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Optimization Direct: Introduction and recent case studies

Informs 2016 Solving Planning and Scheduling Problems with CPLEX

EX Optimization Studio* solves large-scale optimization problems and enables better business decisions and resulting financial benefits in areas such as supply chain management, operations, healthcare, retail, transportation, logistics and asset management. It has been applied in sectors as diverse as manufacturing, processing, distribution, retailing, transport, finance and investment. CPLEX Optimization Studio is an analytical decision support toolkit for rapid development and deployment of optimization models using mathematical and constraint programming. It combines an integrated development environment (IDE) with the powerful Optimization Programming Language (OPL) and high-performance ILOG CPLEX optimizer solvers. CPLEX Optimization Studio enables clients to: Optimize business decisions with high-performance optimization engines. Develop and deploy optimization models quickly by using flexible interfaces and prebuilt deployment scenarios. Create real-world applications that can significantly improve business outcomes. Optimization Direct has partnered with and entered into a technology licensing and distribution agreement with IBM. By combining the founders' industry and software experience and IBM’s CPLEX Optimization Studio product with the arsenal of Optimization modeling and solving tools from IBM provides customers the most powerful capabilities in the industry.

ODHeuristics

Presented in this short document is a description of how IMPL handles missing-values or missing-data when estimating dynamic models which inherently involve time-lagged or time-shifted input and output variables. Missing-values in a data set imply that for some reason the data is not available most likely due to a mal-functioning instrument or even lack of proper accounting. Missing-data handling is relatively well-studied especially for time-series or dynamic data given that it is not as easy as removing, ignoring or deleting bad sections of data when static or steady-state models are calibrated (Honaker and King, 2010; Smits and Baggelaar, 2010; Fisher and Waclawski, 2015). Unfortunately, all of their methods involve what is known as “imputation” i.e., replacing or substituting missing-data with some reasonably assumed value which is at the very least is a biased estimate. When regression techniques such as PLS and PCR are used (Nelson et. al., 2006) then missing-data can be handled without imputation by computing the input-output covariance matrices excluding the contribution from the missing-values given the temporal and structural redundancy in the system. However, it is shown in Dayal (1996) that using PLS and other types of regression techniques such as Canonical Correlation Regression (CCR) and Reduced Rank Regression (RRR) to fit non-parsimonious and non-parametric finite impulse/step response models (FIR/FSR), that this is not as reliable as fitting lower-ordered transfer functions especially considering the robust stability of the resulting model predictive controller if that is its intended use.

Missing-Value Handling in Dynamic Model Estimation using IMPL

Presented in this short document is a description of how to estimate deterministic and stochastic non-parametric finite impulse response (FIR) models in IMPL applied to industrial gas furnace data identical to that found in TSE-GFD-IMF using parametric transfer-functions. The methodology of time-series analysis or system identification involves essentially three (3) stages (Box and Jenkins, 1976): (1) model structure identification, (2) model parameter estimation and (3) model checking and diagnostics. We do not address (1) which requires stationarity and seasonality assessment/adjustment, auto-, cross- and partial-correlation, etc. to establish the parametric transfer function polynomial degrees especially when we are using non-parametric FIR estimation. Instead we focus only on the parameter estimation and diagnostics. These types of parameter estimation problems involve dynamic and nonlinear relationships shown below and we solve these using IMPL’s Sequential Equality-Constrained QP Engine (SECQPE) and Supplemental Observability, Redundancy and Variability Estimator (SORVE). Other types of non-parametric identification known as Subspace Identification (Qin, 2006) and can used to estimate state-space models.

Finite Impulse Response Estimation of Gas Furnace Data in IMPL Industrial Mod...

Our Industrial Modeling Service (IMS) involves several important (but rarely implemented) methods to significantly improve and advance your existing models and data. Since it is well-known that good decision-making requires good models and data, IMS is ideally suited to support this continuous-improvement endeavour. IMS is specifically designed to either co-exist with your existing design, planning, scheduling, etc. applications or these same models and data can be used seamlessly into our Industrial Modeling and Programming Language (IMPL) to create new value-added applications. The following techniques form the basis of our IMS offering.

Industrial Modeling Service (IMS-IMPL)

Dither Signal Design Problem (DSDP) for Closed-Loop Estimation Industrial Mod...

This short note describes a relatively simple methodology, procedure or approach to increase the performance of already installed industrial models used for optimization, control, simulation and/or monitoring purposes. The method is called Excess or X-Model Regression (XMR) where the concept of “excess modeling” or an X-model is taken from the field of thermodynamics to describe the departure or residual behaviour of real (non-ideal) gases and liquids from their ideal state (Kyle, 1999; Poling et. al., 2001; Smith et. al., 2001). It has also been applied to model the non-ideal or nonlinear behaviour of blending motor gasoline octanes with its synergistic and antagonistic interactional effects (Muller, 1992). The fundamental idea of XMR is to calibrate, train, fit or estimate, using actual data and multiple linear regression (MLR) or ordinary least squares (OLS), the deviations of the measured responses from the existing model responses. The existing model may be a glass, grey or black-box model (known or unknown, linear or nonlinear, implicit/open or explicit/closed) depending on the use of the model. That is, for optimization and control the model structure and parameters are available given that derivative information is required although for simulation and monitoring, the model may only be observed through the dependent output variables given the necessary independent input variables.

