On the newsvendor problem with multiple inputs under a carbon emission constraint

In this thesis, we consider two problems in the newsvendor setting with multiple inputs, under a carbon emission constraint and non-linear production functions. In the first problem, we assume a strict carbon cap and find the optimal production quantity and input allocation that will maximize the expected profit under this constraint. In the second problem, we consider an emission trading scheme where an advance purchase of carbon emission permits is made at an initial price before the random demand is realized. When the demand is realized and new carbon trade prices are revealed, it is possible to buy additional permits or to sell an excess amount. The aim is to decide on the optimal allocation of the inputs as well as the carbon trading policy so as to maximize the expected profit. In both problems, the production quantity is linked to multiple inputs via the Cobb-Douglas and Leontief production functions. Optimal policy structures are derived and numerical examples are provided.