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    The Beer Game slides The Beer Game slides Presentation Transcript

    • Artificial Agents Play the Beer Game Eliminate the Bullwhip Effect and Whip the MBAs Steven O. Kimbrough D.-J. Wu Fang Zhong FMEC, Philadelphia, June 2000; file: beergameslides.ppt
    • The MIT Beer Game
      • Players
        • Retailer, Wholesaler, Distributor and Manufacturer.
      • Goal
        • Minimize system-wide (chain) long-run average cost.
      • Information sharing: Mail.
      • Demand: Deterministic.
      • Costs
        • Holding cost: $1.00/case/week.
        • Penalty cost: $2.00/case/week.
      • Leadtime: 2 weeks physical delay
    • Timing
      • 1. New shipments delivered.
      • 2. Orders arrive.
      • 3. Fill orders plus backlog.
      • 4. Decide how much to order.
      • 5. Calculate inventory costs.
    • Game Board
    • The Bullwhip Effect
        • Order variability is amplified upstream in the supply chain.
        • Industry examples (P&G, HP).
    • Observed Bullwhip effect from undergraduates game playing
    • Bullwhip Effect Example (P & G)
      • Lee et al., 1997, Sloan Management Review
    • Analytic Results: Deterministic Demand
      • Assumptions :
        • Fixed lead time.
        • Players work as a team.
        • Manufacturer has unlimited capacity.
      • “ 1-1” policy is optimal -- order whatever amount is ordered from your customer.
    • Analytic Results: Stochastic Demand (Chen, 1999, Management Science )
      • Additional assumptions:
        • Only the Retailer incurs penalty cost.
        • Demand distribution is common knowledge.
        • Fixed information lead time.
        • Decreasing holding costs upstream in the chain.
      • Order-up-to (base stock installation) policy is optimal .
    • Agent-Based Approach
      • Agents work as a team.
      • No agent has knowledge on demand distribution.
      • No information sharing among agents.
      • Agents learn via genetic algorithms.
      • Fixed or stochastic leadtime.
    • Research Questions
      • Can the agents track the demand?
      • Can the agents eliminate the Bullwhip effect?
      • Can the agents discover the optimal policies if they exist?
      • Can the agents discover reasonably good policies under complex scenarios where analytical solutions are not available?
    • Flowchart
    • Agents Coding Strategy
        • Bit-string representation with fixed length n .
        • Leftmost bit represents the sign of “ + ” or “ - ”.
        • The rest bits represent how much to order.
        • Rule “ x+1 ” means “if demand is x then order x+1 ”.
        • Rule search space is 2 n-1 – 1.
    • Experiment 1a: First Cup
      • Environment:
        • Deterministic demand with fixed leadtime.
        • Fix the policy of Wholesaler, Distributor and Manufacturer to be “1-1”.
        • Only the Retailer agent learns.
      • Result: Retailer Agent finds “1-1”.
    • Experiment 1b
      • All four Agents learn under the environment of experiment 1a.
      • Über rule for the team.
      • All four agents find “1-1”.
    • Result of Experiment 1b
      • All four agents can find the optimal “1-1” policy
      • Artificial Agents Whip the MBAs and Undergraduates in Playing the MIT Beer Game
    • Stability (Experiment 1b)
      • Fix any three agents to be “1-1”, and allow the fourth agent to learn.
      • The fourth agent minimizes its own long-run average cost rather than the team cost.
      • No agent has any incentive to deviate once the others are playing “1-1”.
      • Therefore “1-1” is apparently Nash.
    • Experiment 2: Second Cup
      • Environment:
        • Demand uniformly distributed between [0,15].
        • Fixed lead time.
        • All four Agents make their own decisions as in experiment 1b.
      • Agents eliminate the Bullwhip effect.
      • Agents find better policies than “1-1”.
    • Artificial agents eliminate the Bullwhip effect.
    • Artificial agents discover a better policy than “1-1” when facing stochastic demand with penalty costs for all players.
    • Experiment 3: Third Cup
      • Environment:
        • Lead time uniformly distributed between [0,4].
        • The rest as in experiment 2.
      • Agents find better policies than “1-1”.
      • No Bullwhip effect.
      • The polices discovered by agents are Nash.
    • Artificial agents discover better and stable policies than “1-1” when facing stochastic demand and stochastic lead-time.
    • Artificial Agents are able to eliminate the Bullwhip effect when facing stochastic demand with stochastic leadtime .
    • Agents learning
    • The Columbia Beer Game
      • Environment:
        • Information lead time: (2, 2, 2, 0).
        • Physical lead time: (2, 2, 2, 3).
        • Initial conditions set as Chen (1999).
      • Agents find the optimal policy: order whatever is ordered with time shift, i.e.,
        • Q 1 = D (t-1), Q i = Q i-1 (t – l i-1 ).
    • Ongoing Research: More Beer
      • Value of information sharing.
      • Coordination and cooperation.
      • Bargaining and negotiation.
      • Alternative learning mechanisms: Classifier systems.
    • Summary
      • Agents are capable of playing the Beer Game
        • Track demand.
        • Eliminate the Bullwhip effect.
        • Discover the optimal policies if exist.
        • Discover good policies under complex scenarios where analytical solutions not available.
      • Intelligent and agile supply chain.
      • Multi-agent enterprise modeling.
    • A framework for multi-agent intelligent enterprise modeling