Production Planning Under Uncertainty Using Bayesian Inference and Stochastic Programming PDF Download
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Author: Robert Lincoln Clay
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Languages : en
Pages : 0
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Author: Robert Lincoln Clay
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Languages : en
Pages : 0
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Author: Vibhor Vineet
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Languages : en
Pages : 0
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Effective planning strategies are essential to minimize high costs of production and inventory. Uncertainty and seasonal variation in product demand is a major issue that contributes to a substantial share of production planning costs. Hence, it is important to consider the uncertain information while designing a production planning model. This thesis is aimed at presenting a comparative analysis of deterministic and stochastic approaches towards finding optimal solutions for demand uncertainty problems. The first model is a generic mixed-integer programming model to maximize total profit. Decision variables are identified and random values are substituted by their expected values considering uncertainty to obtain the expected value solutions. Second model is formulated as a stochastic programming model by adding scenarios and probabilities in the deterministic model to explicitly account for the uncertainties in the product demand. The models are programmed and solved by LINGO optimization solver based on data collected from a brewing company. Several test problems are solved by varying the input parameters, product demand and probability of existence of scenarios to study the sensitivity of the models. A statistical comparative analysis is conducted on all the example problems by measuring the Expected Value of Perfect Information (EVPI), Value of Stochastic Solution (VSS) and the results are discussed.
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Languages : fr
Pages : 20
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Author: Stacy Dawn Lewis
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Category : Production planning
Languages : en
Pages : 82
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Languages : en
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Author: Kai Huang
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Category : Approximation theory
Languages : en
Pages :
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In this thesis, we study a series of closely related multi-stage stochastic programming models in production planning, from both a modeling and an algorithmic point of view. We first consider a very simple multi-stage stochastic lot-sizing problem, involving a single item with no fixed charge and capacity constraint. Although a multi-stage stochastic integer program, this problem can be shown to have a totally unimodular constraint matrix. We develop primal and dual algorithms by exploiting the problem structure. Both algorithms are strongly polynomial, and therefore much more efficient than the Simplex method. Next, motivated by applications in semiconductor tool planning, we develop a general capacity planning problem under uncertainty. Using a scenario tree to model the evolution of the uncertainties, we present a multi-stage stochastic integer programming formulation for the problem. In contrast to earlier two-stage approaches, the multi-stage model allows for revision of the capacity expansion plan as more information regarding the uncertainties is revealed. We provide analytical bounds for the value of multi-stage stochastic programming over the two-stage approach. By exploiting the special simple stochastic lot-sizing substructure inherent in the problem, we design an efficient approximation scheme and show that the proposed scheme is asymptotically optimal. We conduct a computational study with respect to a semiconductor-tool-planning problem. Numerical results indicate that even an approximate solution to the multi-stage model is far superior to any optimal solution to the two-stage model. These results show that the value of multi-stage stochastic programming for this class of problem is extremely high. Next, we extend the simple stochastic lot-sizing model to an infinite horizon problem to study the planning horizon of this problem. We show that an optimal solution of the infinite horizon problem can be approximated by optimal solutions of a series of finite horizon problems, which implies the existence of a planning horizon. We also provide a useful upper bound for the planning horizon.
Author: J.K. Sengupta
Publisher: Springer Science & Business Media
ISBN: 3642701639
Category : Business & Economics
Languages : en
Pages : 295
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Understanding the stochastic enviornment is as much important to the manager as to the economist. From production and marketing to financial management, a manager has to assess various costs imposed by uncertainty. The economist analyzes the role of incomplete and too often imperfect information structures on the optimal decisions made by a firm. The need for understanding the role of uncertainty in quantitative decision models, both in economics and management science provide the basic motivation of this monograph. The stochastic environment is analyzed here in terms of the following specific models of optimization: linear and quadratic models, linear programming, control theory and dynamic programming. Uncertainty is introduced here through the para meters, the constraints, and the objective function and its impact evaluated. Specifically recent developments in applied research are emphasized, so that they can help the decision-maker arrive at a solution which has some desirable charac teristics like robustness, stability and cautiousness. Mathematical treatment is kept at a fairly elementary level and applied as pects are emphasized much more than theory. Moreover, an attempt is made to in corporate the economic theory of uncertainty into the stochastic theory of opera tions research. Methods of optimal decision rules illustrated he re are applicable in three broad areas: (a) applied economic models in resource allocation and economic planning, (b) operations research models involving portfolio analysis and stochastic linear programming and (c) systems science models in stochastic control and adaptive behavior.
Author: Masoumeh Kazemi Zanjani
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Category : Combinatorial optimization
Languages : en
Pages : 0
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Languages : en
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Author: Meenakshi Prajapati
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Category : Production planning
Languages : en
Pages : 66
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Production planning plays a vital role in the management of manufacturing facilities. The problem is to determine the production loading plan consisting of the quantity of production and the workforce level - to fulfill a future demand. Although the deterministic version of the problem has been widely studied in the literature, the stochastic production planning problem has not. The application of production planning models could be limited if the stochastic nature of the problem, for example, uncertainty in future demand, is not addressed. This study addresses such a stochastic production planning problem under uncertain demand and its application in an enclosure manufacturing facility. The thesis first addresses the forecast of the demand where seasonal fluctuation is present. A decomposition model is utilized in the forecast and compared with other forecasting methods. Although forecast models could be used to improve the accuracy of forecast, error and uncertainty still exists. To deal with this uncertainty, a two stage stochastic scenario based production planning model is developed to minimize the total cost consisting of production cost, labor cost, inventory cost and overtime cost under uncertain demand. The model is solved with data from a local manufacturing facility and the results are compared with various deterministic production models to show the effectiveness of the developed stochastic model. Parametric analysis are performed to derive managerial insights related to issues such as overtime usage and inventory holding cost and the proper selection of scenarios under pessimist, neutral and optimist forecasts. An extension of the stochastic model, i.e., a robust model is also solved in an effort to minimize changes in the solutions under various scenarios. The stochastic production planning model has been implemented in the manufacturing facility, provided guidance for material acquisition and production plans and has dramatically increased the company’s bottom line. As a result, it’s estimated an approximately annual savings of $340,000 in inventory cost can be achieved for the company in the next few years.
