José M. Pinto

Efficient MILP formulations and valid cuts for multiproduct pipeline scheduling

Companies are faced with an ever-increasing competitive environment, larger commodity requirements and the need for rapid response to several uncertainties related to distribution and transportation scheduling. The problem addressed in this paper is composed by the short-term scheduling of a real world logistic complex that comprises the distribution of several petroleum derivatives from a single oil refinery to several depots through a single pipeline. The objective of this work is to generalize and to improve the efficiency of the MILP formulation proposed by Rejowski Jr. and Pinto [Comput. Chem. Eng. 27 (2003) 1229]. The model satisfies all operational constraints, such as mass balances, distribution constraints, product demands, sequencing constraints and logical constraints for pipeline operation. Firstly, the original formulation proposed by the authors is stated in a generalized form. Then, special and non-intuitive practical constraints, which minimizes product contamination inside the pipeline segments, are added to the original MILP and the resulting model is analyzed in terms of computational performance and solution quality. Finally, a set of integer cuts that are based on demands and pipeline segment initial inventories is included in the original formulation. All proposed examples are tested in three different demand scenarios. Results show that the formulations with the special constraints find the optimal solution with a higher value when compared to a feasible one of the respective problems without this assumption. When the delivery cuts were considered on the formulation with the special constraints for high demand scenario cases, they improved the CPU time in at least almost 70% when compared to the formulations that did not considered this set of valid cuts.

A mathematical programming approach for cyclic production and cleaning scheduling of multistage continuous plants

The objective of this paper is to address the cyclic scheduling of cleaning and production operations in multiproduct multistage plants with performance decay. A mixed-integer nonlinear programming (MINLP) model based on continuous time representation is proposed that can simultaneously optimize the production and cleaning scheduling. The resulting mathematical model has a linear objective function to be maximized over a convex solution space thus allowing globally optimal solutions to be obtained with an outer approximation algorithm. Case studies demonstrate the applicability of the model and its potential benefits in comparison with a hierarchical procedure for the production and cleaning scheduling problem.

MIXED-INTEGER PROGRAMMING TECHNIQUES FOR THE SCHEDULING OF FUEL OIL AND ASPHALT PRODUCTION

This paper addresses the development and solution of mixed-integer (MIP) optimization models to a real-world fuel oil and asphalt production scheduling problem at the Petrobras Revap refinery, which is responsible for approximately 80% of all fuel oil consumed in Brazil.

A global optimization approach for metabolic flux analysis based on labeling balances

Abstract The flux quantification step in metabolic flux analysis (MFA) includes the mathematical modeling of metabolism (based on both metabolite and isotope balancing) and its optimization, which minimizes a weighted distance between measurements and model predictions. When GC–MS is used for assessing the 13 C-labeling in intracellular metabolites, the metabolic flux quantification problem originates a non-convex optimization model with bilinear constraints for which the existence of multiple local minima is a special difficulty. In the present work, we propose a global optimization technique that relies on a spatial branch and bound search. A linearization technique is applied on the constraints from labeling balances, in order to obtain a convex relaxed problem that provides a lower bound to the global optimum; due to the nature of the linearization, the initial variable (measured) and parameter (non-measured) bounds strongly affect the model convergence. The global optimization algorithm estimates fluxes in the central metabolism of Saccharomyces cerevisiae, based on experimental data previously reported [Gombert, A. K., dos Santos, M. M., Christensen, B., Nielsen, J. (2001). Network identification and flux quantification in the central metabolism of Saccharomyces cerevisiae under different conditions of glucose repression. Journal of Bacteriology , 183 (4), 1441–1451]. To attain global convergence, a detailed bound tightening procedure is developed. Measured labelings and non-measured net fluxes are the branching variables, and the branching is performed on the one that has the largest difference between its values in the convex and non-convex models. Results were compared to the ones obtained using an evolutionary algorithm that requires extensive computational effort to achieve a feasible solution. We found that there are local solutions with important differences on the central pathways. In the global optimum, the calculated fluxes for the central pathways are similar to the best result obtained by evolutionary search, whereas the quadratic errors for both variable sets, measured labelings and fluxes, are smaller.

MINLP Models for the Synthesis of Optimal Peptide Tags and Downstream Protein Processing

The development of systematic methods for the synthesis of downstream protein processing operations has seen growing interest in recent years, as purification is often the most complex and costly stage in biochemical production plants. The objective of the work presented here is to develop mathematical models based on mixed integer optimization techniques, which integrate the selection of optimal peptide purification tags into an established framework for the synthesis of protein purification processes. Peptide tags are comparatively short sequences of amino acids fused onto the protein product, capable of reducing the required purification steps. The methodology is illustrated through its application on two example protein mixtures involving up to 13 contaminants and a set of 11 candidate chromatographic steps. The results are indicative of the benefits resulting by the appropriate use of peptide tags in purification processes and provide a guideline for both optimal tag design and downstream process synthesis.

