Outline The role of information What is information? Different types of information Controlling information

September, 1999 © 1999 Warren B. Powell Slide 2 How do we optimize systems like this? The role of information

September, 1999 © 1999 Warren B. Powell Slide 3 The role of information Consider how we normally solve big optimization problems: MondayTuesdayWednesday

September, 1999 © 1999 Warren B. Powell Slide 4 The role of information Normally, we would formulate a big optimization problem:

September, 1999 © 1999 Warren B. Powell Slide 5 The role of information Normally, we would formulate a big optimization problem: Integer!

September, 1999 © 1999 Warren B. Powell Slide 6 The role of information

September, 1999 © 1999 Warren B. Powell Slide 7 The role of information Control class (move plane) Decision horizon (e.g. 8 hours) Attribute subspace Planner A q =

September, 1999 © 1999 Warren B. Powell Slide 8 The role of information The forward reachable set.

September, 1999 © 1999 Warren B. Powell Slide 9 “Harry” The role of information

September, 1999 © 1999 Warren B. Powell Slide 10 The role of information The information wall: Data errors “The wall” Information cost

September, 1999 © 1999 Warren B. Powell Slide 11 The role of information How do we optimize … Harry?

September, 1999 © 1999 Warren B. Powell Slide 12 The role of information How do we make decision makers smarter? You have to raise their “IQ”! You mean hire smarter people? No, we have to give them more information What’s that?

Outline The role of information What is information? Different types of information Controlling information

September, 1999 © 1999 Warren B. Powell Slide 14 What is information? What is data? … knowledge? … information? Advertisement from Business Week

September, 1999 © 1999 Warren B. Powell Slide 15 What is information? Data: Bits and bytes

September, 1999 © 1999 Warren B. Powell Slide 16 What is information? Knowledge »Knowledge comes in two forms: Exogeneously derived data Relationships which allow us to use knowledge to make inferences about data elements that are not yet known to our system. »Can we have knowledge about something that we do not know perfectly?

September, 1999 © 1999 Warren B. Powell Slide 17 What is information? Example »Commodities prices »Assume that we derive the functional relationship:

September, 1999 © 1999 Warren B. Powell Slide 18 What is information? Without the “knowledge” of this functional relationship, our “knowledge” of the future price would be captured by: With the knowledge of the functional relationship: Likelihood Price Likelihood

September, 1999 © 1999 Warren B. Powell Slide 19 What is information? The field of information theory captures the information content about a piece of data using entropy:

September, 1999 © 1999 Warren B. Powell Slide 20 What is information? Information classes:

September, 1999 © 1999 Warren B. Powell Slide 21 What is information? e1e1 e4e4 e7e7 e8e8 e5e5 e3e3 e6e6 e1e1 e2e2 e2e2 a =

September, 1999 © 1999 Warren B. Powell Slide 22 What is information? The “knowledge base” »This is what we know at time t: »When we have multiple agents, we have to represent what each agent knows:

September, 1999 © 1999 Warren B. Powell Slide 23 What is information? e1e1 e4e4 e7e7 e8e8 e5e5 e3e3 e6e6 e1e1 e2e2 e1e1 e4e4 e7e7 e8e8 e5e5 e3e3 e6e6 e1e1 e2e2 e1e1 e4e4 e7e7 e8e8 e5e5 e3e3 e6e6 e1e1 e2e2 e1e1 e4e4 e7e7 e8e8 e5e5 e3e3 e6e6 e1e1 e2e2 We have multiple sets of information:

September, 1999 © 1999 Warren B. Powell Slide 24 What is information? The “knowledge base”

September, 1999 © 1999 Warren B. Powell Slide 25 What is information? What is a… decision?

September, 1999 © 1999 Warren B. Powell Slide 26 What is information? Exogenous input Endogenous input (decisions)

September, 1999 © 1999 Warren B. Powell Slide 27 What is information? Systems evolve through a cycle of exogenous and endogenous information Time

September, 1999 © 1999 Warren B. Powell Slide 28 What is information? Both kinds of information evolve over time: A plan is a forecast of a decision.

September, 1999 © 1999 Warren B. Powell Slide 29 What is information? We can’t always predict the future... be the set of possible events in the future.   is the new information that will become available in the future.  = ( )

September, 1999 © 1999 Warren B. Powell Slide 30 What is information? P.2) System dynamics: »Evolution due to exogenous information processes Time = The “history” of the information process … But this assumes that we never forget anything!

