| A note on due-date assignment and single machine scheduling with a learning/aging effect (2009) | |||||||||||||
Abstract | |||||||||||||
| This paper considers the learning/aging effect in an n job single machine scheduling problem with common due date. The objective is to determine the optimal common due date and the optimal sequence of jobs that minimizes a cost function in the presence of learning/aging effect. The cost function depends on the individual job earliness and tardiness values: i.e., Sigma(n)(j=1) {E-[j] + T-[j]}. This is a well-known problem when the learning/aging effect is not considered and it is shown in earlier studies that there are more than one optimal sequence and optimal common due dates. It is shown in earlier studies that there are 2(r-1) optimal sequences to this problem if n is odd, and 2(r) optimal sequences if n is even. The value of r is (n + 1)/2 if n is odd, and the value of r is n/2 if n is even. In this paper, we derive two bounds B-alpha and B-alpha* for the learning index alpha. We show that when B-alpha < alpha < 0, then the optimal sequence is unique and provide an O(n log n) algorithm to obtain this unique optimal sequence and the optimal common due date. We also show that when alpha | |||||||||||||
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