Minimizing earliness and tardiness of job completions about a fuzzy due date

We examine the problem of scheduling n jobs on a single machine. Each job i is associated with a weight w_i and a processing time p_i, and the objective of the problem is to minimize the weighted earliness and tardiness of job completions from a common due date D, where D is a fuzzy number, governed by a triangular membership function. A fuzzy distance function is introduced first to measure the deviations of job completions from the fuzzy due date. Then, a property of an optimal schedule is obtained, and a pseudo-polynomial algorithm that can find the optimal schedule under a condition is derived. Numerical results are also reported to show the effectiveness of the algorithm in general cases where the condition is not satisfied