A modied branch and bound algorithm for a vague ow-shop scheduling problem

Uncertainty plays a signicant role in modeling and optimization of real world systems. Among uncertain approaches, fuzziness describes impreciseness while for ambiguity another denition is required. Vagueness is a probabilistic model of uncertainty being helpful to include ambiguity into modeling dierent processes especially in industrial systems. In this paper, a vague set based on distance is used to model a ow-shop scheduling problem being an important problem in assembly production systems. The vagueness being used as octagon numbers are employed to represent vague processes for the manufacturing system. As a modeling eort, rst a ow-shop scheduling problem is handled with vagueness. Then, for solving and analyzing the proposed vague ow-shop scheduling model, a modied Branch and Bound algorithm is proposed. As an implementation, an example is used to explain the performance and to analyze the sensitivity of the proposed vague approach. The validity of the proposed model and modied algorithm is demonstrated through a robust ranking technique. The outputs help the decision makers to counteract the vagueness and handle operational decisions in ow-shop scheduling problems within dynamic environments.