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.