Download Applications of Stochastic Constraint Programming in Supply Chain

Introduction
Research overview
Applications of
Stochastic Constraint Programming
in Supply Chain and Operations
Management
Dr Roberto Rossi1
1 Management Science & Business Economics,
The University of Edinburgh Business School, UK
Logistics, Decision and Information Sciences,
Wageningen University, the Netherlands
The University of Edinburgh, March 2012
Conclusions
Introduction
Research overview
Conclusions
Background information
Introducing myself...
Current
Lecturer
Management Science
Roberto Rossi
PhD (Cork)
MEng (Bologna)
BEng (Bologna)
External Assistant Professor
Logistics Decision and Information Sciences
External Fellow
Wageningen School of Social Sciences
Past
Lecturer
University College Cork (UCC)
Postdoctoral researcher
Cork Constraint Computation Center (4C)
PhD Student
Centre for Telecommunication Value Chain Research, 4C, UCC
Introduction
Research overview
Conclusions
Background information
Introducing myself...
Current:
Roberto Rossi
Assistant Professor
Logistics, Decision and Information Sciences
Research Projects
Microbiological Risk Assessment in
Logistic Chain Modeling
Logistics Modelling of
Pork Supply Chains
Past:
Lecturer
University College Cork, Ireland
Postdoctoral Researcher
Cork Constraint Computation Center
PhD Student
Cork Constraint Computation Center
University College Cork, Ireland
Ph.D (Cork)
M.Eng (Bologna)
B.Eng (Bologna)
Introduction
Research overview
Conclusions
Background information
Areas of expertise
SC/OM
P oduct low
In orma ion low
Re ail demand
Prod cer
Transport
DC
Consumer demand
Transport
Reta ou let
Transport
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+
Consumer
AI
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+
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+
Producer
DC
Re ail s ore
+
Demand centro d
Operations Research
Introduction
Research overview
Conclusions
Background information
Areas of expertise
SC/OM
P oduct low
In orma ion low
Re ail demand
Prod cer
Transport
DC
Consumer demand
Transport
Reta ou let
Transport
AI
Consumer
+
+
+
Cross-fertilization
of ideas
+
+
+
+
Producer
DC
Re ail s ore
+
Demand centro d
Operations Research
Introduction
Research overview
Conclusions
Background information
R Rossi, S A Tarim, B Hnich and S Prestwich, "Constraint Programming for
Stochastic Inventory Systems under Shortage Cost", submitted to
Annals of Operations Reseach
io
n
...
S A Tarim, B Hnich, R Rossi and S Prestwich,
"Cost-based Filtering Techniques for Stochastic Inventory
Control under Service Level Constraints", Constraints,
Springer Verlag, Vol 14(2):137 176, 2009
tio
R Rossi, S A Tarim, R Bollapragada,
"Constraint-based Local Search for Computing
Non-Stationary Replenishment Cycle Policy
under Stochastic Lead-times", IJOC, forthcoming
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Research Topics & Recent Publications (2009/10)
R Rossi, S A Tarim, B Hnich, S Prestwich and Cahit Guren,
"A Note on Liu-Iwamura's Dependent-Chance Programming"
European Journal of Operations Reseach,Vol 198(3):983 986, 2009
Introduction
Research overview
Conclusions
Background information
Research Topics & Recent Publications (2009/10)
R Rossi, S A Tarim, B Hnich and S Prestwich,
"Cost based Domain Filtering for Stochastic Constraint Programming",
In proceedings of The 14th International Conference on Principle and
Practice of Constraint Programming (CP 2008), Sep 14 18, 2008,
Sydney, Australia, Lecture Notes in Computer Science, Springer Verlag,
LNCS 5202, pp 235 250, 2008
SCM and OM
R Rossi, S A Tarim, B Hnich and S Prestwich,
"Computing Replenishment Cycle Policy under
Non stationary Stochastic Lead Time", International
Journal of Production Economics, Elsevier,
Vol 127(1) 180 189, 2010
R Rossi, S A Tarim, B Hnich and S Prestwich,
"Dynamic Programming for computing (Rn,Sn) policy
parameters", International Journal of
Production Economics, Elsevier, forthcoming
R Rossi, S A Tarim, B Hnich, S Prestwich and
S Karacaer, "Scheduling Internal Audit Activities:
A Stochastic Combinatorial Optimization
Problem", Journal of Combinatorial Optimization,
Vol 19(3) 325 346, 2010
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..
Approaches
.
S A Tarim, B Hnich, S Prestwich and R Rossi,
"Finding Reliable Solutions Event Driven Probabilistic
Constraint Programming", Annals of Operations Research,
Springer Verlag, Vol 171(1) 77 99, 2009
S A Tarim, U Ozen, M K Dogru, R Rossi,
"An Efficient Hybrid Approach for Computing
(Rn,Sn) Policy Parameters", submitted to the
European Journal of Operational Research
Introduction
Research overview
Background information
Research Statement
My research is focused on
automated reasoning.
I develop systems that aim to be
robust and scalable in such a way as
to enable computers to act
intelligently in increasingly complex
real world settings and in uncertain
environments.
