Supply Chain Modeling Language for Optimization -Implementation in Python-

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Supply Chain Modeling Language for
Optimization-Implementation in Python-

• Mikio KUBO
• Tokyo University of Marine Science of Technology

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Agenda

• Whats the SCML (Supply Chain Modeling Language)
• How to implement the SCML in Python
• (Applications)

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What is the SCML?
proposed in 2009 by M. K. (international
scheduling symposium)
Supply Chain Optimization Models
Solvers (using metaheuristics and/or MIP/CP
solvers)
SCML
SCML.py
Combinatorial Optimization Models
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Supply chain optimization models

• resource constrained scheduling (RCS)
• lot-sizing (LS)
• logistics network design (LND)
• safety stock allocation (SSA)
• economic order quantity (EOQ)
• inventory policy optimization (IPO)
• vehicle routing (VR)

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Combinatorial optimization problems

• set covering problem (SC)
• generalized assignment problem (GA)
• rectangular packing problem (RP)
• facility location problem (FL)
• multi-constrained knapsack problem (MK)
• graph coloring problem (GC)
• graph partitioning problem (GP)
• maximum stable set problem (MSS)
• (constrained) bin packing problem (BP)
• quadratic assignment problem (QA)

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Previous SCO models
Flow models (LND, FL)
Scheduling models (RCS, LS, VR)
Multi-echelon inventory models (IPO, SSA, EOQ, LS)
Constrained optimization models (Algebraic
modeling languages)
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Previous SCO models
Network(Node, Arc), Product
Activity, Resource
Flow models (LND, FL)
Scheduling models (RCS, LS, VR)
Multi-echelon inventory models (IPO, SSA, EOQ, LS)
Constrained optimization models (Algebraic
modeling languages)
Product (BOM)
Variable, Constraint
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Activity based view of linear programming
Dantzig-Wolfe (1963)
matrix Aaij
row (constraint) resource
b
-
system input of resource
activity i consumes resource j by aij
column (variable) activity Xj
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Problem class
Gurobi (MIP) GLPK (MIP/Free) SCOP (CP)
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Entities of the SCML

• temporal
• piecewise
• horizon
• state
• solver
• etc., ...

• activity
• resource
• product
• node
• arc

Basic entities
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Activity

• Every action that requires the resources,
  consumes and/or produces the product, and derives
  the cost

Fixed Cost Variable Cost
consume
produce
activity
product
product
require
resource
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Resource

• Every entity of limited availability required
  and/or consumed by activitiesOur focus is on
  the physical, human, and financial resources.

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Product

• Products are consumed and/or produced by
  activities
• Products are items or commodities through the
  network

consume
produce
activity
product
product
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Product

• Products are consumed and/or produced by
  activities
• Products are items or commodities through the
  network

arc
node
node
product
product
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Node and arc

• Network is defined by the set of nodes and arcs

arc
node
node
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Declaration and attributes
activity declaration activity activity-name
attributes

• activity
• resource
• product
• node
• arc

attribute duedate integer weight
integer consume product-name unit real
... produce product-name unit real ... ...
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Key concepts for implementing the SCML in Python

• Inheritance / Composition
• Hierarchy
• Global / Local

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Inheritance
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Entity class

• Entity has a name and attributes (defined by
  arguments as a dictionary)class Entity()
  def __init__(self, name"",args)
• self.namename
• self.attributescopy.deepcopy(args)

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An activity object for LS

• act1Activity("act1",variablecost1,
  fixedcost53,,leadtime3, resources"res1"1,co
  nsume"parts1"1,"parts2"2,produce"prod1"1
  )
• Class Activity(Entity)

consume
prod1
parts1
activity
produce
parts2
resource
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Composition
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Hierarchy

• Hierarchy can be defined on every entity using
  attribute children
• Every attribute of a parent is copied to its
  children (same as inheritance)

activity
children
Mode
Mode
Mode
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Example an activity object for RP

• item1Activity("item1, cost10,
  childrenmode1" resources"width"3,"heig
  ht"2 ,mode2 resources"width"2,"heig
  ht"3, cost5)

mode2 (cost5)
mode1 (cost10)
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Global / Local

• Local products can be defined on nodes
• Local activities and resources can be defined on
  arcs, i.e., arcs can own activities and resources
• Otherwise, entities are called global.

arc
node
node
produce
consume
activity
product
product
require
resource
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Lot-sizing (LS) model

• horizon, activity, resource, product

consume
product
activity
produce
resource
product
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Example for solving LS in python (1)

• from SCML import import everything from
  SCML module
• sampleSCML() generate SCML class
  object
• sample.setHorizon(5) set the planning horizon
  to 5
• generate the product class objects
• prod1Product("prod1",demand5,5,6,7,8,
  holdingcost5,leadtime
  1)
• parts1Product("parts1",holdingcost1,leadtime3)
• parts2Product("parts2",holdingcost1,leadtime1)
  
• generate the resource class object
• res1Resource(res1,capacity(0,inf)25)

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Example for solving LS in python (2)

• generate the activity class object
• act1Activity("act1",variablecost1,fixedcost53,
  resources"res1"1,consume"parts1"1,"parts2"
  2,generate"prod1"1)
• add the generated objects into the problem class
• sample.addActivity(act1)
• sample.addProducts(prod1,parts1,parts2)
• sample.addResource(res1)
• sample.solve(LS) solve by the lot-sizing
  solver

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Future plans

• Applications (hybrid models)
• Lot-sizing Inventory policy optimization
• Logistics network design Resource constrained
  scheduling Lot-sizing
• Excel interface for beginners
• A book on the SCML (will be published in 2010-11
  from Asakura Publishers)