Tactical and Strategic Sales Management for Intelligent Agents Guided By Economic Regimes

Transcription

1 Tactical and Strategic Sales Management for Intelligent Agents Guided By Economic Regimes RSM Erasmus University, The Netherlands Man-Machine Interaction Group Delft University of Technology, May 28th 28 Work done with: John Collins, Maria Gini, Alok Gupta, and Paul Schrater

2 Outline 2 3 4

3 Economic theory suggests that economic environments exhibit 3 dominant market patterns: scarcity, balanced, and over-supply. We call these distinguishable conditions economic regimes. The long term objective of our work is to show how knowledge of current and anticipated regimes can enable an agent to make better operational and strategic decisions.

4 Relationship: Prices, Order Probability, and Regimes Scarcity: Order Probability Balanced: Order Probability Over-supply: Order Probability Normalized Price (np) Normalized Price (np) Reverse cumulative density function represents probability of order. Experimental: Order Probability Normalized Price Normalized Price (np)

5 Application Areas () Identification of economic regimes: Strategical decision making Tactical decision making Price and price trend forecasting. Forecasting of economic regimes shifts: Whole seller (e.g. book store). Production plant (e.g. Daimler). Automated supply-chain management, e.g., i2 SAP

6 Application Areas (2) The approach we propose works in any market: Computational process is completely data driven. No classification of the market structure (monopoly vs competitive, etc) is needed.

7 TAC SCM Overview

8 TAC SCM - Scenario Suppliers Agents Customers IMD MinneTAC Pintel RFQs TACTex RFQs Basus Offers Macrostar PSUTac Offers Mec Orders RedAgent Orders Queenmax Shipments DeepMaize Shipments Watergate Mintor Mertacor

9 Use Regime Prediction For Sales Strategies Allocation (Strategic Decision): Allocating parts and production capacity to most profitable computers. Allocating computers to current vs future sales. 2 Pricing (Tactical Decision): Find the best prices to move the desired inventory.

10 Pricing Chain External Input Data Internal Agent Data Derived Data Daily Price Report Yesterday s Accepted Offers Resource Constraints Cost Basis Current Demand Price Monitor Sales Performance Inventory Status Demand Prediction Economic Regime Model Median Price Probability of Order Model Allocation Trend Prediction Median Price Prediction Calculation of Offer Prices

11 Related Work Demand and Price Prediction - Ghani, 25 PDA auctions on ebay - Ghose et al., 26 used books sales on Amazon - Kephart et al., 2 information goods and shopbots - Massey et al., 25 reaction caused by regime shifts - Osborn et al., 22 Macro-Economic regimes - Pauwels et al., 22 windows of change in marketing Demand and Price Prediction in TAC SCM Benisch et al., 24, Ketter et al., 24, Pardoe et al., 24, Wellman et al., 25

12 Proposed Approach Off-line Estimation of price density. 2 Identification of regimes. 2 Real-time Identification of regimes. 2 Prediction of regime distributions. 3 Prediction of price density. 4 Prediction of price trends. 5 Prediction of order probability. 6 Sales Pricing

13 Estimating Price Density Functions () Estimate price density functions and use them to define regimes. A Gaussian mixture model (GMM) can estimate arbitrary density functions. GMM is a semi-parametric approach: fast computing less memory

14 Estimating Price Density Functions (2) We use a Gaussian mixture model (GMM): p(np) = N p(np ζ i )P(ζ i ) i= where p(np) is the density of the normalized price (np). p(np ζ i ) = N[µ i, σ i ](np) is the i-th Gaussian of the normalized price density from the GMM. P(ζ i ) is the prior probability of the i-th Gaussian. Fixed means µ i and fixed variances σ 2 i.

15 Estimating Price Density Functions (3) The EM-Algorithm determines the prior probability, P(ζ i), of each Gaussian, where i =,,N. Assumption: N = 6. Product Quantity x 4 5 Product Quantity p(np) p(np) Product Quantity 5 x 4 Product Quantity p(np) 2 p(np) Product Quantity x 4 5 Product Quantity p(np) p(np) Normalized Price (np) Normalized Price (np) Normalized Price (np) Low Market Medium Market High Market Using Bayes rule we determine the posterior probability: P(ζ i np) = p(np ζ i)p(ζ i) N i= p(np ζi) P(ζi) i =,,N

16 Proposed Approach Off-line Estimation of price density. 2 Identification of regimes. 2 Real-time Identification of regimes. 2 Prediction of regime distributions. 3 Prediction of price density. 4 Prediction of price trends. 5 Prediction of order probability. 6 Sales Pricing

