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Artificial Agents Play the Beer Game Eliminate the Bullwhip Effect and Whip the MBAs

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Experiment 1a: First Cup. Environment: Deterministic demand with fixed leadtime. ... Q1 = D (t-1), Qi = Qi-1 (t li-1). Ongoing Research: More Beer. Value of ... – PowerPoint PPT presentation

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Title: Artificial Agents Play the Beer Game Eliminate the Bullwhip Effect and Whip the MBAs


1
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

2
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

3
Timing
  • 1. New shipments delivered.
  • 2. Orders arrive.
  • 3. Fill orders plus backlog.
  • 4. Decide how much to order.
  • 5. Calculate inventory costs.

4
Game Board

5
The Bullwhip Effect
  • Order variability is amplified upstream in the
    supply chain.
  • Industry examples (PG, HP).

6
Observed Bullwhip effect from undergraduates game
playing

7
Bullwhip Effect Example (P G)
  • Lee et al., 1997, Sloan Management Review

8
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.

9
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.

10
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.

11
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?

12
Flowchart
13
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 x1 means if demand is x then order x1.
  • Rule search space is 2n-1 1.

14
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.

15
Experiment 1b
  • All four Agents learn under the environment of
    experiment 1a.
  • Ăśber rule for the team.
  • All four agents find 1-1.

16
Result of Experiment 1b
  • All four agents can find the optimal 1-1 policy

17
  • Artificial Agents Whip the MBAs and
    Undergraduates in Playing the MIT Beer Game

18
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.

19
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.

20
Artificial agents eliminate the Bullwhip effect.
21
Artificial agents discover a better policy than
1-1 when facing stochastic demand with penalty
costs for all players.
22
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.

23
Artificial agents discover better and stable
policies than 1-1 when facing stochastic demand
and stochastic lead-time.
24
Artificial Agents are able to eliminate the
Bullwhip effect when facing stochastic demand
with stochastic leadtime.
25
Agents learning

26
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.,
  • Q1 D (t-1), Qi Qi-1 (t li-1).

27
Ongoing Research More Beer
  • Value of information sharing.
  • Coordination and cooperation.
  • Bargaining and negotiation.
  • Alternative learning mechanisms Classifier
    systems.

28
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.

29
A framework for multi-agent intelligent
enterprise modeling
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