On number problems for the open shop problem

Abstract

In discrete optimization problems investigations of the number of feasible or optimal solutions are very difficult. Some interesting results we have found for the so-called open shop problem. By modelling this problem with latin rectangles we can describe the above problems as problems of determing the cardinality of sets of special latin rectangles. Therefore for small parameters well-known results about the number of latin rectangles are useful. Further results are obtained by generalization of investigations on the number of feasible solutions of the job shop problem.