1 From process control to business control: How the philosophy and methods of process control can be applied to businesses: key performance indicators, logistics, markets, management and other? Trial Lecture Deeptanshu Dwivedi 18 th Jan, Trondheim Deeptanshu Dwivedi, From Process Contol to Business Control Deeptanshu Dwivedi, From Process Contol to Business Control
2 Scope of the lecture • Introduction to Process Control • Feedback & Feed forward Control • Optimal Control Theory • Stochastic Control Theory • Model Predictive/ receding horizon control • Self-Optimizing Control Deeptanshu Dwivedi, From Process Contol to Business Control
3 Scope of the lecture • Introduction to Process Control • Feedback & Feed forward Control • Optimal Control Theory • Stochastic Control Theory • Model Predictive/ receding horizon control • Self-Optimizing Control Deeptanshu Dwivedi, From Process Contol to Business Control
4 Process Control • Control in Process Industries –control process variables (like T, P) when manufacturing a product • Objectives of Process Control –Ensure safety –Reduce variability –Increase profits • Process Industries –the chemical industry –oil and gas –the food and beverage industry –the pharmaceutical industry –water treatment industry –etc Deeptanshu Dwivedi, From Process Contol to Business Control
5 Scope of the lecture • Introduction to Process Control • Feedback & Feed forward Control • Optimal Control Theory • Stochastic Control Theory • Model Predictive/ receding horizon control • Self-Optimizing Control Deeptanshu Dwivedi, From Process Contol to Business Control
6 Feedback Control • : tight control with only a very crude model. Simple • : can adapt to new conditions. Robustness • : fundamentally change the dynamics of a system Stabilization Deeptanshu Dwivedi, From Process Contol to Business Control
7 Feedback Control: Example Process Control Reactor System (to maintain temperature) Temperature Controlled Variable Temperature Sensor transmitter Valve position Manipulated variable Feed Flow rate Disturbance Deeptanshu Dwivedi, From Process Contol to Business Control
8 Feedback Control: Analogy Process Control Business/ *Arkun, Y. (2009) Management Room Heater, Reactor Academic Institute* System (to maintain temperature) (maintain effective education) Temperature Grades, Employment, Controlled Variable Publications, Awards Temperature Surveys Sensor transmitter Valve position Changes in the Manipulated variable curriculum, Faculty- Student ratio Feed Flow rate Change in population, Disturbance demographics etc. Deeptanshu Dwivedi, From Process Contol to Business Control
9 Feedback Control: Analogy.. Grades, Employment, Research Grants Publications, Awards Curriculum Faculty-student ratio population, demographics, etc + + Academic Controller Goals ∑ ∑ Institute ─ Surveys Deeptanshu Dwivedi, From Process Contol to Business Control
10 Feed forward Control Disturbance Disturbance Feedforward Feedforward X X Plant Plant Manipulated variable Manipulated variable Take proactive corrective action by measuring disturbance Deeptanshu Dwivedi, From Process Contol to Business Control
11 Feed Forward Control: Analogy Process Control Business/ Management Room Heater, Reactor Academic Institute System (to maintain temperature) (maintain effective education) Feed Flow rate Change in population, Disturbance demographics etc. Model Model/ Forecast Feed forward Especially in business/management problems, there is a large time delay, so feed forward may be a good policy – Use proactive policies using forecasts Deeptanshu Dwivedi, From Process Contol to Business Control
12 Feedback-Feed forward Combination • Difficulty to account for every possible load disturbance in a feed forward system − Uncertainty causes instability • Use feedback/ forecast both to make manage the educational institute Deeptanshu Dwivedi, From Process Contol to Business Control
13 Scope of the lecture • Introduction to Process Control • Feedback & Feed forward Control • Optimal Control Theory • Stochastic Control Theory • Model Predictive/ receding horizon control • Self-Optimizing Control Deeptanshu Dwivedi, From Process Contol to Business Control
