Supply Chain Modeling Language (SCML) Project

Mikio KUBOTokyo University of

Marine Science of Technologyhttp://kubomikio.com

Koji Nonobe @ Hosei University

Mutsunori Yagiura @Nagoya University

J. Pedro Pedroso @ Porto University

Hideki Hashimoto @Nagoya University

What is the SCML?

SCML

Supply Chain Optimization Models

Combinatorial Optimization Problems

Solvers

AMPL Model Files

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

• generalized assignment problem (GAP)• set covering problem (SCP)• rectangular packing problem (RPP)• multi-dimensional knapsack problem (MKP)• facility location problem (FLP)

Related work

• SCOR (supply chain operations reference) model

• SCML (same name!) : supply chain modeling language for simulation

• Algebraic modeling languages

SCOR model

proposed by Supply Chain Council

A reference model designed for effective communication among SC partners

SC= {(plan, source, make deliver, return) ...}

Another SCML

Chatfield et al. (2009)

XML-based document format for simulationBasic entities are:• node and arc (network is essential)• component ( product + resource) ≒• action ( activity)≒• policy (for doing simulation)

Algebraic modeling languages

• AMPL, MOSEL, OPL, GAMS, etc.• solvers (general purpose)

– Mixed integer programming, constrained programming, other nonlinear programming

• using set, parameter, variable, objective function, constraints, etc. (also general purpose)

Previous work

• Activity based view of linear programming Resource constrained scheduling model

• Lot-sizing models • State-task network representation for batch

process• Logistics network design model• Algebraic modeling languages

Activity based view of linear programmingDantzig-Wolfe (1963)

brow =resource

matrix A=[aij]

column =activity (amount: Xj)

＋＋

－

system inputof resource

activity i consumes

resource j by aij

Resource constrained scheduling model

activity

resource

require

activity

precedence relation

Lot-sizing models

resource

resource

BOM (bill of material)

product

State-task network representation

state = product

resource

task =activity

Kandili-Pantelides-Sargent (1993)

Logistics network design model

resource

requirenode node

product

assemble

disassemble

transport

Key entities• activity• resource• product• node• arc• horizon• mode • state, temporal, piecewise, solver …

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

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

• Categorized into:– Renewable– Nonrenewable

Product , node, arc

• A product is an item or commodity through the network

• Network is defined by the set of nodes and arcs

node node

product product

arc

Relation among entities

activity

resource

product productconsume produce

require

node nodearc

Activities and resources can be defined on arcs.(They are called “local.” Otherwise called “global.”)

Products are defined on nodes.

Notations• inf : ∞• integer+: a non-negative integer or +∞• integer: an integer or +∞ or -∞• real+: a non-negative real number or +∞ • real: a real number or +∞ or -∞• range: a pair of two integers (a,b) such that a b≦• ... 　 : allow any number of repetitions• [ ] : optional • { } : select one within the braces

Horizon

horizon declaration: horizon integer+

0 1 2 3 4horizon 4

set the planning horizon to 4

Activity attributes [autoselect] mode-name ...

mode [mode-attributes]

duedate integer+

weight integer+

start { integer+, range, piecewise-name }

completion { integer+, range, piecewise-name }

selected { mode-name, resource-name}

execute interval range [parallel integer+] ...

Interval

①②③④0 1 2 3 4

interval 1 3 => { , }② ③ [1,3)

execute interval 1 3execute interval 3 4 parallel 2

0 1 2 3 4

range

Mode attributesduration integer+

resource-name [max] [ interval range] requirement integer+ cost { integer, piecewise-name } ...

break interval range [max] integer+ ...

parallel interval range [max] integer+ ...

state-name from state-value to state-value

amount interval range real+ (LS, LND)

consume product-name unit real+ ...

produce product-name unit real+ ...

variablecost [interval range] real ...

fixedcost [interval range] real ...

cycletime [interval range] { integer+, range }

leadtime [ interval range] { integer+, range }

Resource attributes

[interval range] capacity integer+... location node-name time integer+cost real

interval 0 1 capacity 1 interval 1 3 capacity 2interval 3 4 capacity 1

0 1 2 3 4

Temporal constraintstemporal declaration:

temporal activity-name activity-name [attributes]

attribute:

type { SS, SC, CS, CC }

delay integer

A B

Completion Start

delay

States

state declaration:state state-name

time integer+ value integer+ ...

Piecewise linear function attributes

piecewise example default inf interval 0 1 init 1 slope 1 interval 1 3 init 1 slope 0

Must be lower semicontinous

interval range init real slope real ...

default real

Product attributessupply [interval range] {real+, range, randvar } ...

demand [interval range] {real+, range, randvar } ...

holdingcost [interval range] real+ ...

backordercost [interval range] real+ ...

inventory [interval range] real+ ...

capacity [interval range] real+ ...

variability real+

safetyratio real+

reorderpoint real+

basestocklevel real+

Nodes

node declaration: node node-name [attributes]

attribute: location latitude longitude weight real+ product-name [product-attributes] ...

Arcs

arc arc-name node-name node-name [attributes]

attribute: cost real time { real+, piecewise-name } distance real+ activity-name [activity-attributes] ... resource-name [resource-attributes] ...

Solvers

solver declaration: solver { RCS, LS, LND, SSA, EOQ, IPO, VR,

SCP, GAP, RPP, MKP, FLP} [attributes]

attribute: option option-name option-value ...

