Errors in forest inventory data can lead to sub-optimal management decisions and dramatic economic losses. Forest inventory approaches are typically evaluated by their levels of precision and accuracy;however, this ov...
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Errors in forest inventory data can lead to sub-optimal management decisions and dramatic economic losses. Forest inventory approaches are typically evaluated by their levels of precision and accuracy;however, this overlooks the specific usefulness of the data in decision-making. By evaluating the value of information (VoI), we can assess the usefulness of the data for specific decision-making problems. We evaluated the VoI through stochastic programming for four airborne laser scanning-based inventory approaches. The stochastic programming model explored the trade-off between the maximal net present value and the minimal conditional value at risk of meeting specified periodic income targets. We evaluated a range of periodic targets and risk aversion preference levels. To compare the performance of the inventory approaches, we used a reference dataset that was acquired using a forest harvester with precise positioning. For a wide range of the trade-offs, inventory approaches with higher-quality information provided the best overall performance. If only one of the extreme objectives was desired, less precise inventory approaches were sufficient to produce high-quality solutions.
作者：
Sahin, KHDiwekar, UMUniv Illinois
Ctr Uncertain Syst Tools Optimizat & Management Dept Bioind Chicago IL 60514 USA Univ Illinois
Dept Chem Engn Inst Environm Sci & Technol Chicago IL 60514 USA
A new nonlinear programming algorithm is proposed for stochastic programming problems. This method relies on sampling to estimate the probabilistic objective function and constraints. The computational burden of exces...
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A new nonlinear programming algorithm is proposed for stochastic programming problems. This method relies on sampling to estimate the probabilistic objective function and constraints. The computational burden of excessive model calculations for determining the search direction is bypassed through a reweighting method using Kernel Density Estimation. The improvements accomplished by this algorithm called Better Optimization of Nonlinear Uncertain Systems (BONUS) are presented through two real world case studies involving parameter design for off-line quality control of a chemical reactor, and optimal capacity expansion for electric utilities in uncertain markets.
In natural resource sectors such as forestry, supply is subject to yield uncertainty, which can make planning decisions a challenge. A common way of dealing with uncertainty is to coordinate the decisions so all units...
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In natural resource sectors such as forestry, supply is subject to yield uncertainty, which can make planning decisions a challenge. A common way of dealing with uncertainty is to coordinate the decisions so all units in a network can better prepare for unpredicted events. This can generate plans that are more robust and reduce the negative impacts of uncertainty. The objective of this study is to evaluate the benefits of including coordination mechanisms in a forest supply chain to better face yield uncertainty. First, a stochastic program is developed to simulate a sawmill production planning decision process, taking wood supply uncertainty into account. Based on this model, six coordination mechanisms are proposed to help reduce the impact of an uncertain wood supply. The impact of uncertainty is measured using the individual transportation cost of each sawmill, the overall network cost, the cost for replanning operations, the volume of extra resources needed, backorders, and the prescribed wood supply from forest sites to sawmills. Historical data from a partnering company in the province of Quebec, Canada, are used to quantify the current level of uncertainty. Compared to the typical strategy of Fixed Supply and Fixed Demand, the Free Supply with Free Demand mechanism generates plans with more stability, offering a 64% reduction in transportation cost, and a reduction of 84 % in the volume of extra resources to be acquired outside the regular sources at a higher cost to prevent production shortage.
This paper presents a formulation and resolution of a two-stage stochastic linear programming model with recourse for sow farms producing piglets. The proposed model considers a medium-term planning horizon and specif...
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This paper presents a formulation and resolution of a two-stage stochastic linear programming model with recourse for sow farms producing piglets. The proposed model considers a medium-term planning horizon and specifically allows optimal replacement and schedule of purchases to be obtained for the first stage. This model takes into account sow herd dynamics, housing facilities, reproduction management, herd size with initial and final inventory of sows and uncertain parameters such as litter size, mortality and fertility rates. These last parameters are explicitly incorporated via a finite set of scenarios. The proposed model is solved by using the algebraic modelling software OPL Studio from ILOG, in combination with the solver CPLEX to solve the linear models resulting from different instances considered. The article also presents results obtained with previous deterministic models assessing the suitability of the stochastic approach. Finally, the conclusions drawn from the study including an outlook are presented.
This paper proposes and tests an approximation of the solution of a class of piecewise deterministic control problems, typically used in the modeling of manufacturing flow processes. This approximation uses a stochast...
