A multi-stage stochastic programming for lot-sizing and scheduling under demand uncertainty

A stochastic lot-sizing and scheduling problem with demand uncertainty is studied in this paper. Lot-sizing determines the batch size for each product and scheduling decides the sequence of production. A multi-stage stochastic programming model is developed to minimize overall system costs including production cost, setup cost, inventory cost and backlog cost. We aim to find the optimal production sequence and resource allocation decisions. Demand uncertainty is represented by scenario trees using moment matching technique. Scenario reduction is used to select scenarios with the best representation of original set. A case study based on a manufacturing company has been conducted to illustrate and verify the model. We compared the two-stage stochastic programming model to the multi-stage stochastic programming model. The major motivation to adopt multi-stage stochastic programming models is that it extends the two-stage stochastic programming models by allowing revised decision at each period based on the previous realizations of uncertainty as well as decisions. Stability test and weak out-of-sample test are applied to find an appropriate scenario sample size. By using the multi-stage stochastic programming model, we improved the quality of solution by 10–13%

Statistical methods for surgery duration estimation

Surgery is a primary source of revenue in a hospital, and scheduling of surgery can significantly impact surgeons’ and patients’ satisfaction and thus revenue. The major objective in surgery scheduling is to minimize the amount of waiting time for patients and maximize the utilization of the operating rooms while considering the needs of surgeons. In this process, accurately estimating surgery durations is among the most important factors. Using data from a large Midwestern hospital, surgery duration estimations were compared to actual durations in a one-year period for the top surgeries. Statistically, a significant difference between actual and estimated durations has been identified. With the goal of decreasing the difference between the estimated and actual durations, multiple linear regression models were created for the most common surgeries and used to analyze the impact various characteristics of surgery cases have on the duration. Due to the high variability of the data, the regression method was not found particularly effective in identifying significant correlations in the input characteristics

Technoeconomic Sensitivity of Biobased Hydrocarbon Production via Fast Pyrolysis to Government Incentive Programs

Fast pyrolysis and upgrading is a promising thermochemical pathway that produces pyrolysis oil that can be upgraded via hydroprocessing into hydrocarbon-based transportation fuels (drop-in biofuels). The internal rate of return (IRR) of a fast pyrolysis and upgrading facility is a function of feedstock cost and projected revenues. We calculate the IRR of a fast pyrolysis and upgrading facility under six different policy scenarios: (1)a baseline scenario in which the facility receives no government support; (2)a scenario in which cap-and-trade (H.R. 2454) is enacted with both carbon price and offsets; (3)a scenario in which the Volumetric Ethanol Excise Tax Credit (VEETC) is modified to include drop-in biofuels; (4)a scenario in which the VEETC is replaced with a variable VEETC; (5)the revised Renewable Fuel Standard (RFS2); and (6)the Cellulosic Biofuel Producer Tax Credit (CBPTC). Combinations of these policy scenarios are also analyzed. We find that the policies responsible for increasing the value of pyrolysis products increase facility IRR the most, whereas policies minimizing facility tax burden have an only marginal effect on IRR

Optimization models for biorefinery supply chain network design under uncertainty

Biofuel industry has attracted much attention due to its potential to reduce dependency on fossil fuels and contribute to the renewable energy. The high levels of uncertainty in feedstock yield, market prices, production costs, and many other parameters are among the major challenges in this industry. This challenge has created an ongoing interest on studies considering different aspects of uncertainty in investment decisions of the biofuel industry. This study aims to determine the optimal design of supply chain for biofuel refineries in order to maximize annual profit considering uncertainties in fuel market price, feedstock yield, and logistic costs. In order to deal with the stochastic nature of parameters in the biofuel supply chain, we develop two-stage stochastic programming models in which Conditional Value at Risk (CVaR) is utilized as a risk measure to control the amount of shortage in demand zones. Two different approaches including the expected value and CVaR of the profit are considered as the objective function. We apply these models and compare the results for a case study of the biomass supply chain network in the state of Iowa to demonstrate the applicability and efficiency of the presented models

Biomass supply contract pricing and environmental policy analysis: A simulation approach

This paper proposes an agent-based simulation model to study the biomass supply contract pricing and policy making in the biofuel industry. In the proposed model, the agents include farmers and a biofuel producer. Farmers\u27 decision-making is assumed to be profit driven, which is formulated as a mixed-integer optimization model, and the biofuel producer\u27s pricing decision is represented with a linear equation with an objective to maximize profits. A case study based on Iowa has been developed to analyze the interactions between the stakeholders and assist determination of the optimal pricing equation for the biofuel producer. Simulation results show that under such a pricing strategy, the biofuel producer can achieve higher profitability than using a fixed price. The impact of government environmental regulations on farmers\u27 decision-making and biomass supply has also been analyzed, and managerial insights have been derived

Techno-economic analysis of biomass to transportation fuels and electricity via fast pyrolysis and hydroprocessing

