Power-intensive processes can lower operating expenses when adjusting production planning according to time-dependent electricity pricing schemes. In this paper, we describe a deterministic MILP model that allows optimal production planning for continuous powerintensive processes. We emphasize the systematic modeling of operational transitions, that result from switching the operating modes of the plant equipment, with logic constraints. We prove properties on the tightness of several logic constraints. For the time horizon of one week and hourly changing electricity prices, we solve an industrial case study on air separation plants, where transitional modes help us capture ramping behavior. We also solve problem instances on cement plants where we show that the appropriate choice of operating modes allows us to obtain practical schedules, while limiting the number of changeovers. Despite the large size of the MILPs, the required solution times are small due to the explicit modeling of transitions.

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We present a compendium of disk galaxy scaling relations and a detailed characterization of their intrinsic scatter. Observed scaling relations are typically characterized by their slope, intercept, and scatter; however, these parameters are a mixture of observational errors and astrophysical processes. We introduce a novel Bayesian framework for computing the intrinsic scatter of scaling relations that accounts for nonlinear error propagation and covariant uncertainties. Bayesian intrinsic scatters are ∼25% more accurate than those obtained with a first-order classical method, which systematically underestimates the true intrinsic scatter. Structural galaxy scaling relations based on velocity (V 23.5), size (R 23.5), luminosity (L 23.5), color (g − z), central stellar surface density (Σ1), stellar mass (M *), dynamical mass (M dyn), stellar angular momentum (j *), and dynamical angular momentum (j dyn) are examined to demonstrate the power and importance of the Bayesian formalism. Our analysis is based on a diverse selection of over 1000 late-type galaxies from the Photometry and Rotation Curve Observations from Extragalactic Surveys compilation with deep optical photometry and extended rotation curves. We determine the tightest relation for each parameter by intrinsic orthogonal scatter, finding M * − V 23.5, R 23.5 − j *, and L 23.5 − j dyn to be especially tight. The scatter of the R 23.5 − L 23.5, V 23.5 − (g − z), and R 23.5 − j dyn relations is mostly intrinsic, making them ideal for galaxy formation and evolutionary studies. Our code to compute the Bayesian intrinsic scatter of any scaling relation is also presented. We quantify the correlated nature of many uncertainties in galaxy scaling relations and scrutinize the uncertain nature of disk inclination corrections and their effect on scatter estimates.

In this paper, we address the optimization of industrial gas distribution systems, which consist of plants and customers, as well as storage tanks, trucks and trailers. A mixedinteger linear programming (MILP) model is presented to minimize the total capital and operating cost, and to integrate short-term distribution planning decisions for the vehicle routing with long-term inventory decisions for sizing storage tanks at customer locations. In order to optimize asset allocation in the industrial gas distribution network by incorporating operating decisions, the model also takes into account the synergies among delivery schedule, tank sizes, customer locations and inventory profiles. To effectively solve large scale instances, we propose two fast computational strategies. The first approach is a two-level solution strategy based on the decomposition of the full scale MILP model into an upper level route selectiontank sizing model and a lower level reduced routing model. The second approach is based on a continuous approximation method, which estimates the operational cost at the strategic level and determines the tradeoff with the capital cost from tank sizing.Three cases studies including instances with up to 200 customers are presented to illustrate the applications of the models and the performance of the proposed solution methods.

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