Minimizing total tardiness on one machine is NP-hard
Mathematics of Operations Research
Improving local search heuristics for some scheduling problems—I
Discrete Applied Mathematics - Special volume: first international colloquium on graphs and optimization (GOI), 1992
A fully polynomial approximation scheme for the total tardiness problem
Operations Research Letters
A decomposition algorithm for the single machine total tardiness problem
Operations Research Letters
On decomposition of the total tardiness problem
Operations Research Letters
Operations Research Letters
A graphical realization of the dynamic programming method for solving NP-hard combinatorial problems
Computers & Mathematics with Applications
Algorithms for some maximization scheduling problems on a single machine
Automation and Remote Control
Graphical algorithm for the knapsack problems
PaCT'11 Proceedings of the 11th international conference on Parallel computing technologies
A note on a single machine scheduling problem with generalized total tardiness objective function
Information Processing Letters
| Hi-index | 0.98 |
The scheduling problem of minimizing total tardiness on a single machine is known to be NP-hard in the ordinary sense. In this paper, we consider the special case of the problem when the processing times p"j and the due dates d"j of the jobs j,j@?N={1,2,...,n}, are oppositely ordered: p"1=p"2=...=p"n and d"1@?d"2@?...@?d"n. It is shown that already this special case is NP-hard in the ordinary sense, too. The set of jobs N is partitioned into k,1@?k@?n, subsets M"1,M"2,...,M"k, M"@n@?M"@m=0@? for @n@m,N=M"1@?M"2@?...@?M"k, such that max"i","j"@?"M"""@n|d"i-d"j|@?min"j"@?"M"""@np"j for each @n=1,2,...,k. We propose algorithms which solve the problem: in O(kn@?p"j) time if 1@?k=p"2=...=p"n mentioned above nor integer processing times to construct an optimal schedule. Finally, we apply the idea of the presented algorithm for the case k=1 to the even-odd partition problem.