INTEGRATING PLANNING AND DESIGN ACTIVITIES IN MATERIAL HANDLING SYSTEMS Award#: DMI April 1999-March 2002, $426,830 PIs: Sunderesh S. Heragu, Robert J. Graves Graduate and Undergraduate Students: Byung-In Kim, Wasawat Nakkiew, Patty Hains Rensselaer Polytechnic Institute Industrial Sponsor: Art St. Onge, St. Onge Company

Order Picking in a Cosmetics Application Pick Order Trays are organized into Trains –Each order tray is a customer order which may contain multiple SKUs –Order tray receives contents of a Drop Buffer Trains proceed along a conveyor line to Pick Zones –Several pick zones may contain the same SKU number due to anticipated demand level –Gantry Cranes in Pick Zones place the SKU in a Drop Buffer

OAPS Order Analysis and Planning FSS Finite Scheduling System Automated Material Handling Devices Information and Status Inquiries and Parameters Tasks Status Current Hierarchical Framework A collection of entities organized into orders, each subordinate to the one above

Basis For New Heterarchical Framework

A collection of entities organized into ranks, interacting among themselves as well as with other ranks OAPS Order Analysis and Planning FSS Finite Scheduling System Automated Material Handling Devices Information and Status Inquiries and Parameters Information and decision-making Information and decision-making

Heterarchical Framework Design, Analysis and Impact Holonic modeling framework development Prototype simulation model development –Use of Gensym Simulation Benefits –Control system designers –Users

Intelligent Agents Intelligent agents representing –Entities and resources –Functioning cooperatively –Accomplishing individual, cell-wide and system-wide goals

Order Picking: Pick-zone Assignment Decision Maker : OAPS Method : Hierarchical & Static Decision Timing : One day before picking Benefit : Ease of Calculation Problem : Separates Planning from Execution -> Lacks ability to handle dynamic situation Original LogicNew Logic Decision Maker : FSS Method : Intelligent Agent Based Heterarchical & Dynamic Decision Timing : The moment when the line-item enters the system Benefit : Synchronized Planning & Execution -> Fault Tolerant -> Last minute changes so pick- ing can be accommodated Problem : More sophisticated calculation

Negotiation Protocol Order Agent Pick-zone Agent Task Announcement Monitoring Bid- board Select Best Bid Delete Task, Bid Confirm Task Monitoring Task-board Make a Bid Bid Submission Heterarchical Implementation for Pick-zone Assignment Bid Board Task Board

Simulation Results Heterarchical Approach: Agent-based Pick-zone Assignment * simulation mode : as-fast-as * task announcement interval : 0.1 sec * negotiation interval: 0.2 sec

Simulation Results with various fixed conveyor speeds Errors of the new model are always less than the original model Average utilization levels are almost the same Standard deviation of utilization levels are almost the same Better system throughput seems possible, 6.3%(0.05/0.80) easily seen Heterarchical System: Agent-based Pick-zone Assignment

Heterarchical System: Agent-based Dynamic Conveyor Speed Adjustment Gantry Complex Agent Gantry Agent Gantry Agent Gantry Agent Gantry Agent 1. Can conveyor speed up(down) ? 2. Everybody is OK with new speed ? 3.No problem, okay here! 3.No I can’t AP-Plex Agent A-Plex Agent Manual Agent (4) I want to reset my conveyor speed. Is it OK to you ? Negotiation Protocol

OAPS: Work Load Balancing between Order Trains Order-Stream is made by OAPS Work Load between trains is unbalanced New OAPS => Developed a Preprocessor to balance loads using non ZIP Code-qualified orders

Simulation Results with various conveyor speeds Throughput improvement in the system by balancing workload and using bidding, 12.5 %(0.10/0.80) easily seen OAPS: Work Load Balancing between Order Trains

Intelligent Agent Based Conveyor Speed Adjustment More frequent oscillations in (a) than in (b) Simple logic at the higher level agent to filter requests - Threshold 0.05 sec * 0.75 sec : starting conveyor feed interval 5 min, 10 min : specified checking interval 0.05 sec : threshold for filtering logic of higher level agent (Gantry Complex agent)

Chaos There is no commonly agreed definition of chaos Commonly accepted characteristics of chaos –sensitive dependence on initial conditions –non integer value of attractor dimension (strange attractor) Test of Chaos –Lyapunov exponents Measure the rate of exponential divergence of nearby trajectories 1) Maximal Lyapunov exponent > 0 => chaos and indicates how much chaos –Correlation Dimension 2) Approximation of attractor dimension Non-integer correlation dimension => chaos 1) J. Theiler, “Estimating fractal dimension,” J. Opt. Soc. Am. A, vol. 7, no. 6, pp , ) P. Grassberger and I. Procaccia, “Characterization of Stranger Attractors,” Physical Review Letters, vol. 50, no. 5, pp , 1983

Measurement of time series data One-dimensional time series data : convert to multi-dimensional data using Attractor reconstruction method 1) and then measure the maximal Lyapunov exponent & correlation dimension It’s not easy to calculate the dimensions even of a simple time series data –El Farol Bar problem 2) Description: 100 people decide independently each week whether go to the bar or not. Space is limited, and if fewer than 60 are present, it is enjoyable. The only information available is the numbers who came in past weeks. Individual possesses and keeps track of a set of predictors. He decides to go or stay according to the currently most accurate predictor in his set Known as a chaos dynamics 1) F. Takens, “Detecting Strange Attractors in Turbulence,” Lecture Notes in Mathematics vol. 898, Springer-Verlag, New York, ) W. B. Arthur, “Inductive Reasoning and Bounded Rationality,” American Economic Review, vol. 84, no. 2, pp , 1994

Difficulty of Chaos Test Maximum Lyapunov exponent –need to have common slope Known Chaos Time series Data El Farol Bar Experimental Data Correlation Dimension –need to have common line segments * Using the method and software provided by R. Hegger and H. Kantz, and T. Schreiber, “Practical implementation of nonlinear time series methods: The TISEAN package,” chaos, vol. 9, no. 2, pp , 1999 Different dr, m Slope = max Lyapunov exponent e Ln(C(e))/Ln(e) ap Correlation Dimension = The y value of horizental line segments No common line segments No common slope

Controlling Chaos Reward mechanism 1) Test on El Farol Problem –Give each agent an initial credit (100) –For each iteration(week), if an agent’s prediction is correct(whether the attendants are greater than 60 or not), it receives 1 credit. Otherwise it receives –1 credit. –If an agent’s credit is less than the initial value(100), it follows the decision with probability of the current credit. 1) T. Hogg and B. A. Huberman, “Controlling Chaos in Distributed Systems,” IEEE Transactions on Systems, Man, and Cybernetics, vol. 21, no. 6, pp , 1991

Chaos Test of the Hybrid Model Test of sensitive dependence on initial condition –Order sequence perturbation –Utilization levels of gantry robots do not sensitively depend on the initial order sequence Because of difficulty of calculating maximal Lyapunov exponent, we don’t use it

Dynamic Conveyor Speed Pure heterarchical model can become unstable (a & b) Introduction of higher level agent (gantry complex agent) can control the unstable dynamics

Summary Heterarchical System: Agent Based Pick-zone Assignment outperforms the original: 1. Conveyor speed can be adjusted dynamically 2. Throughput rate can be increased because bidding allows dynamic system response 3. Fault tolerance improved Work load balancing between trains is desirable (OAPS or Preprocessor)