Minimizing maximum lateness in a single machine scheduling problem with fuzzy processing times and fuzzy due dates

Abstract

A single machine scheduling problem with fuzzy processing times and fuzzy due dates is considered. Two approaches to this problem are investigated. In the first one it is assumed that for each job J i, i=1,…,n , there is given a real valued function f i of its fuzzy completion time and its fuzzy due date. The objective is to minimize the maximum value among f i values. It is shown that if the cost functions f i are F-monotone with respect to fuzzy completion time (the concept of F-monotonicity is defined in the paper), the generalized Lawler's algorithm can be used for solving the problem. Four problems, being special cases of the above general problem, are also considered. In the second approach, called a goal approach, each sequence of jobs is evaluated by fuzzy maximum of weighted lateness and the objective is to maximize the degree of possibility that this value is not greater than a certain fuzzy number (fuzzy goal), provided by a decision maker. The efficient solution method for this problem is proposed, in which again the Lawler's algorithm is essentially used.