Lecture 2

Transportation Problem

Given information:

• Origins
• Destinations
• Costs per unit
• Limitations of supply / demand

Steps to kick-off solution…

1. Decision Variables
2. Objective Function
3. Constraints

Travelling Salesman

The salesman travels to many cities on route once, returning to the 1st city without ever having repeated a city visited on his way from his home town and returning back to his hometown.

Information given

• the distances/costs from city to city

Specialised type of problem: Value 0 or 1 – 0 1 – Zero One Programming Problems

Solution

• Decision variables; can only be x = 1 or 0, he either takes that route or does not. Integers also, as he can’t take a half route…
• Objective function; Minimise the cost of his travels, but add all his planned travels.
• Constraints;

Capital Budgeting Problem

Cash Flow changes over a timeline:

Solution:

• Decision variables:
  • cash available
  • cash invested
  • remaining funds
  • returns
• Objective Function:
  • maximise earnings, cash available…
• Constraints:
  • limitations on funds

Cargo Loading Problem

Vessel to be loaded with multi-types in order to maximise profitability…

Decision variables: types of units, number of units per type…

Objective Function: maximisation

Constraints: limitations

Catering Problem

Effective management of repeatable goods (eg. table napkins)

Decision Variables: new, cleaned, soiled, remaining…

Objective Function: Minimise costs…

Constraints: limitations

Gotta go.