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We present a mixed integer nonlinear mathematical programming model, covering a broad range of operations research (OR)-related topics. The case is designed to allow students to use knowledge acqui...

We present a mixed integer nonlinear mathematical programming model, covering a broad range of operations research (OR)-related topics. The case is designed to allow students to use knowledge acquired from OR and management science classes to model, analyze, and provide concrete solutions for the considered problem. Because of its high practicality, this exercise is an ideal tool to make the OR domain more accessible and to learn how to balance a problem’s complexity with the availability of algorithms for its solution. The case has been proposed as a competitive challenge and has been assigned both to students pursuing a bachelor’s degree in management engineering and students pursuing a master’s degree in industrial engineering. Students were grouped into working teams, and all teams competed against each other to get the best solution to win the challenge. Both the work-in-team and the challenge settings have been enjoyed by the students. During three lectures of 90 minutes, a brief review of OR-related tools and a detailed description and analysis of the case study have been provided to the students. Successive periodic debriefing meeting sessions have been scheduled to engage and monitor students during project development. Online supplemental files are available at https://doi.org/10.1287/ited.2018.0202ca .

We derive conditions under which the time-step, or the myopic, approach to generation capacity planning in the power industry yields solutions identical to the solution obtained by an equivalent dynamic model that views the capacity expansion program simultaneously over time. The conditions are derived for thermal power systems for which the capacity expansion program is formulated using a convex, nonlinear mathematical programming model.

This paper is concerned with Holder, Lipschitz and differential properties of the optimal solutions of a nonlinear mathematical programming problem with perturbations in some fixed direction. These properties are obtained with virtually minimal regularity conditions using an approach based on duality and stability. The Holder property is used to obtain the directional derivative for the optimal value function.