On Solving Bi-objective Interval Valued Neutrosophic Assignment Problem

Abstract

The assignment problem (AP) is a well-researched combinatorial optimization problem in which the overall assignment cost or time is minimized by assigning multiple items (tasks) to several entities (workers). Today's optimization challenges cannot be adequately addressed by a single-objective AP, hence the bi-objective AP (BOAP) is taken into consideration. This problem frequently occurs in practical applications with ambiguous parameters in real life. Henceforth, in this article the uncertain parameters are presented as interval valued neutrosophic numbers. In the present study, we formulate bi-objectives assignment problem (BOAP) having cost and time parameters as an interval valued neutrosophic numbers. We proposed interactive left-width method to solve the interval valued neutrosophic BOAP (IVNBOAP). In this method interval valued neutrosophic numbers is reduced to interval numbers using score function. Then, the bi-objective interval assignment problem (BOIAP) is reduced to a deterministic BOAP using the left-width attributes on each objective function. The reduced deterministic objective function is separated and constructed as a multi-objective AP. In the solution procedure, the global weighted sum method is adopted to convert the multi-objective AP into a single objective problem (SOP) and solved using Lingo 18.0 software. Finally, numerical examples are illustrated to clarify the steps involved in the proposed method and results are compared with the other existing methods.

Keywords

• interval assignment problem
• interval-valued neutrosophic numbers
• interactive left-width method
• optimal compromise solution
• global weighted sum method