Pade approximants for the transient optimization of hedging control policies in manufacturing

A renewal equation is developed for the cost functional over finite horizon in manufacturing systems under an arbitrary time-invariant hedging control policy. The kernel of that renewal equation is a first return time probability density function. An auxiliary system of partial differential equations is subsequently used to recursively generate (stable) Pade approximants for that return density function, and hence for the finite horizon cost functional. The Pade approximants are expressed as functions of the arbitrary constant critical levels of the hedging policy. At that stage, (hedging) parameter optimization can be carried out to yield horizon dependent best invariant hedging production policies.