On the Multi-item Full-information Secretary Problem
by Professor Israel David
Abstract: n identical units have to be sold, one at a time, to coming bidders, until a certain deadline T. The bids arrive as a Poisson process and they are i.i.d. It is sought to maximize the expected total revenue from the n units. We characterize the optimal policy. Then, concentrating on the case where each coming bid may take on a finite number /C/ of values, we show how to solve for the pertinent critical-times and for the value-functions recursively, via first-order linear differentiable equations that one can intergrate.
Presently, MATLAB solves the problem symbolically when nx/C/<12. For the other cases we implement an approximate numerical solution in polynominal time (O(nx/C/xT)).
For More Information: Dr. Mark Fackrell M.Fackrell@ms.unimelb.edu.au