Tractable approximations of randomness
Whether it be manufacturing, economics or project management, measures of interest change in a random rather than deterministic way over time. Solution of these problems often relies on approximations, themselves routed in probabilities and statistics. Dynamic programming is an optimisation approach that breaks down complex problems into simpler, more tractable ones. The EU-funded project 'Efficient approximation for stochastic optimization' (STOCHASTICOPT) developed a general and easy-to-use methodology for deriving simplified approximation algorithms (fully polynomial time approximation schemes (FPTASs)) for complex stochastic problems. The STOCHASTICOPT technique was used to solve a basic inventory and manufacturing problem. It is currently being applied to additional issues in these fields as well as to finance. Inventory control requires complicated decision making about many products, particularly in large industrial plants. In stochastic inventory control, a complex decision on a large number of products can be broken down into smaller decisions on individual products. The FPTASs are admirably suited to solving these single-product problems. Conventional FPTASs applied to finance have focused on either minimising cost or maximising revenue. STOCHASTICOPT provided a very important new dimension with FPTASs designed to maximise profit, the difference between revenue and cost. The FPTASs were applied to several aspects of cost functions that relate the cost of making a product (the output) relative to the cost of the inputs. Finally, scientists expanded the framework to a more general (not limited) timeframe and applied it to study the time–cost trade-off as related to project scheduling. Mathematical models make predictions about the evolution of systems based on given inputs and can be invaluable decision-making tools. STOCHASTICOPT has developed models for optimisation of stochastic processes that promise to enhance the competitiveness and efficiency of EU industries from manufacturing to finance.