Optimal scheduling of a lube oil and paraffin production plant

This paper presents MILP models for the optimal scheduling of a lube oil and paraffin production plant. The plant is composed of processing units that operate in continuous and discontinuous modes, and some also may execute the same task. There is finite storage capacity and most of the tanks are dedicated to a specified product, except for the basic lube oils that can be stored in any available tank. There are upper bounds for campaign changes in the units as well as shutdowns of the discontinuous units. Two mathematical formulations were developed under a discrete and continuous-time representation and compared to each other as well as to other continuous-time MILP models. Results with significant reduction in the computational time are generated with the continuous-time proposed model and allow the model application for real-world time horizons with a significant level of scheduling detail.

Optimal control of product quality for batch nylon-6,6 autoclaves

Dynamic optimization problems are usually solved by transforming them into nonlinear programming (NLP) models with either sequential or simultaneous approaches. In this paper, the potential and limitations of both procedures in solving a general batch nylon-6,6 autoclave optimization model are evaluated and discussed. Nylon-6,6 is a highly value-added good produced in large-scale under many different specifications. Highly nonlinear behavior, lack of on-line measurements of polymer qualities and several disturbances inherent to this process motivate its optimal operation. In addition, the operation during the finishing stage of the batch polycondensation is crucial since it largely determines the final product molecular weight and quality. Results show that both strategies can be successfully applied to solve the dynamic optimization problem only after an expressive level of investments in terms of modeling implementation. However, the simultaneous strategy has the advantage that specification constraints can be directly enforced in the model, thus generating better and more robust results.

An integrated network-based mechanistic model for tumor growth dynamics under drug administration

Cancer chemotherapy complexity ranges from the routes that the drug must follow before reaching the tumor site (pharmacokinetics), to the drug effects on tumor depletion (pharmacodynamics). Previous researchers, in their majority, have focused either on the pharmacokinetics (PK) or on the pharmacodynamics (PD) aspects of chemotherapy. Moreover, models that account for the molecular mechanisms of cancer development have limited scope in addressing the protein signals involved in tumor progression. For instance, the recently developed models for the p53 network, for which a number of mutations have been reported, must be integrated for further understanding of the disease. Here, we propose an integrated model that is composed of a compartmental PK/PD representation for drug therapy that incorporates p53 and cell cycle regulation. In particular, the dynamics of p53 and its network components, such as Mdm2, pRb, cyclin-cdks, are modeled under drug administration. The results show that the proposed model is a realistic representation of the physiological expectations in a multi-scale, integrative approach.

Mixed integer nonlinear programming techniques for the short term scheduling of oil refineries

Abstract In this work, models are proposed that rely on mixed-integer nonlinear programming and on the discrete representation of the time domain along the scheduling horizon. The proposed models contain raw-material supply conditions, demand for products, initial inventories and qualities, and capacity constraints for processing, storage and transfer. From these data, an optimization solver that relies on an implementation of the outer approximation method obtains a solution that supports the production scheduler. The models were developed and solved at a growing level of complexity. Real-world problems with a time horizon of two days were solved that resulted in models with over 1000 binary variables and 10000 constraints.

Piecewise polynomial interpolations and approximations of one-dimensional functions through mixed integer linear programming

Piecewise polynomial functions are extensively used to approximate general nonlinear functions or sets of data. In this work, we propose a mixed integer linear programming (MILP) framework for generating optimal piecewise polynomial approximations of varying degrees to nonlinear functions of a single variable. The nonlinear functions may be represented by discrete exact samplings or by data corrupted by noise. We studied two distinct approaches to the problem: (1) the generation of interpolating piecewise polynomial functions, in which the approximating function values in the extremes of each polynomial segment coincide with the original function values; and (2) a de facto approximation strategy in which the polynomial segments are free, except for the enforcement of continuity of the overall approximation. Our results from the implemented models show that the procedure is capable of efficiently approximating nonlinear functions and it has the added capability of allowing for the straightforward implementation of further constraints on solutions, such as the convexity of polynomial segments. Finally, the models for the generation of piecewise linear approximations and interpolations were applied for the linearization of mixed integer nonlinear programming (MINLP) models extracted from the MINLP library. These models were linearized by the reformulation of their nonlinearities as piecewise linear functions with varying numbers of segments, resulting in MILP models that were solved to optimality and the solutions from the linearized models were compared with global optimal solutions from the original problems.