Mathematics with altitude
A simple mathematical model could save industry billions of pounds, new research has found.
Logistics engineering research at the University of Plymouth is moving closer to producing a universal mathematical model that could keep aeroplanes and trains in service, manoeuvre armies efficiently, and even prevent space missions from being aborted.
Caroline Smith, senior lecturer in the department of mathematics and statistics, has been developing a logistics model for the airline industry.
She says that costly but often simple problems, such as having a plane grounded because a new bolt has to be flown from the other side of the world, could be almost eradicated with proper logistics technology modelling, education and management. And the same formula could be applied to almost any other industry.
"In a lot of cases problems are solved in a certain way because that's the way it has always been done," said Dr Smith, who has just won this year's Young Logistician's Award from the International Society of Logistics.
"In many cases managers simply don't have a clue. But if they could just stop and think, they wouldn't have to throw as much money at problems."
The mathematical models integrate all the factors crucial to cost-effective operations, such as reliability, maintainability, materials flow and quality assurance. Predictions are made, "what-if" scenarios are identified and their probabilities are quantified.
A typical area where logistical modelling could have an instant impact is in aircraft repairs.
Dr Smith explained: "When an aeroplane needs to be repaired, it will often have to go in a jig, a sort of dry dock for planes. The current mentality seems to be that if a jig costs Pounds 10 million a company will buy as few jigs as possible. This may mean having a queue of grounded planes waiting for their repairs. The millions of pounds saved are usually lost in dribs and drabs, because there are too many grounded planes."
A mathematical model could weigh up the probabilities of different scenarios, and help inform a company about whether the cost of the grounded planes would be less than the cost of buying more jigs.
This could be extended to all aspects of the operation, including the deployment of spare parts and trained staff. Dr Smith said: "You wouldn't want a plane grounded somewhere where you have no staff, but you wouldn't want to train and pay staff all over the world if they have nothing to do."
Logic is often overlooked, such as designing seats that fit all types of plane so only one type of spare is needed. More complicated factors can also go into the formula, such as looking at the life span of nuts and bolts, and working out where and when replacements are most likely to be needed.
All these elements, from common sense to risk management, could be brought into the model.
"We could soon be in a position to tell an airline, if you have two jigs, six spare parts, five staff and two screwdrivers, then the probability of you being grounded at any one point is 0.775," Dr Smith said.
The basic principles of the logistic models can be applied to other industries. Dr Smith is already looking into the applications of the model for disaster relief, where quick response with all the right resources is crucial. They could also be applied to space missions, where the required self-sufficiency dictates that everything needed on the mission for a range of different scenarios is to hand.
Dr Smith said: "We do not have one great big model that solves everybody's problems. But the principles are applicable very widely. In a fixed model, you can just start putting different numbers in the gaps and things will change."