Time-cost tradeoff in a three-dimensional assignment problem (Q1123126)

The paper discusses the three-dimensional assignment problem with two objective functions. The prototype problem is that there are n jobs, n machines, and n workers. The decision variable \(x_{ijk}\) has a value of 1 if the j-th job is assigned to the i-th worker to be performed on the k-th machine, otherwise the value is 0. Both cost and throughput time are to be minimized. These objectives are usually conflicting, therefore a multiobjective approach is necessary. The authors define a tradeoff ratio which helps evaluating a sequence of solutions with increasing cost and decreasing time. A pair with minimum ratio is accepted as optimal solution of the problem. Some heuristic arguments are also given.