17 Definition of Regimes We define the N-dimensional vector η(np) = [P(ζ np),p(ζ 2 np),..., P(ζ N np)] Compute η(np j ) which is η evaluated at the np j price. 2 Cluster these collections of vectors using k-means. 3 The center of each cluster corresponds to a regime R k. P(c R ) P(c R ) P(c R ) P(c R 2 ) P(c R 2 ) P(c R 2 ) P(c R 3 ) P(c R 3 ) P(c R 3 ) P(c R 4 ) P(c R 4 ) P(c R 4 ) P(c R 5 ) P(c R 5 ) P(c R 5 ) P(c 3 np).6.4 P(c 3 np).6.4 P(c 3 np) P(c np) P(c np) P(c np) P(c 2 np) P(c 2 np) P(c 2 np) Low Market Medium Market High Market

18 Off-line Regime Identification Marginalizing over the components ζ i we obtain: p(np R k ) = N p(np ζ i)p(ζ i R k ) i= where R k is a specific regime. Using Bayes rule we determine the posterior probability: P(R k np) = p(np R k )P(R k ) R k= p(np R k)p(r k ) k =,, M The prior probabilities P(R k ) are determined by a counting process over a collection of entire games.

19 Learned Regime Probabilities offline Regime Probability P(R k np) EO.9 O B.8 S ES Regime Probability P(R k np) EO.9 O B.8 S ES Regime Probability P(R k np) EO O B S ES Normalized Price Normalized Price Normalized Price Low Market Medium Market High Market P(R k np) k =,,M calculated off-line from 26 games.

20 Proposed Approach Off-line Estimation of price density. 2 Identification of regimes. 2 Real-time Identification of regimes. 2 Prediction of regime distributions. 3 Prediction of price density. 4 Prediction of price trends. 5 Prediction of order probability. 6 Sales Pricing

21 Information Available in the Customer Market Every day each agent receives: Requests for Quotes (RFQs): computer type, number of computers, due date, reserve price. 2 A price report which includes the lowest and highest price paid per computer type from the previous day.

22 Online Identification of the Dominant Regime Normalized Price Maximum Price Mean Price.2 Mid Range Price Smoothed Price Minimum Price Time in Days Daily price report 372@tac3 medium market: Minimum and maximum order prices. Every day we estimate the current regime by calculating the double smoothed mid-range normalized price ñp day based on the daily price report. 2 We select the regime which has the highest probability, i.e. argmax k M P(Rk ñp day ).

23 Regime Probability Real-time P(R np).6.4 EO O B S ES P(R np).6.4 EO O B S ES P(R np).6.4 EO O B S ES Time in Days Time in Days Time in Days Low Market Medium Market High Market P(R k ñp day ) k =,, M calculated online for game 372@tac3.

24 Regime Market Parameters () Factory Utilization (FU) in % 5 Regime Change FU np Offer/Demand Normalized Price (np) Finished Goods Inventory (FG) 2 Regime Change FG np Offer/Demand.5 Normalized Price (np) ES S B O B S B O EO Day ES S B O B S B O EO Day Factory Utilization (FU) Finished Goods Inventory (FG) Game 372tac3 - medium market segment: Ratio offer/demand, normalized prices, and regime transitions.

25 Regime Market Parameters (2).8.6 Finished Goods Factory Utilization Ratio Offer/Demand Normalized Price Correlation Coefficients EO Over supply Balanced Scarcity ES Regime Training set (8 games) Correlation coefficients between regimes and quantity of finished goods inventory, factory utilization, the ratio of offer to demand, and normalized price (np) in the medium market segment. All values are significant at the p =. level.

26 Proposed Approach Off-line Estimation of price density. 2 Identification of regimes. 2 Real-time Identification of regimes. 2 Prediction of regime distributions. 3 Prediction of price density. 4 Prediction of price trends. 5 Prediction of order probability. 6 Sales Pricing

27 Online Prediction of Regimes () We model the prediction of the next regime as a Markov prediction process: The posterior regime probabilities are predicted for current and future days based on yesterday s smoothed mid-range normalized price ñp.

28 Online Prediction of Regimes (2) Repeated one-day prediction: P(r d+h ñp d ) = r d+n r d { } P(r d ñp d ) T h+ (r d r d ), where T h+ (r d r d ) = h T (r d r d ) n=

29 Proposed Approach Off-line Estimation of price density. 2 Identification of regimes. 2 Real-time Identification of regimes. 2 Prediction of regime distributions. 3 Prediction of price density. 4 Prediction of price trends. 5 Prediction of order probability. 6 Sales Pricing

30 Prediction of Price Density N p( np t+n ñp t ) = P(ζ j,t+n )p(np ζ j ) j= Sample np from to.25 in increments of..5 Estimated Density Current Day.45 Probability Density [p(np)] Normalized Price [np] Example: Game 377tac3

31 Evaluation of Price Prediction RMS Price Prediction Error Mean Markov C P Mean Markov P 5% (Median) Markov C P 5% (Median) Markov P Mean Exp Smoother Regimes Exp Smoother Planning Horizon [Day] RMS error over a varying planning horizon.

