Environmentally Friendly Facility Location Based On Complementary Demand Function

For an enterprise, both in the startup phase and in the stage of development, an important issue is the facility location, since this issue concerns the long-term operation of the firm. Moreover, as the real estate market is now flourishing and the price of the house estate is still increasing, the value of house estates, the acquisition cost and so on compel the enterprise attach importance to this problem. On the other hand, along with the growing competition, most enterprises produce multiple products in order to improve their strength. Besides, the environmental consciousness of people is strengthening gradually, so, considering personal corporate image and enterprises benefits, the firm must pay attention to carbon emission reduction at the same time. In our paper, we focus on the facility location of a firm producing multiple-products in the frame of the carbon emissions trading mechanism.This paper first introduces the complementary demand function and the carbon emissions trading mechanism, which are used in our model. The complementary demand function is a function that is improved reasonably from a given demand function and the carbon emissions trading mechanism is a rule in Kyoto Protocol. Then, we construct a facility location of a firm producing two products based the above two concepts. Because the complementary demand function is defined from the complementary problem, there will be equilibrium constraints in our model. Fortunately, taking the structure of this model into account, this model can be equivalent to mixed integer quadratic0-1program without equilibrium constraints through the big M-coefficient method. This quadratic model is proven not to be convex, which has wide applications and causes much study. The non-convexity of our model is due to the bilinear function in the objective function. Based on the linearization to those bilinear functions and the idea of branch-and-bound, we give a Branch-and-Refine algorithm, not only to branch for the integer variables, but also for continuous variables so as to make the approximate problem close to the primal problem.