Operational Research (O.R.) case studies

What’s the problem?

You are a shop manager… You are opening a new branch and need to employ staff You want to keep your labour costs as low as possible

Inexperienced staff are cheaper… …but experienced staff are more productive

How many experienced and inexperienced staff should you take on?

What do we need to know? How much do you need to pay staff? Inexperienced staff cost £5 an hour Experienced staff cost £8 an hour

How productive are inexperienced and experienced staff? Inexperienced staff are two thirds as productive as experienced staff

You need the equivalent of 20 experienced members of staff How many staff do you need?

Anything else you need to consider? Head Office states that you must employ at least one experienced member of staff for every three inexperienced members of staff

Let’s summarise the problem We want to employ the equivalent of at least 20 experienced members of staff with at least one experienced member of staff for every three inexperienced members of staff with the minimum possible labour cost

This is an example of Linear Programming

Linear Programming Problems The aim is to choose the best combination of a number of quantities to optimise the outcome, subject to certain constraints

Another example of where this is used Factories that make several products: deciding how many of each to make weighing up several factors for each product such as the profit to be made, the demand, the time needed to produce it, etc.

Over the next few lessons, we will look at ways of approaching problems of this type… What next?