríos, Ignacio; Weintraub, Andrés; Wets, Roger J.-B.

doi:10.1080/14697688.2015.1114365

Cited by 14 publications

(8 citation statements)

References 20 publications

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“…The method is also suitable for many applications where the objective function cannot be computed in a closed form such as the so-called black-box optimization problems [27] and the stochastic knapsack problem [22]. In forestry, this method is well suited for harvest scheduling problem with wood price and demand uncertainties because we can extract samples from historical demand and price without the need to model the price like done in [10,28]. Compared to stochastic programming which require the so-called non-anticipativity constraints [13,29], SAA model is relatively smaller in terms of number of constraints (and possibly in terms of number of variables, depending on the formulation) since it does not require such constraints.…”

Section: Discussionmentioning

confidence: 99%

Multistage Sample Average Approximation for Harvest Scheduling under Climate Uncertainty

Bagaram¹,

Tóth²

2020

Preprint

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Forest planners have traditionally used expected growth and yield coefficients to predict future merchantable timber volumes. However, because climate change affects forest growth, the typical forest planning methods using expected value of forest growth can lead to sub-optimal harvest decisions. We proposed in this paper to formulate the harvest planning with growth uncertainty due to climate change problem as a multistage stochastic optimization problem and use sample average approximation (SAA) as a tool for finding the best set of forest units that should be harvested in the first period even though we have a limited knowledge of what future climate will be. The objective of the harvest planning model is to maximize the expected value of the net present value (NPV) considering the uncertainty in forest growth and thus in revenues from timber harvest. The proposed model was tested on a small forest with 89 stands and the numerical results showed that the approach allows to have superior solutions in terms of net present value and robustness in face of different climate scenarios compared to the approach using the expected growth and yield. The SAA methods requires to generate samples from the distribution of the random parameter. Our results suggested that a sampling scheme that focuses on generating high number of samples in distant future stages is favorable compared to having large sample sizes for the near future stages. Finally, we demonstrated that, depending on the level of forest growth change, ignoring this uncertainty can negatively affect forest resources sustainability.

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Section: Discussionmentioning

confidence: 99%

Multistage Sample Average Approximation for Harvest Scheduling under Climate Uncertainty

Bagaram¹,

Tóth²

2020

Preprint

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“…( 5) else (6) for n in fixed nodes which successor are not fixed do (7) for m ∈ I n do (8) PHVF(θ, Ω(m), k + 1) ( 9) end for (10) end for (11) end if (12) return x ω (13) end function ALGORITHM 3: PH variable fixing. [11,14,21,24,25,29,33] and more importantly [34] who describe scenario generation in the forest management framework. We tested our algorithm on six different forests with three being real forests, and the data of which are publicly available 1 (P1, P34, P36).…”

Section: Experimental Designmentioning

confidence: 99%

A Parallelized Variable Fixing Process for Solving Multistage Stochastic Programs with Progressive Hedging

Bagaram

Tóth

Jaross³

et al. 2020

Advances in Operations Research

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Long time horizons, typical of forest management, make planning more difficult due to added exposure to climate uncertainty. Current methods for stochastic programming limit the incorporation of climate uncertainty in forest management planning. To account for climate uncertainty in forest harvest scheduling, we discretize the potential distribution of forest growth under different climate scenarios and solve the resulting stochastic mixed integer program. Increasing the number of scenarios allows for a better approximation of the entire probability space of future forest growth but at a computational expense. To address this shortcoming, we propose a new heuristic algorithm designed to work well with multistage stochastic harvest-scheduling problems. Starting from the root-node of the scenario tree that represents the discretized probability space, our progressive hedging algorithm sequentially fixes the values of decision variables associated with scenarios that share the same path up to a given node. Once all variables from a node are fixed, the problem can be decomposed into subproblems that can be solved independently. We tested the algorithm performance on six forests considering different numbers of scenarios. The results showed that our algorithm performed well when the number of scenarios was large.

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“…Forest management operates under uncertainty; however, through empirical testing, the probability of the uncertainty can be estimated. In a forestry context, stochastic programming has been used to schedule forest harvesting and road building decisions (Alonso-Ayuso et al 2011;Andalaft et al 2003), to planning the management response to forest fires (Boychuk and Martell 1996;Ntaimo et al 2012), and to adjust to changes in timber prices (Piazza and Pagnoncelli 2014;Rios et al 2016). For forest management planning, estimates of uncertainty can be evaluated through empirical data on inventory errors, and through time series data on growth model errors.…”

Section: Introductionmentioning

confidence: 99%

Determining the appropriate timing of the next forest inventory: incorporating forest owner risk preferences and the uncertainty of forest data quality

Eyvindson

Petty

Kangas

2017

Annals of Forest Science

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& Key message The timing to conduct new forest inventories should be based on the requirements of the decision maker. Importance should be placed on the objectives of the decision maker and his/her risk preferences related to those objectives. & Context The appropriate use of pertinent and available information is paramount in any decision-making process. Within forestry, a new forest inventory is typically conducted prior to creating a forest management plan. The acquisition of new forest inventory data is justified by the simple statement of "good decisions require good data." & Aims By integrating potential risk preferences, we examine the specific needs to collect new forest information. & Methods Through a two-stage stochastic programming with recourse model, we evaluate the specific timing to conduct a holding level forest inventory. A Monte Carlo simulation was used to integrate both inventory and growth model errors, resulting in a large number of potential scenarios process to be used as data for the stochastic program. To allow for recourse, an algorithm to sort the simulations to represent possible updated forest inventories, using the same data was developed. & Results Risk neutral decision makers should delay obtaining new forest information when compared to risk averse decision makers. & Conclusion New inventory data may only need to be collected rather infrequently; however, the exact timing depends on the forest owner's objectives and risk preferences.

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Building a stochastic programming model from scratch: a harvesting management example

Cited by 14 publications

References 20 publications

Multistage Sample Average Approximation for Harvest Scheduling under Climate Uncertainty

Multistage Sample Average Approximation for Harvest Scheduling under Climate Uncertainty

A Parallelized Variable Fixing Process for Solving Multistage Stochastic Programs with Progressive Hedging

Determining the appropriate timing of the next forest inventory: incorporating forest owner risk preferences and the uncertainty of forest data quality

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