UNIVERSIDAD NACIONAL DE CAJAMARCA HISTORIA DE LA INVESTIGACION DE OPERACIONES INTRODUCCION Ing. MANUEL ROBERTO AZAHUANCHE OLIVA.

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UNIVERSIDAD NACIONAL DE CAJAMARCA HISTORIA DE LA INVESTIGACION DE OPERACIONES INTRODUCCION Ing. MANUEL ROBERTO AZAHUANCHE OLIVA

Desarrollos clave de la segunda mitad del siglo XX Programación lineal (Restricciones con desigualdades)

Kuhn Tucker (1951) Condiciones a satisfacer por una optimización no lineal Contribuciones ( s) Algoritmos para optimización no lineal

Khachain and Karmarkar (~1980) Nuevo métodos de puntos interiores Desarrollos continuados en diferentes problemas (optimización entera, estocástica, global, etc.) Actualmente sigue con un gran desarrollo

Optimización basada en modelos Decisiones a tomar modelo Método de resolución y software Solución La formulación y el método de resolución permiten la solución ? Es importante ver los efectos de un error del modelo en la solución De sencillo a muy complejo De fácil a imposible (hoy) EL PROBLEMA Y SU SOLUCIÓN

Opciones para la resolución de optimización basada en modelos Soluciones gráficas Soluciones analíticas (Newton, Euler, etc.) Métodos numéricos EL PROBLEMA Y SU SOLUCIÓN

Opciones para la resolución de optmización basada en modelos Gráfica Variable, x Función objetivo, f(x) Comenta: Ventajas Desventajas Dónde está el óptimo EL PROBLEMA Y SU SOLUCIÓN

Opciones para la resolución de optmización basada en modelos Analítica EL PROBLEMA Y SU SOLUCIÓN Comenta: Ventajas Desventajas

Opciones para la resolución de optmización basada en modelos Numérica EL PROBLEMA Y SU SOLUCIÓN Comenta: Ventajas Desventajas

WHAT ARE EXAMPLES OF OPTIMIZATION? 1. Economics: Plant design Tower decision capital cost operating cost increase in NT reduces energy increases equipment best NF reduces energy lower P no refrigerationhigher F cw (?) Exch A smaller exchangercooler T cw XD, XB-- separation cost and downstream processes --

WHAT ARE EXAMPLES OF OPTIMIZATION? 2. Economics: Plant operations Opt. P- must know condenser performance and limits XD and XB- energy/yield tradeoff Tf- tradeoff energy in feed/reboil; tray limitations Feed rate- run at peak efficiency; meet sales requirements

What is similar and what is different in these two examples of modelling: design and operations? SIMILARDIFFERENT PROCESS DECISIONS DETERMINED USING MODELS How do we combine these factors to determine “best” solution for both?

WHAT ARE EXAMPLES OF OPTIMIZATION? 3. Economics: Company logistics / supply chain management Storage Raw materials Plant Which raw material? Which plant (different yields, etc.) How much inventory? What routes and modes used for transportation? How much inventory?

WHAT ARE EXAMPLES OF OPTIMIZATION? 4. Process Control: Model Predictive Control How can we make the CV follow the set point (---) as closely as possible? Why isn’t control perfect? Not a PID algorithm! IAE = 2.75 ISE = CV The controller calculates the entire transient response. Is this good control performance? Time MV (% open) T AC LC

WHAT ARE EXAMPLES OF OPTIMIZATION? 5. Technical: Model equilibrium as minimizing Free Energy + Equilibrium at constant T and P is Minimum Free Energy

WHAT ARE EXAMPLES OF OPTIMIZATION? 6. Policy: Generate the desired electricity with minimum “pollution” Define “pollution” What is the cost for the policy? What other pollution is produced? gascoalwind nuclear

WHAT ARE EXAMPLES OF OPTIMIZATION? 7. Model calibration: Statistics Get the right data (experimental design) Select model structure & estimate parameters using the data Evaluate the reliability of conclusions F  T Max (information) Min (uncertainty) Min |predicted-measured| sum of squares maximum deviation sum of absolute values A  B k 01 = 1.2e7  … k 02 =...