Conclusions
Introduction
Research overview
Conclusions
Background information
Research Statement
Chacko (1991) defines
decision-making as
“the commitment of resources today
for results tomorrow”
according to Oreskes (Stanford Univ.)
“because decisions involve
expectations about the future, they
always involve uncertainty”
G. Chacko,
Decision-making under
uncertainty: An Applied
Statistics Approach, New
York, 1991, quote on p. 5
Introduction
Research overview
Constraint Programming
Constraint Programming
Sample CSP
V = {x, y, z}
D(x) = {2, 3} D(y) = {1, 2, 3, 4} D(z) = {1, 2}
C = {c1 : x + y ≤ 4, c2 : alldifferent(x,y,z)}
Conclusions
Introduction
Research overview
Conclusions
Constraint Programming
Constraint Programming
Sample CSP
V = {x, y, z}
D(x) = {2, 3} D(y) = {1, 2, 3, 4} D(z) = {1, 2}
C = {c1 : x + y ≤ 4, c2 : alldifferent(x,y,z)}
We apply constraint propagation until no new deduction can be
made...
Introduction
Research overview
Conclusions
Constraint Programming
Constraint Programming
Sample CSP
V = {x, y, z}
D(x) = {2, 3} D(y) = {1, 2, 3, 4} D(z) = {1, 2}
C = {c1 : x + y ≤ 4, c2 : alldifferent(x,y,z)}
We apply constraint propagation until no new deduction can be
made...
Sample CSP
x ∈ {2, 3}
y ∈ {1, 2, 3, 4}
z ∈ {1, 2}
Introduction
Research overview
Conclusions
Constraint Programming
Constraint Programming
Sample CSP
V = {x, y, z}
D(x) = {2, 3} D(y) = {1, 2, 3, 4} D(z) = {1, 2}
C = {c1 : x + y ≤ 4, c2 : alldifferent(x,y,z)}
We apply constraint propagation until no new deduction can be
made...
Sample CSP
x ∈ {2, 3}
y ∈ {1, 2, 3, 4}
z ∈ {1, 2}
(c1 )
−→
x ∈ {2, 3}
y ∈ {1, 2}
z ∈ {1, 2}
Introduction
Research overview
Conclusions
Constraint Programming
Constraint Programming
Sample CSP
V = {x, y, z}
D(x) = {2, 3} D(y) = {1, 2, 3, 4} D(z) = {1, 2}
C = {c1 : x + y ≤ 4, c2 : alldifferent(x,y,z)}
We apply constraint propagation until no new deduction can be
made...
Sample CSP
x ∈ {2, 3}
y ∈ {1, 2, 3, 4}
z ∈ {1, 2}
(c1 )
−→
x ∈ {2, 3}
y ∈ {1, 2}
z ∈ {1, 2}
(c2 )
−→
x ∈ {3}
y ∈ {1, 2}
z ∈ {1, 2}
Introduction
Research overview
Conclusions
Constraint Programming
Constraint Programming
Sample CSP
V = {x, y, z}
D(x) = {2, 3} D(y) = {1, 2, 3, 4} D(z) = {1, 2}
C = {c1 : x + y ≤ 4, c2 : alldifferent(x,y,z)}
We apply constraint propagation until no new deduction can be
made...
Sample CSP
x ∈ {2, 3}
y ∈ {1, 2, 3, 4}
z ∈ {1, 2}
(c1 )
−→
x ∈ {2, 3}
y ∈ {1, 2}
z ∈ {1, 2}
(c2 )
−→
x ∈ {3}
y ∈ {1, 2}
z ∈ {1, 2}
(c1 )
−→
x ∈ {3}
y ∈ {1}
z ∈ {1, 2}
Introduction
Research overview
Conclusions
Constraint Programming
Constraint Programming
Sample CSP
V = {x, y, z}
D(x) = {2, 3} D(y) = {1, 2, 3, 4} D(z) = {1, 2}
C = {c1 : x + y ≤ 4, c2 : alldifferent(x,y,z)}
We apply constraint propagation until no new deduction can be
made...
