Supply Chain Modeling Language for Optimization-Implementation in Python-

Mikio KUBOTokyo University of

Marine Science of Technology

Agenda

• What’s the SCML (Supply Chain Modeling Language)

• How to implement the SCML in Python

• (Applications)

What is the SCML?

SCML

Supply Chain Optimization

Models

Combinatorial Optimization

Models

Solvers(using metaheuristics

and/or MIP/CP solvers)

SCML.py

proposed in 2009 by M. K. (international scheduling symposium)

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)

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)

Previous SCO models

Flow models

(LND, FL)

Multi-echelon inventory models

(IPO, SSA, EOQ, LS)

Constrained optimization models

(Algebraic modeling languages)

Scheduling models

(RCS, LS, VR)

Previous SCO models

Flow models

(LND, FL)

Multi-echelon inventory models

(IPO, SSA, EOQ, LS)

Constrained optimization models

(Algebraic modeling languages)

Scheduling models

(RCS, LS, VR)

Network=(Node, Arc),Product Activity, Resource

Product (BOM)Variable, Constraint

Activity based view of linear programming

brow (constraint)=resource

matrix A=[aij]

column (variable) =activity Xj

＋＋

－

system inputof resource

activity i consumes

resource j by aij

Dantzig-Wolfe (1963)

Problem class

C o n s t ra in t Va r ia b le

R e s o u rc e A c t iv i t y

P ro b le mGurobi (MIP)GLPK (MIP/Free)SCOP (CP)

Entities of the SCML

• activity • resource• product• node• arc

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

Basic entities

Activity

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

activity

resource

product productconsume produce

require

Fixed CostVariable Cost

Resource

• Every entity of limited availability required and/or consumed by activities

Our focus is on the physical, human, and financial resources.

Product

• Products are consumed and/or produced by activities

• Products are items or commodities through the network

activityproduct productconsume produce

Product

• Products are consumed and/or produced by activities

• Products are items or commodities through the network

node node

product product

arc

Node and arc

• Network is defined by the set of nodes and arcs

node nodearc

Declaration and attributes

• activity• resource• product• node• arc

activity declaration activity activity-name [attributes]

attribute:

duedate integer+

weight integer+

consume product-name unit real+ ...

produce product-name unit real+ ...

...

Key concepts for implementing the SCML in Python• Inheritance / Composition

• Hierarchy

• Global / Local

Inheritance

Entity class

Entity has a name and attributes (defined by arguments as a dictionary)

class Entity(): def __init__(self, name="",**args):

self.name=name

self.attributes=copy.deepcopy(args)

An activity object for LSact1=Activity("act1",

variablecost=1, fixedcost=53,,leadtime=3, resources={"res1":1},consume={"parts1":1,"parts2":2},produce={"prod1":1})

Class Activity(Entity):

prod1

resource

activity

consume

produce

parts1

parts2

Composition

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

Mode Mode Modechildren

Example: an activity object for RP

item1=Activity("item1”, cost=10, childrenchildren=“mode1": {resources:{"width":3,"height":2}} ,“mode2”: {resources={"width":2,"height":3}, cost=5})

mode1(cost=10)

mode2(cost=5)

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.

activity

resource

product productconsume produce

require

node nodearc

Lot-sizing (LS) model

• horizon, activity, resource, product

product

resource

activity

consume

produce

product

Example for solving LS in python (1)from SCML import * #import everything from SCML modulesample=SCML() #generate SCML class objectsample.setHorizon(5) #set the planning horizon to 5#generate the product class objectsprod1=Product("prod1",demand=[5,5,6,7,8],

holdingcost=5,leadtime=1)parts1=Product("parts1",holdingcost=1,leadtime=3)parts2=Product("parts2",holdingcost=1,leadtime=1) #generate the resource class objectres1=Resource(“res1”,capacity={(0,“inf”):25})

Example for solving LS in python (2)#generate the activity class object

act1=Activity("act1",variablecost=1,fixedcost=53,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

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)