Fixed-point solution of plant input/location problems

This paper con s id e rs the following gen eralization of th e We be r pla nt locatio n probl e m: th e plant 's o utput leve l is fix e d , and its levels of input from it s s upply point s, as we ll as its location , are a mong th e decis io n variabl es_ Hurt er and W e nd e ll (J.Reg.Sci. , 1972) s ho we d th at thi s problem ad mits a kind of sepa rabilit y wh en the plant's produ ction fun ction li es in a ce rta in class in c ludin g th e Cobb-Dou glas fo rm s.Th e prese nt paper (a) de te rmin es th e exte nt of that fun c ti on-class, (b) carri es o ut th e exp li cit se paration for th e CES ge neraliza ti on of th e Cobb-Do uglas fun c ti o ns, and (c) di sc usses s impl e fix ed-point -type ite rative so lution algo rithm s, simil a r to th at we ll -kn o wn for th e o rdinar y We be r prob le m, for se vera l produ c ti on fun ctions (Co bb-Doug las.CES , a nd variou s two-stage tec hn olog ies).Loca l co nve rge nce of th ese a lgo rithm s is establi sh ed ; co mput a tio na l expe ri e nce will b e repo rt e d in a se para te Part II.Ke y word s : CES; econom ics; Leonti e f; locati on th eo ry; plant loca ti on; produ cti on fun c ti o ns; tran sportatiun ; W ebe r probl e m, math e mati ca l progra mmin g.