Sample CSP
x ∈ {2, 3}
y ∈ {1, 2, 3, 4}
z ∈ {1, 2}
(c1 )
−→
x ∈ {2, 3}
y ∈ {1, 2}
z ∈ {1, 2}
(c2 )
−→
x ∈ {3}
y ∈ {1, 2}
z ∈ {1, 2}
(c1 )
−→
x ∈ {3}
y ∈ {1}
z ∈ {1, 2}
(c2 )
−→
x ∈ {3}
y ∈ {1}
z ∈ {2}
Introduction
Research overview
Stochastic Constraint Programming
Stochastic Constraint Programming (Walsh, 2002)
Sample SCSP
V1 = {x1 } V2 = {x2 }
D(x1 ) = {1, . . . , 4} D(x2 ) = {3, . . . , 6}
S1 = {s1 } S2 = {s2 }
pmf(s1 ) = {(0.5)5, (0.5)4} pmf(s2 ) = {(0.5)3, (0.5)4}
c1 : Pr{s1 x1 + s2 x2 ≥ 30} ≥ 0.75
C=
c2 : Pr{s2 x1 = 12} ≥ 0.5;
L = [hV1 , S1 i, hV2 , S2 i]
Conclusions
Introduction
Research overview
Conclusions
Stochastic Constraint Programming
Stochastic Constraint Programming (Walsh, 2002)
V1
S1
V2
x21
x1
4
Scenario
probability
S2
s2
4
s2
3
C
0.25
c1: 5á3 + 4á4 ³ 30
c2: 4á3 12
s1
5
0.25
c1: 5á3 + 3á4 < 30
c2: 3á3 ­ 12
s1
4
0.25
c1: 4á3 + 4á6 ³ 30
c2: 4á3 12
0.25
c1: 4á3 + 3á6 ³ 30
c2: 3á3 ­ 12
3
x22
6
s2
4
s2
3
Introduction
Research overview
Stochastic Constraint Programming
Stochastic Constraint Programming (Rossi, 2008)
Sample SCSP
V = {x, y, z}
D(x) = {2, 3} D(y) = {1, 2, 3, 4} D(z) = {1, 2}
S = {r }
pmf(r ) = {(0.5)3, (0.5)2}
C = {c1 : Pr{alldifferent(x+r,y,z)} ≥ α}
L = [hV , Si]
Conclusions
Introduction
Research overview
Stochastic Constraint Programming
Stochastic Constraint Programming (Rossi, 2008)
Global Chance-Constraints
(Rossi et al., 2008)
Global Chance-Constraints performing
optimality reasoning are called
Optimization-Oriented Global
Chance-Constraints
(Rossi et al., 2008).
Conclusions
Introduction
Research overview
Stochastic Constraint Programming
Stochastic Constraint Programming (Rossi, 2011)
Constraints:
(1) cumulative(s, e, t, c, m)
Decision variables:
sk ∈ {rk , . . . , dk },
∀k ∈ 1, . . . , |K |
ek ∈ {rk , . . . , dk },
∀k ∈ 1, . . . , |K |
Figure: A CSP for the deterministic multiprocessor scheduling.
Conclusions
Introduction
Research overview
Conclusions
Stochastic Constraint Programming
Stochastic Constraint Programming (Rossi, 2011)
Constraints:
(1) Pr {cumulative(s, e, t, c, m)} ≥ θ
Decision variables:
sk ∈ {rk , . . . , dk },
∀k ∈ 1, . . . , |K |
ek ∈ {rk , . . . , dk },
∀k ∈ 1, . . . , |K |
Stochastic variables:
tk → processing time of order k ∀k ∈ 1, . . . , |K |
Stage structure:
V1 = {s1 , s2 , . . . , s|K | } S1 = {t1 , t2 . . . , t|K | }
V2 = {e1 , e2 , . . . , e|K | } S2 = {}
L = [hV1 , S1 i, hV2 , S2 i]
Figure: A SCSP for chance-constrained multiprocessor scheduling.
Introduction
Research overview
Stochastic Constraint Programming
Ongoing Research
B. Hnich, R. Rossi, S. A. Tarim and S. Prestwich,
"Synthesizing Filtering Algorithms for Global Chance-Constraints",
In Proceedings of the 15th International Conference on Principles and
Practice of Constraint Programming (CP 09), September 21 24, 2009,
Lisbon, Portugal, Lecture Notes in Computer Science, Springer Verlag,
LNCS 5732, pp.439 453, 2009
...a generic filtering
strategy for porting
any existing
global constraint into
a stochastic setting...
in submission to
Artificial Intelligence
Conclusions
Introduction
Research overview
Stochastic Constraint Programming
Ongoing Research
22nd International Joint Conference
on Artificial Intelligence (IJCAI-11)
Conclusions
Introduction
Research overview
Conclusions
Stochastic Constraint Programming
Ongoing Research
V1
S1
V2
Scenario
probability
S2
2/3
x21
x1
4
s2
4
s2
3
s1
5
0
s1
4
1/3
C
c1: 5á3 + 4á4 ³ 30
c2: 4á3 12
3
x22
6
s2
4
s2
3
0
c1: 4á3 + 4á6 ³ 30
c2: 4á3 12
Introduction
Research overview
Conclusions
Final remarks
Further Research Topics
i. Newsvendor under partial demand information (ongoing).
the decision maker knows the distribution of the demand
but not the associated parameters
a set of samples are given in place of the actual
parameters
ii. Sample Average Approximation for Quality Controlled
Logistic in Slaughterhouse Supply Planning (ongoing)
iii. Computing Replenishment Cycle Policy Parameters for
Perishable Items with Non-Stationary Stochastic Demand
Introduction
Research overview
Final remarks
In Preparation
A Springer book on
The Replenishment Cycle Policy
and its applications
A Springer book on
Stochastic Constraint Programming
in collaboration with S. A. Tarim,
B. Hnich, and S. Prestwich
Conclusions
Introduction
Final remarks
Questions
Research overview
Conclusions