Multi-Objective Fixed-Charge Transportation Problem with Random Rough Variables

Abstract

This paper considers a multi-objective fixed-charge transportation problem (MOFCTP) in which the parameters of the objective functions are random rough variables, while the supply and the demand parameters are rough variables. In real-life situations, the parameters of a multi-objective fixed-charge transportation problem may not be defined precisely, because of globalization of the market, uncontrollable factors, etc. As such, the multi-objective fixed-charge transportation problem is proposed under rough and random rough environments. To tackle uncertain (rough and random rough) parameters, the proposed model employs an expected value operator. Furthermore, a procedure is developed for converting the uncertain multi-objective fixed-charge transportation problem into a deterministic form and then solving the deterministic model. Three different methods, namely, the fuzzy programming, global criterion, and ϵ-constrained methods, are used to derive the optimal compromise solutions of the suggested model. To provide the preferable optimal solution of the formulated problem, a comparison is drawn among the optimal solutions that are extracted from different methods. Herein, the ϵ-constrained method derives a set of optimal solutions and generates an exact Paretofront. Finally, in order to show the applicability and feasibility of the proposed model, the paper includes a real-life example of a multi-objective fixed-charge transportation problem. The main contribution of the paper is that it deals with MOFCTP using two types of uncertainties, thus making the decision making process more flexible.

A multiobjective integrated multiproject scheduling and multiskilled workforce assignment model considering learning effect under uncertainty

“…They developed an algorithm to select the goals of objective functions by introducing a utility function. Roy et al studied a multiobjective fixed‐charge transportation problem with random rough variables. They used the constraint method to find a Pareto solution.…”

Fuzzy-rough multi-objective product blending fixed-charge transportation problem with truck load constraints through transfer station

“…At first, Hirsch and Dantzig [12] defined the concept of FCTP. Also there exist some methods [23,24,31] on FCTP which are provided in the literature review. This type of FCTPs was solved by interval programming or rough programming or other type of programming.…”

“…Roy et al [31] presented a FCTP with random rough variables. They analyzed the problem in multi-objective ground under rough programming.…”

“…-Also for transporting the items from sources to destinations, researchers (cf. [25,31,32]) did not consider a stage that separates the whole system into two different steps, which may help to obtain some facilities for TP. -For environment improvement and for customers satisfaction, minimum CO 2 emission from transportation with minimum time of transportation are required as these are essential objectives as of minimum transportation cost.…”

An optimization of solid transportation problem with stochastic demand by Lagrangian function and KKT conditions

“…It has many economic applications. The stochastic transportation problem has been discussed in many papers [21,23,25,34] in several ways and solved by different methods. Mahapatra et al [20,22] and Roy et al [31,33] presented a procedure to solve the multi-choice transportation problem where they have converted the multi-choice transportation problem into a standard mathematical programming through the selection of binary variables, bounds for binary codes, and restriction of binary codes using auxiliary constraints.…”