Gomory's Cuts
Page 1 of 7
Generating Gomory's Cuts for linear integer programming
problems:
the HOW and WHY
A Gomory's Cut is a linear constraint with the property that it is strictly stronger than its Parent, but it
does not exclude any feasible integer
Global Optimization of
Nonconvex MINLP Problems
by Domain and Image
Partitioning: Applications to
Heat Exchanger Networks
Dbora C. Faria and Miguel J. Bagajewicz*
University of Oklahoma
100 E. Boyd St, Room T335
Norman, OK 73019
USA
Keywords: Global Optim
GlobalOptimizationbyBound
Contraction
FunctiontoOptimize:
minimizeO=4XY
SubjectTo:
0X4
0Y8
XY4
0.64XY
UB: -11.6
The optimum can
op
ca
be visually seen
when O= -4X-Y is
graphed for varying
values of
values of O.
From the graph, the
upper bound can
pp
be fo
A GAMS TUTORIAL
A GAMS TUTORIAL WHAT IS GAMS ?
General Algebraic Modeling System Modeling linear, nonlinear and mixed integer optimization problems Useful with large, complex problems
A GAMS TUTORIAL
A GAMS Example
TRANSPORTATION EXAMPLE
A toy problem!. 2
Genetic Algorithm
Search and optimization method
that mimics the natural selection
Terms to define
Chromosome a set of numbers
representing one possible solution
Generation a single loop within GA
loop search
Loops through the reproduction,
mutation, and
ASSIGNMENT 5
CHE 5480
DUE: April 14: Send through e-mail. Include the GAMS and Excel files and a
narrative explaining what was done and how.
#Problem 1
Consider problem 8.33 in Himmelblau.
1- Reformulate as an Indefinite quadratic problem
2- Construct a l
ASSIGNMENT 4
CHE 5480
DUE: March 29: Send through e-mail. Include the GAMS and Excel files and a
narrative explaining what was done and how.
#Problem 1
Consider the following problem:
Min(x3)2+(y2.5)2
SubjectTo:
xy4
0.64Xy
0x4
0y8
1- Show the image region
ASSIGNMENT 3
CHE 5480
DUE: March 4: Send through e-mail. Include the GAMS and Excel files and a
narrative explaining what was done and how.
#Problem 1
Consider the following problem:
Max4x+y
SubjectTo:
xy4
0.64Xy
0x4
0y8
- Draw the feasible region.
- Iden
ASSIGNMENT 2
CHE 5480
DUE: February 15: Send through e-mail. Include the GAMS and Excel files and a
narrative explaining what was done and how.
#Problem 1
Problem 7.1 (Himmelblau book ; chapter 7)
- Use GAMS/CPLEX to solve the problem.
#Problem 2
Problem
ASSIGNMENT 1
CHE 5480
DUE: January 25: Send through e-mail. Include the GAMS and Excel files and a
narrative explaining what was done and how.
#Problem 1
- Solve the above problem analytically.
- Is the function convex?
- Use GAMS/CONOPT to solve the prob
This article was downloaded by:[University of Oklahoma Libraries]
On: 22 September 2007
Access Details: [subscription number 731942891]
Publisher: Taylor & Francis
Informa Ltd Registered in England and Wales Registered Number: 1072954
Registered office: M
Ind. Eng. Chem. Res. 2001, 40, 3585-3604
3585
Design of Multi-echelon Supply Chain Networks under Demand Uncertainty
P. Tsiakis, N. Shah, and C. C. Pantelides*
Centre for Process Systems Engineering, Imperial College of Science, Technology and Medicine, L
Supply Chain Design
This problem considers several production plants, warehouses and distribution centers. The location and number of Warehouses and Distribution centers is to be determined. A multiperiod model is assumed.
Ypjkt Xpijt
Zpkmt Manufacturing
Scheduling of batch plants-Deterministic Model Problem definition
The scheduling problem of a multiproduct batch plant under product demand uncertainty is solved to obtain a scheduling policy such that the expected profit is maximised. The production line
FINANCIAL RISK
CHE 5480 Miguel Bagajewicz
University of Oklahoma School of Chemical Engineering and Materials Science
1
Scope of Discussion
We will discuss the definition and management of financial risk in in any design process or decision making paradi
PLANNING UNDER UNCERTAINTY UNDER REGRET THEORY
by
Ahmed Aseeri
October 5, 2009
MINIMAX REGRET ANALYSIS
Itsafeeling
measurable.
MINIMAX REGRET ANALYSIS
( Regret ) s
Pr ofit from Pr ofit from = Best Alternative Chosen Alternative s s
Ifchosendecisionisthebe
PRO II Training
Natural Gas Basic Engineering
2
Copyright: Miguel Bagajewicz.
No reproduction allowed without consent
Natural Gas Basic Engineering
3
Copyright: Miguel Bagajewicz.
No reproduction allowed without consent
Natural Gas Basic Engineering
4
Cop
PIPELINE ENGINEERING
FLUID FLOW
Mechanical Energy Balance
V 2 gz + vdp + = Wo - 2
F
(1-1)
potential energy change
expansion work
Kinetic energy Work added/ Sum of friction change subtracted by losses compressors or pumps/expanders
Note that the balance i
PROCESS SYSTEMS ENGINEERING
Managing Financial Risk in Planning
under Uncertainty
Andres Barbaro and Miguel J. Bagajewicz
School of Chemical Engineering and Materials Science, University of Oklahoma, Norman, OK 73019
DOI 10.1002/aic.10094
Published online
CAPACITYINVESTMENT
PLANNINGMODEL
CHE5480Spring2003
UniversityofOklahoma
SchoolofChemicalEngineeringandMaterialsScience
Prof.M.Bagajewicz
1
ProcessPlanningUnderUncertainty
GIVEN:
Process Network
Process
Forecasted Data
Forecasted
DETERMINE:
Set of Processe
Use of Inventory and Option Contracts to Hedge
Financial Risk in Planning Under Uncertainty
Andres Barbaro and Miguel J. Bagajewicz
School of Chemical Engineering and Materials Science, University of Oklahoma, Norman, OK 73019
DOI 10.1002/aic.10095
Publis
Ind. Eng. Chem. Res. 2003, 42, 6125-6134
6125
Integrating Budgeting Models into Scheduling and Planning Models
for the Chemical Batch Industry
J. Romero, M. Badell, M. Bagajewicz, and L. Puigjaner*,
Chemical Engineering Department, Universidad Politecnica
CAPACITY PLANNING INVESTMENT DETERMINISTIC
MODEL
SETS
I : Processes, i = 1,., NP
J : Raw materials and Products, j = 1,., NC
T: Time periods , t = 1,., NT
L: Markets , l = 1,., NM
VARIABLES
Yit: An expansion of process I in period t takes place (Yit=1), d
ASSIGNMENT 2
CHE 5480
DUE: February 10. Send through e-mail. Include the simulation file and a narrative explaining what was done and how.
#Problem 1 (Exercise 1-14 in notes)
Consider the shown in the following figure:
Supply: 5,722,000 m3/d Km 0 638 115
ASSIGNMENT 1
CHE 5480
DUE: January 27: Send through e-mail. Include the simulation file and a narrative explaining what was done and how.
#Problem 1
-Solve the above problem analytically and verify if it really works for a stream of methane using the simu
PIPELINE ENGINEERING
ALTERNATIVE PLANNING MODELS
With the advance of mixed integer linear and non-linear programming methods, the
optimization and planning of systems became more systematic. When intensive computations
became viable, these planning models