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Supply Chain Modeling Language (SCML) Project
Mikio KUBO
Tokyo University of Marine Science of Technology
http://kubomikio.com
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Koji Nonobe @ Hosei University
Mutsunori Yagiura @Nagoya University
J. Pedro Pedroso @ Porto University
Hideki Hashimoto @Nagoya University
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What is the SCML?
SCML
Supply Chain Optimization Models
Combinatorial Optimization Problems
Solvers
AMPL Model Files
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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
• generalized assignment problem (GAP)
• set covering problem (SCP)
• rectangular packing problem (RPP)
• multi-dimensional knapsack problem (MKP)
• facility location problem (FLP)
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Related work
• SCOR (supply chain operations reference) model
• SCML (same name!) : supply chain modeling language for simulation
• Algebraic modeling languages
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SCOR model
proposed by Supply Chain Council
A reference model designed for effective communication among SC partners
SC= {(plan, source, make deliver, return) ...}
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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)
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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)
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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
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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
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Resource constrained scheduling model
activity
resource
require
activity
precedence relation
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Lot-sizing models
resource
resource
BOM (bill of material)
product
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State-task network representation
state = product
resource
task =activity
Kandili-Pantelides-Sargent (1993)
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Logistics network design model
resource
require
node node
product
assemble
disassemble
transport
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Key entities
• activity• resource• product• node• arc• horizon• mode • state, temporal, piecewise, solver …
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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
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Resource
• Every entity of limited availability
Our focus is on the physical, human, and financial resources.
• Categorized into:– Renewable– Nonrenewable
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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
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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.
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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
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Horizon
horizon declaration:
horizon integer+
0 1 2 3 4horizon 4
set the planning horizon to 4
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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+] ...
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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
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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 }
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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
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Temporal constraintstemporal declaration:
temporal activity-name activity-name [attributes]
attribute:
type { SS, SC, CS, CC }
delay integer
A B
Completion Start
delay
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States
state declaration:
state state-name time integer+ value integer+ ...
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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
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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+
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Nodes
node declaration:
node node-name [attributes]
attribute:
location latitude longitude
weight real+
product-name [product-attributes] ...
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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] ...
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Solvers
solver declaration:
solver { RCS, LS, LND, SSA, EOQ, IPO, VR, SCP, GAP, RPP, MKP, FLP} [attributes]
attribute:
option option-name option-value ...
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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”
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Scheduling model• [horizon], activity, mode, resource,
nonrenewable, temporal, state
activity
resource
require
activitytemporal
modes require
nonrenewable
state
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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
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Lot-sizing model
• horizon, activity, mode, resource, product
product
resource
activity
consume
produce
product
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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
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BOM representation using SCML
product
resourcechild parent
activity
activity
activity
resource
consume
produce
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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
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Logistics network design (LND) model
• horizon, activity, resource, product, node, arc
activity
resource
product productconsume produce
require
node node
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An example of LND model source1
source2
apple
bottle
plantin plantout customer
juice juice
vehicle
ship
line2
line1 vehicle
apple
bottle
juice×2
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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
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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
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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
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Vehicle routing model• activity, resource, node, arc, piecewise
depotor origin
a customeror destination
“move” activity
vehicle resource
weightresource
volumeresource
completion piecewise
start piecewise
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Inventory models
• horizon, product, activity, resource
• (network type) economic ordering quantity model (EOQ)
• safety stock allocation model (SSA)
• inventory policy optimization model (IPO)
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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)
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Set covering problemCostCost 5646335 5646335
row 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
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Generalized assignment problem
agents=>resources
jobs=> activities
bi=>capacity
aij =>requirement
cij =>cost
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Rectangular packing problem
rectangle=>activity withmultiple modes
width=>resource
height=>resource
cost => piecewise
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Multi-dimensional knapsack problem
constraints=>resources
items=> activities
bi=>capacity
aij =>requirement
profit pj => -cost
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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)