September, 1999 © 1999 Warren B. Powell Slide 31 What is information? Better notation: Our current knowledge base New information Our new knowledge base

September, 1999 © 1999 Warren B. Powell Slide 32 What is information? When exogenous information arrives, the update is usually pretty simple: So how does a decision x t change the system?

September, 1999 © 1999 Warren B. Powell Slide 33 What is information? Our decision function usually looks like: 0 xqxq   bqbq A q x q min c q x q

September, 1999 © 1999 Warren B. Powell Slide 34 What is information? The modify function:

September, 1999 © 1999 Warren B. Powell Slide 35 What is information? Discuss: decision functions

September, 1999 © 1999 Warren B. Powell Slide 36 What is information? The information cycle: The modify function uses decisions to create information... … The decision function turns information into decisions.

Outline The role of information What is information? Different types of information Controlling information

September, 1999 © 1999 Warren B. Powell Slide 38 Different types of information What types of information are there?

September, 1999 © 1999 Warren B. Powell Slide 39 Different types of information There are four classes of information: »What we “know”: »Forecasts of exogenous information: »Future plans: »“Values”: the impact of our decisions on other problem components.

September, 1999 © 1999 Warren B. Powell Slide 40 Different types of information How do we increase ? »We start with We can expand the scope...

September, 1999 © 1999 Warren B. Powell Slide 41 Different types of information Using knowledge: »Decision functions that only use knowledge are called myopic. »Over the last two decades, we have seen a dramatic increase in our ability to collect, transmit and store “information” (knowledge).

September, 1999 © 1999 Warren B. Powell Slide 42 Different types of information How do we increase ? »We start with We can expand the scope... Or we can expand the time horizon, but future events are not in

September, 1999 © 1999 Warren B. Powell Slide 43 Different types of information How do we increase ? »We can add forecasting: »What do we forecast? Resources –Arrivals (e.g. customer demands) –Departures (cancellations, equipment breakdowns, people quitting). Process parameters (the Modify function) –Prices/costs –Times –Engineering parameters

September, 1999 © 1999 Warren B. Powell Slide 44 Different types of information Types of forecasts: Number of units required Likelihood of occurrence % Point Number of units required Likelihood of occurrence % Distributional

September, 1999 © 1999 Warren B. Powell Slide 45 T01 Time Evolution of Simulation TSTS 00 EE 00 EE 00 EE EE00 EE00 EE00 00 Different types of information

September, 1999 © 1999 Warren B. Powell Slide 46 Different types of information Planning horizon Percent of posterior bound Deterministic, rolling horizon We need more information! Posterior bound That’s not very good

September, 1999 © 1999 Warren B. Powell Slide 47 Different types of information How do we increase ? »We can do planning: A plan is a forecast of a decision.

September, 1999 © 1999 Warren B. Powell Slide 48 Different types of information Types of planning: »Plans »Patterns »Policies

September, 1999 © 1999 Warren B. Powell Slide 49 Different types of information The second form of head knowledge is patterns - standard actions given the state of the system. Movements of sleeper teams for a trucking company:

September, 1999 © 1999 Warren B. Powell Slide 50 Different types of information Concept: pattern matching »Old modeling approach: Bottom up modeling Objectives “Physics” “Behavior” To get the right “behavior” we have to specify the right costs and the right constraints. If you don’t like the behavior, you have to fix the data!

Yellow Freight System

September, 1999 © 1999 Warren B. Powell Slide 52 Different types of information Concept: pattern matching »New modeling approach: Top down, bottom up modeling Cost function “Behavior” Aggregation function Pattern database from history Scaling parameter The difference between the model solution and historical patterns.

September, 1999 © 1999 Warren B. Powell Slide 53 Different types of information Historical: The flows are not the same, but they have the same pattern. Forecasted

September, 1999 © 1999 Warren B. Powell Slide 54 Different types of information So far, we have three types of decision functions: »Myopic »With forecasts: »With forecasts and plans: »Now we have to bring in our impact on others.

