A Chance‐constrained Distribution Model—An Application to the Forest Products Industry

The ascendancy of vertical marketing structures as total systems has brought about considerable interest in designing distribution systems. Various administered and co‐operative alignments have been successful in the marketplace by enabling lower total costs through central buying practices and by producing a more predictable demand pattern. As these planned systems begin to create de facto competition among individual firms, the need for methods of discovering optimal vertical arrangements will increase. One method of finding optimal arrangements of interacting phenomena is by modelling—and linear programming techniques have been found to be particularly useful. The transportation problem or distribution model was one of the first applied special cases of linear programming. Mathematical solutions to this “special case” of linear programming began appearing in the literature during World War II. Since that time, the management science literature has been replete with significant contributions in the transportation area such as those of Hitchcock, Dantzig, Chames and Cooper, and Orden.