14 Optimal Control Theory • Deals with optimization of dynamic systems from one state to another • Optimal control problem* Maximize T ( , , ) [ ( ), ] J F x u t dt S x T T 0 , subject to ( , , ), (0) x f x u t x x 0 Aimis tofind, *& * u x *,optimalcontrol u *,optimaltrajectory x • Problem may be solved numerically *Sethi & Thompson (2009) Deeptanshu Dwivedi, From Process Contol to Business Control
15 Optimal Control Theory.. u* 0 T x* 0 T Deeptanshu Dwivedi, From Process Contol to Business Control
16 Optimal Control: Optimum cash Optimum cash balance: firms need cash on hand • If too much cash – loss in terms opportunity cost (securities have higher rate of interest) • If too little cash – will need to sell securities (=loss due to brokerage fees) • Find tradeoff between cash and securities Deeptanshu Dwivedi, From Process Contol to Business Control
17 Optimal Control: Optimum cash.. Objective* Maximize [ ( ) ( )] J x T y T Constraints | |, (0) x rx d u u x x 1 0 (state equations) , (0) y r y u y y 2 0 Constraints ( ) U u T U 2 1 (control equations) where, the cash balance in NOK x y= security balance in NOK instantaneous rate of demand for cash d rate of sale of securities u interest rate earned on the cash balance r 1 interest rate earned on the security balance r 2 the broker 's commission in dollars *Sethi & Thompson (2009) Deeptanshu Dwivedi, From Process Contol to Business Control
18 Optimal Control: A Production-Inventory System.. • Inventory: Production-inventory are need to manage fluctuations in costumer demand for the product • Pros – Immediately available for demand – Inventory stock may be used in reaction to market prices • Cons – Cost of storage – Opportunity cost of firm’s money tied in unused inventory Deeptanshu Dwivedi, From Process Contol to Business Control
19 Optimal Control: A Production-Inventory System.. maximize Objective* T 2 2 t [ ( ) ( ) ] J e h I I c P P dt 0 Constraint ( ) ( ), (0) I P t S t I I 0 (state equation) where, inventory level I production rate P sales rate at time S inventory goal I production goal P inventory holding cost coefficient h production cost coefficient c *Sethi & Thompson (2009) nonnegative discou nt rate Deeptanshu Dwivedi, From Process Contol to Business Control
20 Optimal Control: Nerlove-Arrow Advertising Model • Advertising is an investment to make Goodwill • Goodwill , G(t) G u G – u is advertizing effort, say in NOK – Depreciates with time at a rate δ (as consumers “drift” to other brands) Deeptanshu Dwivedi, From Process Contol to Business Control
21 Optimal Control: Nerlove-Arrow Advertising Model.. maximize Objective* T t [ ( , , ) ] J e R p G Z u dt 0 where, revenue R price p Goodwill G exogenous variables like, consumer income, population size etc. Z advertizingeffort u Constraint , 0) G u G G G (state equation) 0 *Sethi & Thompson (2009) Deeptanshu Dwivedi, From Process Contol to Business Control
22 Scope of the lecture • Introduction to Process Control • Feedback & Feed forward Control • Optimal Control Theory • Stochastic Control Theory • Model Predictive/ receding horizon control • Self-Optimizing Control Deeptanshu Dwivedi, From Process Contol to Business Control
23 Stochastic Control • A stochastic control problem: – What is the optimal magnitude of a choice variable at each time in a dynamical system under uncertainty • Stochastic process: ( ) ( ( )) ( ( )) ( ) dX t b X t dt X t dB t , where drift term b diffusion term { ( )} standard Brownian motion B t • X(t) may be exogenous factors Deeptanshu Dwivedi, From Process Contol to Business Control
24 Stochastic Optimal Control: : A Production- Inventory System.. maximize Objective* T t 2 2 [ { ( ) ( ) } ] J E e h I I c P P dt 0 [ ] is the expectation of E I I ( ( ) ( )) ( ), (0) Constraint I P t S t dt d B t I I 0 where, (state equation) inventory level I production rate P sales rate at time S inventory goal I production goal P inventory holding cost coefficient h production cost coefficient c nonnega tive discount rate / ( / ) dB dt whitenoise sales return inventory spoilage *Morimoto, Hiroaki (2010) Deeptanshu Dwivedi, From Process Contol to Business Control
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