Sumários
Scheduling & Blending
24 janeiro 2022, 11:00 • Pedro Castro
Classification of scheduling problems. Alternative concepts of time representation. State- and Resource-Task Network process representations.
Implementation in Excel of a single unit scheduling problem with multiple orders (using either the general precedence or time slots concept).
Blending in petroleum refineries. Alternative formulations of the pooling problem. Reformulation Linearization Technique for the relaxation of quadratically constrained problems.
Guidelines for solving the final project.
Mixed-Integer Linear Programming (MILP)
20 janeiro 2022, 11:00 • Pedro Castro
Most common restrictions in MILP problems.
Generalized Disjunctive Programming (GDP) for the formulation of problems with continuous and binary variables.
Systematic reformulations of a GDP: big-M and convex-hull.
Linearization of a bilinear term involving a continuous and a binary variable.
Exercises 6 and 7 (pen and paper).
Integer Programming (IP)
18 janeiro 2022, 08:30 • Pedro Castro
Linear relaxation and branch-and-bound. Derivation of constraints with binary variables from logic propositions. Exact linearisation of bilinear terms involving the product of two binary variables. Derivation of an integer cut.
A Non-convex Nonlinear Formulation
17 janeiro 2022, 11:00 • Pedro Castro
Formulation and implementation of a nonlinear programming problem (NLP) in Excel. The problem consists of packing 8 circles in a rectangle with a fixed dimension so as to minimize the other dimension. This is a non convex problem where the initialisation plays an important role in solution quality.
Analysis of KKT conditions
13 janeiro 2022, 11:00 • Pedro Castro
The role of Lagrangean multipliers. The special cases of Linear and Quadratic Programming.