2008-02-12christopher j. hazard 1 resource allocation and routing in multi-vehicle warehousing:...

Resource Allocation and Routing in Multi-vehicle Warehousing:

Alphabet Soup

Christopher J. HazardNorth Carolina State University

[email protected]

2008-02-12 Christopher J. Hazard 2

Outline

• Motivation & Kiva Systems• Alphabet Soup

– Problem– Demo– Testbed & code details

• Viable Solutions– Abstraction with MILP & Stochastic

programming– Market oriented programming


Retailer,Customer

The Problem

MFG

MFG

Pallets

Cases, Eaches

Shipping Boxes,

Cartons

Reserve Forward Shipping


Kiva Systems

• Philosophy– People Hands >> Robot Hands (for now)

– All products mobile– Move products to hands

• Solution– Robots move “pods” to humans on perimeter– System completely manages fulfillment


Kiva Systems Pods & Robots


Kiva Systems Picking Workflow


Kiva Systems Installation


Kiva Systems Installation (2)


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


What is Alphabet Soup?

LetterStation Word

Station

Abstraction of Physical Routing in Warehouses, Manufacturing, Assembly

LetterStation

WordStation


Alphabet Soup Testbed Mechanics

• Maximum speed & acceleration clamped

• Time penalty for collisions

• “Perfect sensing”

• Robot coordination important– High level for controlling robots


Alphabet Soup Demos

• Small example

• Large example

• Greedy vs. market

• Java + LWJGL, GPL 2+

• http://research.csc.ncsu.edu/alphabetsoup


Alphabet Soup High Level View

Map

Simulation World

Word Stations

Letter Stations

Managers

Render Window

Word ListBuckets

Bucketbots

Quadtree

• Extend base classes– implement behavior

• Statistics

Waypoint Graph


Alphabet Soup Code Overview• base

– Bucket– Bucketbot– BucketbotTask– LetterStation– SummaryReport– WordList– WordStation

• userinterface– RenderWindow– BucketbotRender,

BucketRender, etc.– Renderable

Bold: will probably useItalics: interface

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


Alphabet Soup Code Overview (2)• simulators.graphexample

– BucketbotManagerExample– LetterManagerExample– SimulationWorldGraphExample– WordOrderManagerExample

• simulators.greedytaskallocation– BucketbotAgent– BucketbotGlobalResources– LetterManager– SimulationWorldGreedyTaskAllo

cation– WordOrderManager

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


Code Walkthrough

• alphabetsoup.config• graphexample

– SimulationWorldGraphExample– WordOrderManagerExample– LetterManagerExample– BucketbotManagerExample

• greedytaskallocation– BucketbotAgent

• waypointgraph– BucketbotManager– BucketbotDriver– GenerateWaypointGraph


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.• Don’t be afraid to change code

– Add own classes, initialize in SimulationWorld

• Consider DOE (Design Of Experiment)


Waypoints & Bucket Storage• Waypoint graph

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


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


Goals

1. Prevent deadlock

2. Maximize throughput• Minimize congestion

3. Minimize # of robots, buckets, stations

4. Minimize idle time

5. Minimize energy (distance, #pickups & setdowns)

6. Minimize variance of task times


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?


Possible “Solutions”

• Stochastic Programming

• Further abstraction with MILP

• Market oriented programming


Stochastic Programming

• Many recourse problems

• How to model probability distributions?– What level of abstraction?

• Joint distributions highly dependent on coordination schemes

• Use MDP’s?


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: ||items||2 x ||stations||• 1000 items, 10 stations 10M constraints for timing


Market-Oriented Programming

• Resource allocation– Agents– Markets/Auctions– Resources– Valuations

• Transform optimization problems

• Interface: price & resource

• Sometimes altruistic or honest agents

[Wellman ‘96]


Dual of MILP as Market

• Constraints to prevent discriminatory pricing– Adds O(||items of a type||2 x ||stations||) more

constraints– Preliminary results suggest may not affect

optimality for steady-state– Simpler to solve?

• Simplify problem further?


Representing an Economy

Item Type I

Agent Type A Agent Type

Item Type

Item Can Be Sold By

Auction

Auction with Multiple Item or Agent Types


Representing an Economy (2)

arrow anonymous price? linear price?no yesno no yes yesyes no


Economy 1

Word

Letter Bundle

Letter

Bucket

Letter Station

Transportation

Bucketbot

Storage Right

Storage

Letter Bundle

Letter Builder

Word Station

Word Queue


Economy 2

Letter Bundle

Storage RightLetter Bundle

Letter

Bucket

Letter Station

Letter Builder

Transportation

Storage

Bucketbot

Word Station

Word Word Queue


Economy 3

Letter BundleBundle Slot

Letter

Word

Bucket

Letter Builder

Transportation

Word Queue

Bucketbot

Storage Right

Storage

Letter Station

Word Station


Segmenting the Market

A X

B X'

C

X

A

B

X'

C


Communicating Price Information Between Market Segments

• Information channel– Auctioneers– “Middleman” agents

• Information timing– Tâtonnement-like– Reactive


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)


“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


Available Resources

• In Alphabet Soup release– Working anonymous linear-price market model:

simulators.markettaskallocation– Start of implementation of non-linear price market model:

simulators.combinatorialmarkettaskallocation

• 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


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


Acknowledgements

• Peter Wurman– Kiva Systems

• Raff D’Andrea– Kiva Systems, Cornell

2008-02-12christopher j. hazard 1 resource allocation and routing in multi-vehicle warehousing:...

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