Hierarchies

activity (resource, product) attributes : children activity (resource, product)-name ... [type { and, or } ] Modes: children of an activity with type “or”Vehicle capacities (weight, volume,...) :

children of a resource (vehicle) with type “and”

Scheduling model• [horizon], activity, mode, resource,

nonrenewable, temporal, state

activity

resource

require

activitytemporal

modes require

nonrenewable

state

Scheduling model (example)resource writer

interval 0 3 capacity 1

interval 4 6 capacity 1

interval 7 10 capacity 1

interval 11 inf capacity 1

activity A duedate 5 weight 20

mode duration 1

writer interval 0 1 requirement 1

activity B duedate 9 weight 5

mode duration 2

writer interval 0 2 requirement 1

break interval 0 2 max 1

...

solver RCS

option time 100

Lot-sizing model

• horizon, activity, mode, resource, product

product

resource

activity

consume

produce

product

BOM• BOM (bill of materials) : G=(N,A)

p

q

product

resource

φpq: the units of product p to produce one unit of product q.

child product of q parent product of q

φpq

BOM representation using SCML

product

resourcechild parent

activity

activity

activity

resource

consume

produce

Lot-sizing model (example)horizon 5

product prod1

holdingcost 0 inf 5

demand interval 0 1 5

demand interval 1 2 7

demand interval 2 3 3

demand interval 3 4 6

demand interval 4 5 4

product parts1

holdingcost 0 inf 1

...

resource res1

interval 0 inf capacity 25

activity act1

mode duration 1

variablecost interval 0 inf 1

fixedcost interval 0 inf 53 #setup cost

leadtime interval 0 inf 3 #setup time

res1 interval 0 inf requirement 1

consume parts1 unit 1

consume parts2 unit 2

generate prod1 unit 1

solver LS

Logistics network design (LND) model

• horizon, activity, resource, product, node, arc

activity

resource

product productconsume produce

require

node node

An example of LND model source1

source2

apple

bottle

plantin plantout customer

juice juice

vehicle

ship

line2

line1 vehicle

apple

bottle

juice×2

LND model (SCML example) 1horizon 2

product apple

holdingcost 5 inf 5

product bottle

holdingcost 1 inf 5

product juice

variability 1

safetyratio 1.65

node source1

apple

supply interval 0 inf 100

node source2

bottle

supply interval 0 inf 100

node plantin

node plantout

juice

holdingcost 10

node customer

juice

demand interval 0 inf 10

holdingcost 30

LND model (SCML example) 2arc source1 plantin

trans_apple #activity

vehicle cost 10 #resource

arc source2 plantin

trans_bottle #activity

ship cost 30 #resource

arc plantin plantout

prod_juice_online1

prod_juice_online2

line1 cost 50

line2 cost 100

arc plantout customer

trans_juice

vehicle cost 20

activity trans_apple

mode duration 1

variablecost 0 inf 1

cycletime 0 inf 1

vehicle requirement 1

consume apple unit 1

produce apple unit 1

activity trans_bottle

mode duration 1

variablecost 0 inf 1

cycletime 0 inf 1

ship requirement 1

consume bottle unit 1

produce bottle unit 1

LND model (SCML example) 3activity prod_juice_online1

mode duration 1

variablecost 0 inf 10

cycletime 0 inf 5

line1 requirement 1

consume apple unit 2

consume bottle unit 1

produce juice unit 1

...

resource line1

interval 0 inf capacity 100

cost 70

resource line2

interval 0 inf capacity 100

cost 20

resource vehicle

interval 0 inf capacity 2

resource ship

interval 0 inf capacity 10

solver LND

Vehicle routing model• activity, resource, node, arc, piecewise

depotor origin

a customeror destination

“move” activity

vehicle resource

weightresource

volumeresource

completion piecewise

start piecewise

Inventory models

• horizon, product, activity, resource

• (network type) economic ordering quantity model (EOQ)

• safety stock allocation model (SSA)• inventory policy optimization model (IPO)

Inventory models and BOM

product

resource

activity

capacity (IPO)

demand, holdingcostbasestocklevel, backordercost (IPO)

fixedcost, cycletime (range) (EOQ) leadtime (range), cycletime (integer+), duration (SSA) leadtime (integer+), cycletime (integer+) (IPO)

Set covering problemCostCost　　５６４６３３５　　５６４６３３５row row １　１００１１０１１　１００１１０１row row ２　１１０１０００２　１１０１０００row row ３　１１０００１１３　１１０００１１row row ４　０１１００１０４　０１１００１０row row ５　００１１１００５　００１１１００

・・・・・・

columns

Rows => Resources

Columns => Activities

Generalized assignment problem

agents=>resources

jobs=> activities

bi=>capacity

aij =>requirement

cij =>cost

Rectangular packing problem

rectangle=>activity withmultiple modes

width=>resource

height=>resource

cost => piecewise

Multi-dimensional knapsack problem

constraints=>resources

items=> activities

bi=>capacity

aij =>requirement

profit pj => -cost

Other problems

• facility location problem– defined on nodes: (x, y coordinates and weight)

• traveling salesman problem– defined on nodes: (x,y coordinates) ; Euclidian TSP – defined on nodes and arcs (cost); general TSP

• bin packing problem– defined on activities (items) and a resource (bin

size)