A TOPSIS-Based Improved Weighting Approach With Evolutionary Computation

Although optimization of weighted objectives is ubiquitous in production scheduling, the literature concerning the determination of weights used in these objectives is scarce. Authors usually suppose that weights are given in advance, and focus on the solution methods for the specific problem at hand. However, weights directly settle the class of optimal solutions, and are of utmost importance in any practical scheduling problem. In this study, we propose a new weighting approach for single machine scheduling problems. First, factor weights to be used in customer evaluation are found by solving a nonlinear optimization problem using the covariance matrix adaptation evolutionary strategy (CMAES) under fuzzy environment that takes a pairwise comparison matrix as input. Next, customers are sorted using the technique for order of preference by similarity to ideal solution (TOPSIS) by means of which job weights are obtained. Finally, taking these weights as an input, a total weighted tardiness minimization problem is solved by using mixed-integer linear programming to find the best job sequence. This combined methodology may help companies make robust schedules not based purely on subjective judgment, find the best compromise between customer satisfaction and business needs, and thereby ensure profitability in the long run.