4. Solution method
For the ILND model of the supplier, it’s a mixed integer programming
(MIP) model. All most all commercial mathematical
software packages have integrated with the toolbox, which could
be used to solve this type of problems. Here, we used Yalmip toolbox
, which is integrated in the popular mathematical
software Matlab 7.0 and could solve the MIP model efficiently.
For the order quantity determination model for the retailer, the
existing literatures have proved its concavity, which guaranteed its
second derivative is larger than zero . Consequently,
if we deem E½Hðd; QÞ as the consecutive function of
Qk; 8k 2 K, the maximal points could be obtained via: