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Critical chain buffer management (CCBM) has been extensively studied in recent years. This paper investigates a new formulation of CCBM, the multimode chance-constrained CCBM problem. A flow-based mixed-integer linear programming model is described and the chance constraints are tackled using a scenario approach. A reinforcement learning (RL)-based algorithm is proposed to solve the problem. A factorial experiment is conducted and the results of this study indicate that solving the chance-constrained problem produces shorter project durations than the traditional approach that inserts time buffers into a baseline schedule generated by solving the deterministic problem. This paper also demonstrates that our RL method produces competitive schedules compared to established benchmarks. The importance of solving the chance-constrained problem and obtaining a project buffer tailored to the desired probability of completing the project on schedule directly from the solution is highlighted. Because of its potential for generating shorter schedules with the same on-time probabilities as the traditional approach, this research can be a useful aid for decision makers. [ABSTRACT FROM AUTHOR]

Generating electricity by co-combusting biomass and coal, known as biomass cofiring, is shown to be an economically attractive option for coal-fired power plants to comply with emission regulations. However, the total carbon footprint of the associated supply chain still needs to be carefully investigated. In this study we propose a stochastic biobjective optimization model to analyze the economic and environmental impacts of biopower supply chains. We use a life cycle assessment approach to derive the emission factors used in the environmental objective function. We use chance constraints to capture the uncertain nature of energy content of biomass feedstocks. We propose a cutting plane algorithm which uses the sample average approximation method to model the chance constraints and finds high confidence feasible solutions. In order to find Pareto optimal solutions we propose a heuristic approach which integrates the ϵ -constraint method with the cutting plane algorithm. We show that the developed approach provides a set of local Pareto optimal solutions with high confidence and reasonable computational time. We develop a case study using data about biomass and coal plants in North and South Carolina. The results indicate that, cofiring of biomass in these states can reduce emissions by up to 8%. Increasing the amount of biomass cofired will not result in lower emissions due to biomass delivery. [ABSTRACT FROM AUTHOR]

We study the polyhedral structure of the static probabilistic lot-sizing problem and propose valid inequalities that integrate information from the chance constraint and the binary setup variables. We prove that the proposed inequalities subsume existing inequalities for this problem, and they are facet-defining under certain conditions. In addition, we show that they give the convex hull description of a related stochastic lot-sizing problem. We propose a new formulation that exploits the simple recourse structure, which significantly reduces the number of variables and constraints of the deterministic equivalent program. This reformulation can be applied to general chance-constrained programs with simple recourse. The computational results show that the proposed inequalities and the new formulation are effective for the static probabilistic lot-sizing problems. [ABSTRACT FROM AUTHOR]