A min-max resource allocation problem with substitutions

In this paper, a model for a resource allocation problem with substitution is presented. The model extends a previous one proposed by Luss and Smith for resource allocation without substitutions. In general, two resources are substitutable if they can be used in place of one another in the allocation process. If two resources are substitutable for the same set of activities, then they can be combined into and treated as a single resource; otherwise, substitution needs to be dealt with explicitly. One application of the resource allocation problem with substitutions arises from the assembly of electronic components onto circuit boards. Typically, several components can be assembled in the same locations of a board, they then become substitutes of one another. The problem here is to determine how much to produce of the circuit boards and how to efficiently allocate the components so as to minimize the maximum weighted deviation from target demands of the boards. It is explained how the proposed model can be solved by a parametric transportation algorithm, present some computational results and discuss a nonlinear extension.