MULTIPERIOD ALLOCATION OF SUBSTITUTABLE RESOURCES

We consider multiperiod resource allocation problems, where excess res ources in one period can be used in subsequent periods and certain sub stitutions among the resources are feasible. The major issues addresse d here are: (i) determine whether there are sufficient resources to su stain specified levels for the various activities, and if so, (ii) fin d a feasible allocation scheme. We address these issues by finding a m aximal flow in a related network. Assuming that the substitutional rel ations are transitive, the related network is relatively small; each r esource is represented by a single node and only part of the possible substitutions are represented by arcs. Having an efficient method is i mportant as often these issues must be repeatedly addressed as part of more complex algorithms, such as those for minimax resource allocatio n problems. We also present a more general allocation problem for whic h the issues above are addressed by finding a maximal flow in a relate d multiperiod transportation problem. The resulting network is, howeve r, significantly larger than the former one. Potential applications fo r these multiperiod allocation problems are found, for example, in the manufacturing of high-tech products.