Xmr im

Distillation Curve Optimization Using Monotonic Interpolation

Presented in this short document is a description of how to model and solve multi-utility scheduling optimization (MUSO) problems in IMPL. Multi-utility systems (co/tri-generation) are typically found in petroleum refineries and petrochemical plants (multi-commodity systems) especially when fuel-gas (i.e., off-gases of methane and ethane) is a co- or by-product of the production from which multi-pressure heating-, motive- and process-steam are generated on-site. Other utilities include hydrogen, electricity, water, cooling media, air, nitrogen, chemicals, etc. where a multi-utility system is shown in Figure 1 with an intermediate or integrated utility (both produced and consumed) such as fuel-gas, steam or electricity. Itemized benefit areas just for better management of an integrated steam network can be found in Pelham (2013) where his sample multi-pressure steam utility flowsheet is found in Figure 2.

Multi-Utility Scheduling Optimization (MUSO) Industrial Modeling Framework (M...

Presented in this short document is a description of how to model and solve advanced parameter estimation (APE) problems in IMPL. APE is the term given to the application of estimating, fitting or calibrating parameters in models involving a network, topology, superstructure or flowsheet. When estimating parameters with multiple linear regression (MLR), ordinary least squares (OLS), ridge regression (RR), principal component regression (PCR) and partial least squares (PLS) there is no explicit model but simply an X-block and Y-block of data. Hence, these methods are referred to as “non-parametric” or “data-based” methods as opposed to the “parametric” or “model-based” method used here. To solve these types of problems we use what is commonly referred to as “error-in-variables” (EIV) regression which is conveniently implemented as nonlinear data reconciliation and regression (NDRR) using the technology found in Kelly (1998a; 1998b; 1999) and Kelly and Zyngier (2008a). The primary benefit of using EIV (NDRR) over the other regression methods is that we can easily handle the inclusion of conservation laws and constitutive relations, explicitly, a must for any industrial estimation problem (IEP).

Advanced Parameter Estimation (APE) for Motor Gasoline Blending (MGB) Indust...

Hybrid Dynamic Simulation (HDS) Industrial Modeling Framework (HDS-IMF)

Presented in this short document is a description of modeling and solving partial differential equations (PDE’s) in both the temporal and spatial dimensions using IMPL. The sample PDE problem is taken from Cutlip and Shacham (1999 and 2014) and models the process of unsteady-state heat transfer or conduction in a one dimensional (1D) slab with one face insulated and constant thermal conductivity as discussed by Geankoplis (1993).

Partial Differential Equations (PDE’s) Industrial Modeling Framework (PDE-IMF)

Presented in this short document is a description of what is well-known as Advanced Process Control (APC) applied to a small linear three (3) manipulated variable (MV) by two (2) controlled variable (CV) problem. These problems are also known as Model Predictive Control (MPC) (Grimm et. al., 1989) and Moving Horizon Control (MHC). Figure 1 shows the 3 x 2 APC problem configured in our unit-operation-port-state superstructure (UOPSS) (Kelly, 2004, 2005; Zyngier and Kelly, 2012) as an Advanced Planning and Scheduling (APS) problem as opposed to a traditional APC problem. Although there is a tremendous amount of stability, performance and robustness theory associated with APC which can be directly assumed to APS problems (Mastragostino et. al., 2014), our approach is to show that APC can equally be set into an APS framework except that APS has far less sensitivity technology due to its inherent discrete and nonlinear modeling complexities i.e., especially non-convexities. In order to eliminate the steady-state offset between the actual value and its target, it is well-known to apply bias-updating though other forms of “parameter-feedback” is possible. Typically, APS applications only employ “variable-feedback” i.e., opening or initial inventories, properties, etc. but this alone will not alleviate the steady-state offset as demonstrated by Kelly and Zyngier (2008).

Advanced Production Control Using Julia & IMPL

Presented in this short document is a description of our three separate techniques to analyze the data by checking, clustering and componentizing it before it is used by other IMPL’s routines especially in on-line/real-time decision-making applications. We also have other data consistency or analysis techniques which have been described in other IMPL documents and these relate to the application of data reconciliation and regression with diagnostics but require an explicit model (model-based) whereas the techniques below do not i.e., they are data-based techniques.

