In this paper we consider a practical lot-sizing problem faced by an industrial company. The company plans the production for a set of products following a Make-To-Order policy. When the productive capacity is not fully used, the remaining capacity is devoted to the production of those products whose orders are typically quite below the established minimum production level. For these products the company follows a Make-To-Stock (MTS) policy since part of the production is to fulfill future estimated orders. This yields a particular lot-sizing problem aiming to decide which products should be produced and the corresponding batch sizes. These lot-sizing problems typically face uncertain demands, which we address here through the lens of robust optimization. First we provide a mixed integer formulation assuming the future demands are deterministic and we tighten the model with valid inequalities. Then, in order to account for uncertainty of the demands, we propose a robust approach where demands are assumed to belong to given intervals and the number of deviations to the nominal estimated value is limited. As the number of products can be large and some instances may not be solved to optimality, we propose two heuristics. Computational tests are conducted on a set of instances generated from real data provided by our industrial partner. The heuristics proposed are fast and provide good quality solutions for the tested instances. Moreover, since they are based on the mathematical model and use simple strategies to reduce the instances size, these heuristics could be extended to solve other multi-item lot-sizing problems where demands are uncertain.

A new continuous-time model for long-term scheduling of a gas engine power plant with parallel units is presented. Gas engines are shut down according to a regular maintenance plan that limits the number of hours spent online. To minimize salary expenditure with skilled labor, a single maintenance team is considered which is unavailable during certain periods of time. Other challenging constraints involve constant minimum and variable maximum power demands. The objective is to maximize the revenue from electricity sales assuming seasonal variations in electricity pricing by reducing idle times and shutdowns in high-tariff periods. By first developing a generalized disjunctive programming model and then applying both big-M and hull reformulation techniques, we reduce the burden of finding the appropriate set of mixed-integer linear constraints. Through the solution of a real-life problem, we show that the proposed formulations are very efficient computationally, while gaining valuable insights about the system.

This paper discusses a power-based transformation technique that is especially useful when solving polynomial optimization problems, frequently occurring in science and engineering. The polynomial nonlinear problem is primarily transformed into a suitable reformulated problem containing new sets of discrete and continuous variables. By applying a term-wise disaggregation scheme combined with multi-parametric elements, an upper/lower bounding mixed-integer linear program can be derived for minimization/maximization problems. It can then be solved to global optimality through standard methods, with the original problem being approximated to a certain precision level, which can be as tight as desired. Furthermore, this technique can also be applied to signomial problems with rational exponents, after a few effortless algebraic transformations. Numerical examples taken from the literature are used to illustrate the effectiveness of the proposed approach.

In this paper we address the optimal sizing and scheduling of isolated hybrid systems using an optimization framework. The hybrid system features wind and photovoltaic conversion systems, batteries and diesel backup generators to supply electricity demand. A Mixed-Integer Linear Programming formulation is used to model system behavior over a time horizon of one year, considering hourly changes in both the availability of renewable resources and energy demand. The optimal solution is achieved with respect to the minimization of the levelized cost of energy (LCOE) over a lifetime of 20 years. Results for a case study show that the most economical solution features all four postulated subsystems.

In this paper, we present the derivation of the multiparametric disaggregation technique (MDT) by Teles et al. (J. Glob. Optim., 2011) for solving nonconvex bilinear programs. Both upper and lower bounding formulations corresponding to mixed-integer linear programs are derived using disjunctive programming and exact linearizations, and incorporated into two global optimization algorithms that are used to solve bilinear programming problems. The relaxation derived using the MDT is shown to scalemuchmore favorably than the relaxation that relies on piecewise McCormick envelopes, yielding smallermixed-integer problems and faster solution times for similar optimality gaps. The proposed relaxation also compares well with general global optimization solvers on large problems.

We address nonconvex mixed-integer bilinear problems where the main challenge is the computation of a tight upper bound for the objective function to be maximized. This can be obtained by using the recently developed concept of multiparametric disaggregation following the solution of a mixed-integer linear relaxation of the bilinear problem. Besides showing that it can provide tighter bounds than a commercial global optimization solver within a given computational time, we propose to also take advantage of the relaxed formulation for contracting the variables domain and further reduce the optimality gap. Through the solution of a real-life case study from a hydroelectric power system, we show that this can be an efficient approach depending on the problem size. The relaxed formulation from multiparametric formulation is provided for a generic numeric representation system featuring a base between 2 (binary) and 10 (decimal).

This article proposes a multi-objective mixed-integer linear programming model to assist event managers in obtaining and evaluating non-dominated solutions to the problem of selecting a daily lineup of shows and activities for a festival – be it cultural, sports, ceremonial or any other kind. The model, which is especially adequate for designing festivals with public funding, has five objectives, relating to financial, logistical and how renowned the festival artists or acts are. It includes support for multiple days, multiple stages and differ- ent types of shows, all subject to constraints imposed by the intrinsic nature of the festival itself. The output of the model is a set of optimized daily lineups for the activities that constitute the festival, each correspond- ing to a particular compromise between the five objectives. The approach is demonstrated with a case study for a 5-day festival, for which non-dominated solutions are derived, presented and discussed. Results show that the model can provide a good variety of solutions while ensuring the persistence of the more desirable shows. The model is a novel decision support tool to assist in designing festival lineups that provide optimal audience experience, a key factor in attracting spectators, tourists and increasing comeback value.