Lecture 1 continued…
Work Scheduling Problem
1st – The decision variables relate to staff working for the week. How many people are working per day. So let x be the number of people working per day, for a week so 7 days , i.e. greater than and equal to 1 till day 7. No fractions apply so it has to be an integer.
2nd – Objective function: Reduce the amount of staff that has to work, taking into account union rules.
3rd – What restrictions are they applying? So detail the constraints.
They give you the number of people working daily, but the union says that the people cannot work straight through for 7 days, they have a 2 day break in between: so
- x1,—, —, x4, x5, x6, x7
- x1, x2,—, —, x5, x6, x7
- x1, x2, x3, —, —, x6, x7
- x1, x2, x3, x4, —, —, x7
- x1, x2, x3, x4,x5, —, —
- —,x2, x3, x4, x5, x6, —
- —,—, x3, x4, x5, x6, x7
The idea being to have 5 days that are consecutive with 2 days break in the centre. These are or can be greater than and equal to the number of people they have working per day.
Industrial Problem – similar to profit maximisation
The constraint is time. Ensure that the time units stays consistent throughout the calculation.
Advertising
Monthly to maximise total exposure for advertising.
What is known?
- Cost of the adverts per magazine
- Circulation Numbers per magazine
- Percentage principal buyers per magazine
- Budget amounts
- Restrictions per magazine
Portfolio Optimisation Problem
Increasing your return based on the
- natural return of the various portfolios
- your available funds
- any restrictions based on fund type / risk
Ok done – going to do the next two examples offline and then drink up my hot water.