Abstract
In this paper, we consider the problem of scheduling N jobs on a single machine to minimise total tardiness. Both the modified due date (MDD) rule and the heuristic of Wilkerson and Irwin (W-I) are very effective in reducing total tardiness. We show that in fact the MDD rule and the W-I heuristic are strongly related in the sense that both are based on the same local optimality condition for a pair of adjacent jobs, so that a sequence generated by these methods cannot be improved by any further adjacent pair-wise interchange.
Highlights
There is a plethora of methods, both simple and complex, that have been developed to solve the total tardiness problem
We show that the modified due date (MDD) rule and the Wilkerson and Irwin (W-I) heuristic are strongly related in the sense that both are based on the same local optimality condition for a pair of adjacent jobs, so that a sequence generated by these methods cannot be improved by any further adjacent pair-wise interchange
We show that the MDD rule is strongly related to the heuristic of Wilkerson and Irwin (W-I) in that it generates a sequence that satisfies the local optimality conditions
Summary
There is a plethora of methods, both simple and complex, that have been developed to solve the total tardiness problem. We show that the MDD rule is strongly related to the heuristic of Wilkerson and Irwin (W-I) in that it generates a sequence that satisfies the local optimality conditions. This is a useful result since it demonstrates that these two “classical” techniques are much more similar than has generally been recognized. Rachamadugu (1987) has presented local pair-wise optimality conditions for the general weighted tardiness problem. He has shown that the MDD rule is a special case of the optimality conditions.
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