32 Proposed Approach Off-line Estimation of price density. 2 Identification of regimes. 2 Real-time Identification of regimes. 2 Prediction of regime distributions. 3 Prediction of price density. 4 Prediction of price trends. 5 Prediction of order probability. 6 Sales Pricing

33 Price Trend Prediction Tr n = sgn( np d+n np d ), n =,,h.2 Relative Price Trend Real PT Mean Markov PT % Markov PT 5% Markov PT 9% Markov PT Exp Smoother PT Day [t] Example: Game 377tac3

34 Evaluation of Trend Prediction 75 Trend Success Rate in % Expected Mean Markov C P 55 Expected Mean Markov P Median Markov C P Median Markov P Exp Smoother Planning Horizon [Day] Success rate over a varying planning horizon.

35 Proposed Approach Off-line Estimation of price density. 2 Identification of regimes. 2 Real-time Identification of regimes. 2 Prediction of regime distributions. 3 Prediction of price density. 4 Prediction of price trends. 5 Prediction of order probability. 6 Sales Pricing

36 Prediction of Order Probability P(order np) = CDF(np) Where the CDF is related to a probability density function p(np) by CDF(np) = np p(np )dnp in the TAC SCM case np max =.25, so that CDF(np max ) =.

37 Example Order Probability Curve 9 8 Order Probability [%] Markov C P Markov P Exp Smoother Normalized Price [np] Real-time order probability curve for day 5 for the low market segment in game 377@tac3.

38 Order Probability Prediction Results Estimated Order Probability with Errorbars 9% 75% 5% 25% % Markov C P Markov P Exp Smoother np(%) np(25%) np(5%) np(75%) np(9%) Normalized Price by Density Percentile Daily order probability estimation (mean/std) for the th, 25th, 5th, 75th, and 9th percentile using different predictors.

39 Proposed Approach Off-line Estimation of price density. 2 Identification of regimes. 2 Real-time Identification of regimes. 2 Prediction of regime distributions. 3 Prediction of price density. 4 Prediction of price trends. 5 Prediction of order probability. 6 Sales Pricing

40 Optimizing sales quotas () To optimize profits over time, an agent needs to know: Current and future prices Its own costs Available inventory and production capacity If per-unit profit for good g sold on day d at price price d,g is Φ d,g, then total profit over a horizon h is Φ = h Φ d,g A d,g d= g G

41 Optimizing sales quotas (2) LP solver can optimize total profit, subject to: Sales quotas cannot exceed expected demand Uncommitted finished-goods and raw-materials inventories Inventories are augmented by expected deliveries and components available from suppliers over the planning horizon h Quotas not satisfied from finished goods are constrained by factory capacity

42 Setting sales prices P(order price) To sell our quota, we set prices using our order probability model. A/D eff O/D eff P adj P price act price price

43 Tuning sales prices P(order price) The pricing model is approximate. We tune it using feedback from actual orders. quota demand orders demand P adj P price adj price orig price

44 Mean Profit Results using Different Versions of MinneTAC Mean Profit / Standard deviation (in $M) Strategic: Price-Follower Regimes Combo Regimes Tactical: Linear Linear Linear Regimes Agent: MinneTAC.347/ /4.7.78/ /3.764 TacTex / / / /5.385 DeepMaize6F 8.839/ / / /4.8 PhantAgent6 8.49/ / / /5.437 Maxon6F 4.243/ / / /4.8 Rational5.739/ / / /4.527 Experimental setup with controlled market conditions and different variations of MinneTAC for order probability, price and price trend predictions. Each column is an average of 23 games.

45 Future Work () Ensemble price predictions Train regime transition matrices: On different time periods (start, mid, and end of the game). Include the effect of substitutability among market segments and products. Market segments vs product learning. Develop procurement strategies that take advantage of regime forecasting.

46 Future Work (2) Integrate regime forecasting in decision making process. Apply reinforcement learning to map economic regimes to operational regimes. operational regimes to actions. Implement and evaluate approach in other application domains, e.g., Stock market Amazon Dutch flower auction Energy markets

47 Conclusions Off-line identification of economic regimes. Real-time identification of economic regimes. Real-time prediction of economic regime distributions and transitions. Real-time prediction of price density, prices and price trends. Real-time prediction of order probability. Contact URL:

48 Prediction of Price Density p( np t+n ñp t ) M = P(np R i )P(R i,t+n ñp t ) = = i= N j= i= M P(ζ j R i ) P(R i,t+n ñp t ) p(np ζ j ) } {{ } P(ζ j,t+n ) N P(ζ j,t+n ) p(np ζ j ) j=