Resource Allocation and Routing in Multivehicle Warehousing: Alphabet Soup

1
Resource Allocation and Routing in Multi-vehicle
WarehousingAlphabet Soup

• Christopher J. Hazard
• North Carolina State University
• cjhazard_at_ncsu.edu

2
Outline

• Motivation Kiva Systems
• Alphabet Soup
• Problem
• Demo
• Testbed code details
• Viable Solutions
• Abstraction with MILP Stochastic programming
• Market oriented programming

3
The Problem
Reserve
Forward
Shipping
MFG
Shipping Boxes, Cartons
Cases, Eaches
Pallets
MFG
Retailer, Customer
4
Kiva Systems

• Philosophy
• People Hands gtgt Robot Hands (for now)
• All products mobile
• Move products to hands
• Solution
• Robots move pods to humans on perimeter
• System completely manages fulfillment

5
Kiva Systems Pods Robots
6
Kiva Systems Picking Workflow
7
Kiva Systems Installation
8
Kiva Systems Installation (2)
9
Kiva Systems Features

• All workers have access to all products
• Order completed by single worker
• Adaptive storage replenishment
• Spatial flexibility
• Route around problems
• Item shape flexibility
• Slots, hanging, shelves
• Optimizes for weight shape

10
What is Alphabet Soup?
Abstraction of Physical Routing in Warehouses,
Manufacturing, Assembly
Letter Station
Word Station
Word Station
Letter Station
11
Alphabet Soup Testbed Mechanics

• Maximum speed acceleration clamped
• Time penalty for collisions
• Perfect sensing
• Robot coordination important
• High level for controlling robots

12
Alphabet Soup Demos

• Small example
• Large example
• Greedy vs. market
• Java LWJGL, GPL 2
• http//research.csc.ncsu.edu/alphabetsoup

13
Alphabet Soup High Level View

• Extend base classes
• implement behavior
• Statistics

Simulation World
Managers
Map
Quadtree
Word List
Letter Stations
Buckets
Render Window
Word Stations
Bucketbots
Waypoint Graph
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Alphabet Soup Code Overview

• base
• Bucket
• Bucketbot
• BucketbotTask
• LetterStation
• SummaryReport
• WordList
• WordStation
• userinterface
• RenderWindow
• BucketbotRender, BucketRender, etc.
• Renderable
• Bold will probably use
• Italics interface

• framework
• Bucket
• Bucketbot
• Circle
• Letter
• LetterColor
• LetterStation
• LetterType
• Map
• MersenneTwisterFast
• Quadtree
• QuadtreeNode
• SimulationWorld
• Updateable
• Word
• WordList
• WordStation

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Alphabet Soup Code Overview (2)

• simulators.graphexample
• BucketbotManagerExample
• LetterManagerExample
• SimulationWorldGraphExample
• WordOrderManagerExample
• simulators.greedytaskallocation
• BucketbotAgent
• BucketbotGlobalResources
• LetterManager
• SimulationWorldGreedyTaskAllocation
• WordOrderManager

• waypointgraph
• BucketbotDriver
• BucketbotManager
• GenerateWaypointGraph
• Waypoint
• WaypointGraphRender

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Code Walkthrough

• alphabetsoup.config
• graphexample
• SimulationWorldGraphExample
• WordOrderManagerExample
• LetterManagerExample
• BucketbotManagerExample
• greedytaskallocation
• BucketbotAgent
• waypointgraph
• BucketbotManager
• BucketbotDriver
• GenerateWaypointGraph

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Misc. Tips

• Need Java 5, Java 6 faster
• For-each loops
• java.util.
• List / ArrayList
• HashMap
• Use provided random generator
• SimulationWorld.rand.nextFloat()
• nextInt(), etc.
• Is the task complete? Check for errors.
• Dont be afraid to change code
• Add own classes, initialize in SimulationWorld
• Consider DOE (Design Of Experiment)

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Waypoints Bucket Storage

• Waypoint graph
• Waypoint layout?
• Word Letter station layout?
• Storage layout?
• Path weights?
• Bucket brigade? (exchange is costly)

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Path Planning

• HUGE impact on throughput
• Robot coordination
• Waypoint/path reservation system?
• Multi-agent planning
• Currently uses A
• waypointgraph.BucketbotDriver
• Checks next couple waypoints
• Bounces around when waiting

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Goals

• Prevent deadlock
• Maximize throughput
• Minimize congestion
• Minimize of robots, buckets, stations
• Minimize idle time
• Minimize energy (distance, pickups setdowns)
• Minimize variance of task times

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Questions to Achieve Goals

• Which letters in which buckets?
• Bucket specializations?
• Which buckets to fulfill words?
• Which stations to assign words and letters?
• Which bucketbots for which buckets?

