This paper discusses the multiple jobs scheduling problem with simultaneous
resources. The problem involves one or more jobs with each job consist of a set of operations.
Each operation is performed by more than one resource simultaneously. Number of units of each
resource used for performing an operation is one or more units. The problem deals with
determining a schedule of operations minimizing total weighted tardiness. In this paper, solution
techniques based on Lagrangian relaxation are proposed. In general, the Lagrangian relaxation
technique consists of three parts run iteratively, i.e., (1) solving individual job problems, (2)
obtaining a feasible solution, and (3) solving a Lagrangian dual problem. For solving the
individual job problems, two approaches are applied, i.e., enumeration and dynamic programming.
In this paper, the Lagrangian relaxation technique using the enumeration and dynamic
programming approaches are called RL1 and RL2, respectively. The solution techniques
proposed are examined using a set of hypothetical instances. Numerical experiments are carried
out to compare the performance of RL1, RL2, and two others solution techniques (optimal and
genetic algorithm techniques). Numerical experiments show that RL2 is more efficient than
RL1. In terms of the solution quality, it is shown that RL2 gives same results compared to the
optimal technique and genetic algorithm. However, both RL2 and genetic algorithm can handle
larger problems efficiently.