Abstract
We consider the problem of scheduling n jobs on a single machine. Each job i has a processing time p/sub i/, a weight w/sub i/, and a due date D/sub i/, which is a fuzzy number with a triangular membership function. The problem is to determine: (i) a job sequence, and (ii) a set of idle times each before one job, so as to minimize the total weighted earliness and tardiness cost under the fuzzy due dates. We first introduce a fuzzy distance function to measure the deviation of the completion time of a job from its fuzzy due date. We show that, given a job sequence, the problem of determining the optimal idle times is a continuous and convex optimization problem with a differentiable objective function, although the objective function after applying the fuzzy distance measure becomes nonlinear. We devise a genetic algorithm (GA) to tackle the problem, using a pigeon-hole coding scheme to represent a sequence and a nonlinear optimizer to determine the idle times. We evaluate the solutions obtained by such a GA as compared to the solutions obtained by treating the due dates as crispy numbers equal to the mean values of its fuzzy partners.
Original language | English |
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Pages | 1079-1084 |
Number of pages | 6 |
DOIs | |
Publication status | Published - 1999 |
Event | 1999 Congress on Evolutionary Computation, CEC 1999 - Washington, DC, United States Duration: 6 Jul 1999 → 9 Jul 1999 |
Conference
Conference | 1999 Congress on Evolutionary Computation, CEC 1999 |
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Country/Territory | United States |
City | Washington, DC |
Period | 6/07/99 → 9/07/99 |