Fixed-point solution of plant input/location problems

Abstract

This paper cons ide rs the following generalization of the We be r plant location probl em: the plant 's output leve l is fix ed , and its levels of input from it s supply point s, as we ll as its location , are among th e decis io n variabl es_ Hurter and W ende ll (J. Reg. Sci. , 1972) s ho wed th at thi s problem ad mits a kind of separabilit y when the plant' s production fun ction li es in a ce rta in class in c luding th e CobbDouglas forms. The prese nt paper (a) de te rmines the exte nt of that fun c tion-class, (b) carri es out the exp li cit se paration for the CES generaliza ti on of the Cobb-Douglas fun c ti ons, and (c) di scusses s imple fix ed-point -type ite rative so lution algo rithm s, simila r to th at we ll -kno wn for the o rdinar y We be r proble m, for severa l produ c tion fun ctions (Cobb-Doug las. CES , a nd variou s two-stage techn ologies). Loca l conve rgence of these a lgo rithms is establi shed ; comput a tio na l expe ri e nce will be report ed in a separa te Part II.