Multiperiod allocation of substitutable resources

We consider multiperiod resource allocation problems, where excess resources in one period can be used in subsequent periods and certain substitutions among the resources are feasible. The major issues addressed here are: (i) determine whether there are sufficient resources to sustain specified levels for the various activities, and if so, (ii) find a feasible allocation scheme. We address these issues by finding a maximal flow in a related network. Assuming that the substitutional relations are transitive, the related network is relatively small; each resource is represented by a single node and only part of the possible substitutions are represented by arcs. Having an efficient method is important as often these issues must be repeatedly addressed as part of more complex algorithms, such as those for minimax resource allocation problems. We also present a more general allocation problem for which the issues above are addressed by finding a maximal flow in a related multiperiod transportation problem. The resulting network is, however, significantly larger than the former one. Potential applications for these multiperiod allocation problems are found, for example, in the manufacturing of high-tech products.