More on complementarity and substitutability in the transshipment problem

This paper studies complementarity in the transshipment problem. In contrast to the typical distinction between complements and substitutes in the operations literature, the distinction here involves the impact of a change in the unit shopping cost for one route on the amount of product shipped via another route. Among other results, I show that each route must have at least one and in some cases two substitutes. Furthermore, for each factory which operates at capacity and each customer who receives exactly his given demand for the product, there is at least one route which has at least one complement.