A capacitated competitive facility location problem

We consider a mathematical model relative to competitive location problems. In such problems, there are two competing sides which subsequently open their facilities aiming to “capture” clients and maximize profit. In our model, we assume that capacitiy of facilities are bounded. The model is formulated as a bi-level integer mathematical program and we study the problem of obtaining its optimal (cooperative) solution. It is shown that the problem can be reformulated as a problem of maximization of a pseudo-Boolean function with the number of arguments equal to the number of places available for facility opening. We propose an algorithm for calculation of an upper bound for values that the function takes on subsets which are specified by partial $(0,1)$-vectors. Bibl. 15.