The Value of Multi-stage Stochastic Programming in Risk-averse Unit Commitment under Uncertainty

Day-ahead scheduling of electricity generation or unit commitment is an important and challenging optimization problem in power systems. Variability in net load arising from the increasing penetration of renewable technologies have motivated study of various classes of stochastic unit commitment models. In two-stage models, the generation schedule for the entire day is fixed while the … Read more

Bounds on Risk-averse Mixed-integer Multi-stage Stochastic Programming Problems with Mean-CVaR

Risk-averse mixed-integer multi-stage stochastic programming forms a class of extremely challenging problems since the problem size grows exponentially with the number of stages, the problem is non-convex due to integrality restrictions and the objective function is a dynamic measure of risk. For this reason, we propose a scenario tree decomposition approach, namely group subproblem approach, … Read more

Lot Sizing with Piecewise Concave Production Costs

We study the lot-sizing problem with piecewise concave production costs and concave holding costs. This problem is a generalization of the lot-sizing problem with quantity discounts, minimum order quantities, capacities, overloading, subcontracting or a combination of these. We develop a dynamic programming (DP) algorithm to solve this problem and answer an open question in the … Read more

A strong conic quadratic reformulation for machine-job assignment with controllable processing times

We describe a polynomial-size conic quadratic reformulation for a machine-job assignment problem with separable convex cost. Because the conic strengthening is based on only the objective of the problem, it can also be applied to other problems with similar cost functions. Computational results demonstrate the effectiveness of the conic reformulation. Citation Appeared in Operations Research … Read more