Complements and substitutes among locations in the two-stage transshipment problem

Abstract

This paper considers complementarity and substitutability among locations for a two-stage transshipment problem with locations being factories, warehouses, and demand centers. A direct generalization of properties known for the transportation problem would be that any two locations of different types are complements and any two locations of the same type are substitutes. Examples show that these properties need not hold for pairs of locations that include at least one warehouse. An algorithm of Nagelhout and Thompson ( European J. Operational Res. 6 (1981) 149–161) for locating warehouses is based on the incorrect supposition that any two warehouses are substitutes, and an example shows that their algorithm need not generate an optimal solution as claimed. For pairs of locations that do not include a warehouse, complementarity and substitutability properties hold just as in the transportation problem.