A previous Iowa State University (ISU) analysis published in 2010 investigated the technical and economic feasibility of the fast pyrolysis and hydroprocessing of biomass, and concluded that the pathway could produce cellulosic biofuels for a minimum fuel selling price (MFSP) of $2.11/gal. The 2010 ISU study was largely theoretical in that no commercial-scale fast pyrolysis facilities were being constructed at the time of publication. The present analysis expands upon the 2010 ISU study by performing an updated techno-economic analysis of the fast pyrolysis and hydroprocessing pathway. Recent advances in pathway technology and commercialization and new parameters suggested by the recent literature are accounted for. The MFSP for a 2000 MTPD facility employing fast pyrolysis and hydroprocessing to convert corn stover to gasoline and diesel fuel is calculated to quantify the economic feasibility of the pathway. The present analysis determines the MFSP of gasoline and diesel fuel produced via fast pyrolysis and hydroprocessing to be$2.57/gal. This result indicates that the pathway could be competitive with petroleum, although not as competitive as suggested by the 2010 ISU study. The present analysis also demonstrates the sensitivity of the result to process assumptions

A Hybrid Two-layer Feature Selection Method Using GeneticAlgorithm and Elastic Net

Feature selection, as a critical pre-processing step for machine learning, aims at determining representative predictors from a high-dimensional feature space dataset to improve the prediction accuracy. However, the increase in feature space dimensionality, comparing to the number of observations, poses a severe challenge to many existing feature selection methods with respect to computational efficiency and prediction performance. This paper presents a new hybrid two-layer feature selection approach that combines a wrapper and an embedded method in constructing an appropriate subset of predictors. In the first layer of the proposed method, the Genetic Algorithm(GA) has been adopted as a wrapper to search for the optimal subset of predictors, which aims to reduce the number of predictors and the prediction error. As one of the meta-heuristic approaches, GA is selected due to its computational efficiency; however, GAs do not guarantee the optimality. To address this issue, a second layer is added to the proposed method to eliminate any remaining redundant/irrelevant predictors to improve the prediction accuracy. Elastic Net(EN) has been selected as the embedded method in the second layer because of its flexibility in adjusting the penalty terms in regularization process and time efficiency. This hybrid two-layer approach has been applied on a Maize genetic dataset from NAM population, which consists of multiple subsets of datasets with different ratio of the number of predictors to the number of observations. The numerical results confirm the superiority of the proposed model

Market Competition and Social Welfare Analysis for E10 and E85 with a 1 Game Theory Model

With the increasing concerns about the petroleum reserve, and the global warming, people have been looking for renewable and environmental friendly energy sources to supplement and replace fossil fuels. Ethanol has been an appropriate substitute to fossil fuels. Currently, E10 and E85 are two of the main transportation fuels with ethanol and they are competing in the market. This study investigates the competition between E10 and E85 with an oligopoly Cournot model and derives three indicators from the equilibrium to measure the performance of the market: E85\u27s market share, E85 price premium which indicate the consumers\u27 additional willingness to pay, and the social welfare which indicates the societal wellbeing from the products. The authors also studied how the government policies impact the market equilibrium, how the industry size affects the market performance of E85, and whether E85 has a bright prospect with the increase of FFVs number. The results not only provide some prospects of E85, but also benefit the policy makers by quantitatively showing the effectiveness of tax credits and other government policies to promote the ethanol industr

Supply chain design and operational planning models for biomass to drop-in fuel production

Renewable fuel is playing an increasingly important role as a substitute for fossil based energy. The US Department of Energy (DOE) has identified pyrolysis based platforms as promising biofuel production pathways. In this paper, we present a general biofuel supply chain model with a Mixed Integer Linear Programming (MILP) methodology to investigate the biofuel supply chain facility location, facility capacity at strategic levels, and biofuel production decisions at operational levels. In the model, we accommodate different biomass supplies and biofuel demands with biofuel supply shortage penalty and storage cost. The model is then applied to corn stover fast pyrolysis pathway with upgrading to hydrocarbon fuel since corn stover is the main feedstock for second generation biofuel production in the US Midwestern states. Numerical results illustrate unit cost for biofuel production, biomass, and biofuel allocation. The case study demonstrates the economic feasibility of producing biofuel from biomass at a commercial scale in Iowa

Shop Floor Lot-sizing and Scheduling with a Two-stage Stochastic Programming Model Considering Uncertain Demand and Workforce Efficiency

Efficient and flexible production planning is necessary for the manufacturing industry to stay competitive in today’s global market. Shop floor lot-sizing and scheduling is one of the most challenging and rewarding subjects for the management. In this study, a two-stage stochastic programming model is proposed to solve a single-machine, multi-product shop floor lot-sizing and scheduling problem. Two sources of uncertainties are considered simultaneously: product demand from the market, and workforce efficiency, which is the major contribution of this study. The workforce efficiency affects the system productivity, and we propose different distributions to model its uncertainty with insufficient information.The model aims to determine optimal lot sizes and the production sequence that minimizes expected total system costs over the planning horizon, including setup, inventory, and production costs. A case study is performed on a supply chain producing brake equipment in the automotive industry. The numerical results illustrate the usefulness of the stochastic model under volatile environment, and the solution quality is analyzed