Study of Theoretical Properties of PSC-Algorithm for the Total Weighted Tardiness Minimization for Planning Processes Automation

Abstract

We investigate and justify the efficiency of PSC-algorithm for solving the NP-hard in the strong sense scheduling problem of the total weighted tardiness of jobs minimization on one machine. The problem is used widely in the automation of planning processes in objects of different nature. As a result of the research, we identify and justify regions of the problem parameter values at which it is solved quickly and at which it requires a large computational effort. For each individual instance, a polynomial subalgorithm of O(n2) complexity constructs a sequence on which we determine the instance’s structure and its characteristics designating the instance’s complexity. We analyze the polynomial component of the PSC-algorithm which checks sufficient signs of optimality at all stages of the problem solving, in contrast to the existing methods. The optimal solution was achieved with the polynomial component for 27.3% of instances. We present experimental data on the solving time for problems with dimensions up to 300 jobs. We show that up to 68% of the generated benchmark instances are solved relatively quickly for any dimension. The PSC-algorithm is competitive by the computation time with the known method of Tanaka et al. and significantly exceeds it on instances from the determined regions of quick solving.