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Possible Solutions

• Stochastic Programming
• Further abstraction with MILP
• Market oriented programming

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Stochastic Programming

• Many recourse problems
• How to model probability distributions?
• What level of abstraction?
• Joint distributions highly dependent on
  coordination schemes
• Use MDPs?

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Further abstraction with MILP

• Many assignment problems
• Assign words to word stations
• Assign letters to words, letter stations,
  buckets, and robots
• Choose event times
• Events take time
• Non-integer times
• Conditionals to ensure proper ordering of events
• Even abstracting away buckets robots
• 15 constraint types
• Many stations x items
• Timing items2 x stations
• 1000 items, 10 stations ? 10M constraints for
  timing

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Market-Oriented Programming
Wellman 96

• Resource allocation
• Agents
• Markets/Auctions
• Resources
• Valuations
• Transform optimization problems
• Interface price resource
• Sometimes altruistic or honest agents

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Dual of MILP as Market

• Constraints to prevent discriminatory pricing
• Adds O(items of a type2 x stations) more
  constraints
• Preliminary results suggest may not affect
  optimality for steady-state
• Simpler to solve?
• Simplify problem further?

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Representing an Economy
Agent Type
Agent Type A
Auction
Item Type
Auction with
Item Type I
Multiple Item
or Agent Types
Item Can
Be Sold By
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Representing an Economy (2)
arrow anonymous price? linear price?
no yes
no no
yes yes
yes no
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Economy 1
Letter Builder
Storage
Letter Station
Letter Bundle
Storage Right
Letter Bundle
Bucketbot
Bucket
Transportation
Letter
Word Station
Word
Word Queue
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Economy 2
Letter Builder
Storage
Letter Station
Letter Bundle
Storage Right
Letter Bundle
Bucketbot
Transportation
Bucket
Letter
Word Station
Word
Word Queue
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Economy 3
Letter Builder
Letter Station
Letter Bundle
Storage
Bundle Slot
Storage Right
Bucketbot
Transportation
Bucket
Letter
Word Queue
Word
Word Station
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Segmenting the Market
A
A
X
X
C
B
X'
B
X'
C
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Communicating Price Information Between Market
Segments

• Information channel
• Auctioneers
• Middleman agents
• Information timing
• Tâtonnement-like
• Reactive

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Auctioneer Communication

• Tâtonnement-like Cheng Wellman 98
• DCOP Modi et al. 03 and Petcu Faltings 05
• Artificially harder problem?
• Inefficient discovery of valuations
• Constraints between agents on both sides
• Reactive
• Exposure problem
• No free disposal
• Sub-problems unaccounted for (e.g. TSP)

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Middleman Agents as Information Channel

• Exposure problem
• No free disposal
• Learning market prices
• Speculators
• Specialization
• Propagate demand for goods not in market
• Leverage uncertainty models
• Tâtonnement issues

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Available Resources

• In Alphabet Soup release
• Working anonymous linear-price market model
  simulators.markettaskallocation
• Start of implementation of non-linear price
  market model simulators.combinatorialmarkettaskal
  location
• Available upon request
• Collisionless evaluator framework
• In C, only random decisions
• Alphabet Soup provides data
• MILP model of collisionless abstraction
• Not validated
• Collaboration tools sourceforge.net,
  wiki/forums, SVN

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Other Ideas

• Apply Alphabet Soup to Mfg/Assembly
• Affect of distributions
• Affect of online optimization stations
• Adaptive storage algorithms
• N-player competitive Alphabet Soup?!?
• Squares, hexagons, and beyond
• Pick/replen station layout

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Acknowledgements

• Peter Wurman
• Kiva Systems
• Raff DAndrea
• Kiva Systems, Cornell