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This paper proposes and tests an approximation of the solution of a class of piecewise deterministic control problems, typically used in the modeling of manufacturing flow processes. This approximation uses a stochastic programming approach on a suitably discretized and sampled system. The method proceeds through two stages: (i) the Hamilton-Jacobi-Bellman (HJB) dynamic programming equations for the finite horizon continuous time stochastic control problem are discretized over a set of sampled times;this defines an associated discrete time stochastic control problem which, due to the finiteness of the sample path set for the Markov disturbance process, can be written as a stochastic programming problem;and (ii) the very large event tree representing the sample path set is replaced with a reduced tree obtained by randomly sampling over the set of all possible paths. It is shown that the solution of the stochastic program defined on the randomly sampled tree converges toward the solution of the discrete time control problem when the sample size increases to infinity. The discrete time control problem solution converges to the solution of the flow control problem when the discretization mesh tends to zero. A comparison with a direct numerical solution of the dynamic programming equations is made for a single part manufacturing flow control model in order to illustrate the convergence properties. Applications to larger models affected by the curse of dimensionality in a standard dynamic programming techniques show the possible advantages of the method.
Scheduling of multipurpose batch chemical plant is always affected by uncertain factors, including processing time of tasks. When the processing time deviates from its nominal value, the task sequence and executing ti...
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Scheduling of multipurpose batch chemical plant is always affected by uncertain factors, including processing time of tasks. When the processing time deviates from its nominal value, the task sequence and executing time based upon the original schedule may become suboptimal or even infeasible. To address this issue, an optimization model based on stochastic programming is proposed for the short-term scheduling of multipurpose batch chemical plant, by introducing task sequence variables and new logical constraints relating multiple binary variables. Additionally, a network-based decomposition solution strategy, accounting for different situations of profits and shared units, is proposed to solve the large-scale problems, which has been shown to provide high quality solutions while consuming substantially less solution time than solving the entire process directly.
Deterministic models, even if used repeatedly, will not capture the essence of planning in an uncertain world. Flexibility and robustness can only be properly valued in models that use stochastics explicitly, such as ...
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Deterministic models, even if used repeatedly, will not capture the essence of planning in an uncertain world. Flexibility and robustness can only be properly valued in models that use stochastics explicitly, such as stochastic optimization models. However, it may also be very important to capture how the random phenomena are related to one another. In this article we show how the solution to a stochastic service network design model depends heavily on the correlation structure among the random demands. The major goal of this paper is to discuss why this happens, and to provide insights into the effects of correlations on solution structures. We illustrate by an example.
After reviewing existing approaches to the general stochastic programming problem, an improved experi mental method is proposed. This method uses a va riety of mathematical programming algorithms and any desired patte...
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After reviewing existing approaches to the general stochastic programming problem, an improved experi mental method is proposed. This method uses a va riety of mathematical programming algorithms and any desired pattern of parameter variation. Statistical analysis of the results allows decision-makers to make probabilistic statements about the values of the decision variables and of the objective function. Illustrative examples are given.
We summarize the fields and problems, where a new iterative method has been applied succesfully. The successive regression approximation technique is easy to apply to problems, where one or more functions can not be e...
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ISBN:
(纸本)9789955282839
We summarize the fields and problems, where a new iterative method has been applied succesfully. The successive regression approximation technique is easy to apply to problems, where one or more functions can not be evaluated exactly, or some of the parameters are random. This is the case with all problems, where some of the functions have to be computed by Monte Carlo techniques. Here probabilistic constrained and two stage problems, a combined model and random linear problems are dealt with.
We propose a new stochastic mixed -integer linear programming model for a home service fleet sizing and appointment scheduling problem (HFASP) with random service and travel times. Specifically, given a set of provide...
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We propose a new stochastic mixed -integer linear programming model for a home service fleet sizing and appointment scheduling problem (HFASP) with random service and travel times. Specifically, given a set of providers and a set of geographically distributed customers within a service region, our model solves the following problems simultaneously: (i) a fleet sizing problem that determines the number of providers required to serve customers;(ii) an assignment problem that assigns customers to providers;and (iii) a sequencing and scheduling problem that decides the sequence of appointment times of customers assigned to each provider. The objective is to minimize the fixed cost of hiring providers plus the expectation of a weighted sum of customers' waiting time and providers' travel time, overtime, and idle time. We compare our proposed model with an extension of an existing model for a closely related problem in the literature, theoretically and empirically. Specifically, we show that our newly proposed model is more compact (i.e., has fewer variables and constraints) and provides a tighter linear programming relaxation. Furthermore, to handle large instances observed in other application domains, we propose two optimization -based heuristics that decompose the HFASP decision process into two steps. The first step involves determining fleet sizing and assignment decisions, and the second constructs a routing plan and a schedule for each provider. We present extensive computational results to show the size and characteristics of HFASP instances that can be solved with our proposed model, demonstrating its computational efficiency over the extension. Results also show that the proposed heuristics can quickly produce high -quality solutions to large instances with an optimality gap not exceeding 5% on tested instances. Finally, we use a case study based on a service region in Lehigh County to derive insights into the HFASP.
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