Università Roma Tre

1. Un-constrained non linear optimization
Gradient and Hessian
Local minimum: first order and second order conditions
Local minimum: the convex case
The gradient method
line search
Rate of Convergence: sublinear, linear, superlinear
the Newton method
The conjugate gradient method
2. Constrained non linear optimization
The Jacobian matrix
The Lagrangian function
Karush-Kuhn-Tucker conditions
Penalty functions and barrier methods
3. Supply chain management
Production systems
The supply chain
Material flow and information flow
Internal and external logistics
4. Inventory control
EOQ model
dynamic lot sizing without backlogging
dynamic lot sizing with backlogging
5. Finite capacity scheduling
The job shop scheduling problem
Scheduling with blocking and no-wait
6. Distribution logistics
The Traveling Salesman Problem
the Vehicle Routing Problem
7. Crew scheduling
The set covering formulation
Column generation
the subgradient algorithm
8. Plant location
Dual ascent algorithm

Lecture notes