Bi-objective trapezoidal fuzzy mixed integer linear program-based distribution center location decision for large-scale emergencies

Abstract

This paper aims at solving three important and challenging issues: (i) How to build a 0-1 mixed integer linear program-based distribution center location model for large-scale emergencies (we call emergency distribution center (EDC) location model for short). (ii) How to develop an effective method to convert the trapezoidal fuzzy EDC location model into a crisp one. (iii) How to demonstrate the validity, flexibility and superiorities of the constructed model and developed method. Considering the acceptance degree of fuzzy constraints to be violated, this paper defines a novel flexible ranking relation for trapezoidal fuzzy numbers (TrFNs) by using the α-cut set and analyzes its desirable properties. A bi-objective trapezoidal fuzzy EDC location model (BTFELM) is built for reflecting the urgency and uncertainty of large-scale emergencies. Some essential definitions and theorems are proposed for equivalently converting the fuzzy constraints of the BTFELM into crisp ones. By employing the graded mean integration representation of TrFN, the BTFELM is ultimately transformed into a single objective crisp EDC location linear program. Wenchuan earthquake case is studied to illustrate the practicality and validity of the proposed method. Furthermore, the sensitivity and comparative analyses are provided to justify the flexibility and superiorities of the proposed method. Finally, the accuracy analyses are conducted to illustrate the reliability of the proposed method.