September, 1999 © 1999 Warren B. Powell Slide 55 Different types of information Consider how we normally solve big optimization problems: MondayTuesdayWednesday

September, 1999 © 1999 Warren B. Powell Slide 56 Different types of information Real problems are decomposed over space... MondayTuesdayWednesday

September, 1999 © 1999 Warren B. Powell Slide 57 Different types of information … and time. MondayTuesdayWednesday

September, 1999 © 1999 Warren B. Powell Slide 58 Different types of information We use approximations of subproblems to model interactions: MondayTuesdayWednesday

September, 1999 © 1999 Warren B. Powell Slide 59 Different types of information … and then approximate the problem we just solved... MondayTuesdayWednesday

September, 1999 © 1999 Warren B. Powell Slide 60 Different types of information … so other people can understand how their decisions impact us! MondayTuesdayWednesday

September, 1999 © 1999 Warren B. Powell Slide 61 Different types of information Using value function approximations, we find ourselves solving problems that look like: Forward reachable set

September, 1999 © 1999 Warren B. Powell Slide 65 R0R0 R1R1 R2R2 D0D0 D2D2 D0D0 D2D2 t = 0t = 1t = 2 D0D0 D1D1 R0R0 R1R1 R2R2 R0R0 R1R1 R2R2 R0R0 R1R1 R2R2 Different types of information

September, 1999 © 1999 Warren B. Powell Slide 66 R0R0 R1R1 R2R2 D0D0 D2D2 D0D0 D2D2 t = 0t = 1t = 2 D0D0 D1D1 R0R0 R1R1 R2R2 R0R0 R1R1 R2R2 R0R0 R1R1 R2R2 Different types of information

September, 1999 © 1999 Warren B. Powell Slide 67 R0R0 R1R1 R2R2 D0D0 D2D2 D0D0 D2D2 t = 0t = 1t = 2 D0D0 D1D1 R0R0 R1R1 R2R2 R0R0 R1R1 R2R2 R0R0 R1R1 R2R2 Different types of information

September, 1999 © 1999 Warren B. Powell Slide 68 Different types of information Planning horizon Percent of posterior bound Deterministic, rolling horizon Adaptive dynamic programming Can we do better? Posterior bound The value of adding V’s to the information set.

September, 1999 © 1999 Warren B. Powell Slide 69 Different types of information LP relaxation Integer solution obtained using value function approximation

September, 1999 © 1999 Warren B. Powell Slide 70 Different types of information There are four classes of information: »Knowledge »Forecast of exogenous events »Plans (forecast of future decisions) »Values (impact of decisions on other subproblems) (data and relationships)

September, 1999 © 1999 Warren B. Powell Slide 71 Different types of information The information set shapes the decision function: »Myopic decision rules »Rolling horizon procedures »Proximal point algorithms »Dynamic programming or

Outline The role of information What is information? Different types of information Controlling information

September, 1999 © 1999 Warren B. Powell Slide 73 Controlling information How do I control an operation? Prices Goals Incentives Data Communications Forecasting Optimization Locomotives Trains Crews

September, 1999 © 1999 Warren B. Powell Slide 74 Controlling information The information optimization problem:

September, 1999 © 1999 Warren B. Powell Slide 75 Controlling information The information flow problem: e1e1 e4e4 e7e7 e8e8 e5e5 e3e3 e6e6 e1e1 e2e2 e1e1 e4e4 e7e7 e8e8 e5e5 e3e3 e6e6 e1e1 e2e2 q q’

© Bill Watterson

September, 1999 © 1999 Warren B. Powell Slide 77 Controlling information The information cost functions:

September, 1999 © 1999 Warren B. Powell Slide 78 Controlling information The information optimization problem is now: Subject to system dynamics. Cost of moving information Cost of moving resources

September, 1999 © 1999 Warren B. Powell Slide 79 Controlling information In many ways, the economics of moving information is very similar to moving flow: »The function may be linear: Phone calls, communication links

September, 1999 © 1999 Warren B. Powell Slide 80 Controlling information In many ways, the economics of moving information is very similar to moving flow: »It may have a fixed charge: Cost of constructing databases, screens, communication links

September, 1999 © 1999 Warren B. Powell Slide 81 Controlling information In many ways, the economics of moving information is very similar to moving flow: »It may be convex:

September, 1999 © 1999 Warren B. Powell Slide 82 Controlling information In many ways, the economics of moving information is very similar to moving flow: »… or concave:

September, 1999 © 1999 Warren B. Powell Slide 83 Controlling information In many ways, the economics of moving information is very similar to moving flow: »It may be separable: »or highly nonseparable. There are joint economies of production, just as in discrete parts manufacturing.

September, 1999 © 1999 Warren B. Powell Slide 84 Controlling information But there is one way in which the flow of information is very different from the flow of resources...

September, 1999 © 1999 Warren B. Powell Slide 85 Controlling information

September, 1999 © 1999 Warren B. Powell Slide 86 Controlling information