# Singapore University of Social Sciences

## Network Optimisation and Modelling (MTH367)

### Synopsis

MTH367 Network Optimisation and Modelling will complement MTH355 Basic Mathematical Optimisation by studying optimisation problems which can be formulated using graphs and networks. These optimisation problems may be solved using linear or integer programming techniques but due to its graphical structure, it is easier to use network algorithmic approaches. Additionally, the course will teach students how such algorithms are implemented using the software Gurobi.

Level: 3
Credit Units: 5
Presentation Pattern: Every July

### Topics

• The Transportation Problem
• The Assignment Problem
• Terminology of Networks
• The Shortest-Path Problem
• The Minimum Spanning Tree Problem
• The Maximum Flow Problem
• The Minimum Cost Flow Problem
• The Network Simplex Method
• Network Models
• Characteristics of Dynamic Programming Problems
• Deterministic Dynamic Programming
• Probabilistic Dynamic Programming

### Learning Outcome

• Formulate a given word problem mathematically as a network optimisation problem.
• Apply the optimality test to justify a solution is optimal.
• Draw the network representation of a given network optimisation word problem.
• Employ the shortest-path algorithm, minimum spanning tree algorithm or maximum flow algorithm to network optimisation problems.
• Use dynamic programming to find the optimal solution(s) of a given optimisation problem.
• Solve network optimisation problems by the network simplex method.