IMPL Data Analysis

Benefits of using IMPL

Presented in this short document is a description of how to estimate a deterministic and stochastic time-series transfer function models in IMPL using IBM’s CPLEX applied to industrial gas furnace data. The methodology of time-series analysis involves essentially three (3) stages (Box and Jenkins, 1976): (1) model structure identification, (2) model parameter estimation and (3) model checking and diagnostics. We do not address (1) which requires stationarity and seasonality assessment, auto-, cross- and partial-correlation, etc. to establish the transfer function polynomial degrees. Instead we focus only on the parameter estimation and diagnostics. These types of parameter estimation problems involve dynamic and nonlinear relationships shown below and we solve these using IMPL’s nonlinear programming algorithm SLPQPE which uses CPLEX 12.6 as the QP sub-solver.

Time Series Estimation of Gas Furnace Data in IMPL and CPLEX Industrial Model...

The processing of a raw material is a phenomenon that varies its quantity and quality along a specific network and logics and logistics to transform it into final products. To capture the production framework in a mathematical programming model, a full space formulation integrating discrete design variables and quantity-quality relations gives rise to large scale non-convex mixed-integer nonlinear models, which are often difficult to solve. In order to overcome this problem, we propose a phenomenological decomposition heuristic to solve separately in a first stage the quantity and logic variables in a mixed-integer linear model, and in a second stage the quantity and quality variables in a nonlinear programming formulation. By considering different fuel demand scenarios, the problem becomes a two-stage stochastic programming model, where nonlinear models for each demand scenario are iteratively restricted by the process design results. Two examples demonstrate the tailor-made decomposition scheme to construct the complex oil-refinery process design in a quantitative manner.

Phenomenological Decomposition Heuristics for Process Design Synthesis of Oil...

Presented in this short document is a description of our technology we call “Sparse Observability”. Observability is the estimatability metric (Bagajewicz, 2010) to structurally determine that an unmeasured variable or regressed parameter is either uniquely solvable (observable) or otherwise unsolvable (unobservable) in data reconciliation and regression (DRR) applications. Ultimately, our purpose to use efficient sparse matrix techniques is to solve large industrial DRR flowsheets quickly and accurately. Most other implementations of observability calculation use dense linear algebra such as reduced row echelon form (RREF), Gauss-Jordan decomposition (Crowe et. al. 1983; Madron 1992), QR factorization which can now be considered as semi-sparse (Swartz, 1989; Sanchez and Romagnoli, 1996), Schur complements, Cholesky factorization (Kelly, 1998a) and singular value decomposition (SVD) (Kelly, 1999). A sparse LU decomposition with complete-pivoting from Albuquerque and Biegler (1996) for dynamic data reconciliation observability computation was used but it is uncertain if complete-pivoting causes extreme “fill-ins” of the lower and upper triangular matrices essentially making them near-dense. There is another sparse observability method using an LP sub-solver found in Kelly and Zyngier (2008) but this requires solving as many LP sub-problems as there are unmeasured variables which can be considered as somewhat inefficient. IMPL’s sparse observability technique uses the variable classification and nomenclature found in Kelly (1998b) given that if we partition or separate the unmeasured variables into independent (B12) and dependent (B34) sub-matrices then all dependent unmeasured variables by definition are unobservable. If any independent unmeasured variable is a (linear) function of any dependent variable then this independent variable is of course also unobservable because it is dependent on another non-observable variable.

Sparse Observability using LP Presolve and LTDL Factorization in IMPL (IMPL-S...

This project demonstrates a machine learning approach to detecting credit card fraud using advanced algorithms and techniques. The project utilizes a dataset containing various features such as transaction amount, merchant location, time of transaction, and others to build a predictive model. The presentation covers data preprocessing steps, feature engineering techniques, and the selection of machine learning algorithms such as logistic regression or random forest. It also discusses model evaluation metrics and the importance of fraud detection in financial institutions for safeguarding against fraudulent activities. Visit: https://bostoninstituteofanalytics.org/data-science-and-artificial-intelligence/

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Retail Pricing Optimization

Optimization Direct: Introduction and recent case studies

Informs 2016 Solving Planning and Scheduling Problems with CPLEX

ODHeuristics

Missing-Value Handling in Dynamic Model Estimation using IMPL

Finite Impulse Response Estimation of Gas Furnace Data in IMPL Industrial Mod...

Industrial Modeling Service (IMS-IMPL)

Dither Signal Design Problem (DSDP) for Closed-Loop Estimation Industrial Mod...

Xmr im

Distillation Curve Optimization Using Monotonic Interpolation

Multi-Utility Scheduling Optimization (MUSO) Industrial Modeling Framework (M...

Advanced Parameter Estimation (APE) for Motor Gasoline Blending (MGB) Indust...

Hybrid Dynamic Simulation (HDS) Industrial Modeling Framework (HDS-IMF)

Partial Differential Equations (PDE’s) Industrial Modeling Framework (PDE-IMF)

Advanced Production Control Using Julia & IMPL

IMPL Data Analysis

Benefits of using IMPL

Time Series Estimation of Gas Furnace Data in IMPL and CPLEX Industrial Model...

Phenomenological Decomposition Heuristics for Process Design Synthesis of Oil...

Sparse Observability using LP Presolve and LTDL Factorization in IMPL (IMPL-S...

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