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In the classic newsvendor problem, a newsvendor must make decide how many newspapers to stock with the aim of maximising profit in the face of uncertain demand. He faces a trade-off between stocking too few papers resulting in missing potential sales and stocking too many papers resulting in an excess of unsold papers at the end of the day. There are many variants of the classic newsvendor problem including multi-product and multi-location models. We consider a multi-location variant in which the newsvendor wishes to maximise the probability of achieving some target profit. We assume the total demand for the product is known but not the distribution of the demand and that the newsvendor has a fixed number of newspapers which he must distribute about the various locations. In the case of one location the solution is trivial; in the case of several locations the solution depends on the distribution of the demand. We discuss the solution to the problem for various demand distributions and then turn to the case of unknown demand. We model the latter case as a zero-sum game against Nature, where the newsvendor wishes to maximise the probability of achieving the target profit and Nature wishes to minimise it. We give a solution to the game in the case of two locations and a solution for some parameters in the case of three locations.

*Last updated Monday, 19 January 2015*