A Distance Based Method for Solving Multi-objective Optimization Problems

A new model for the weighted method of goal programming is proposed based on minimizing the distances between ideal objectives to feasible objective space. It provides the best compromised solution for Multi Objective Linear Programming Problems (MOLPP). The proposed model tackles MOLPP by solving a series of single objective sub-problems, where the objectives are transformed into constraints. The compromise solution so obtained may be improved by defining priorities in terms of the weight. A criterion is also proposed for deciding the best compromise solution. Applications of the algorithm are discussed for transportation and assignment problems involving multiple and conflicting objectives. Numerical illustrations are given for the proposed model

A Model for Uncertain Multi-objective Transportation Problem with Fractional Objectives

Fractional programming problems take into account the situations where the decision maker is interested to maximize or minimize the ratios of some functions rather than a simple function. Fractional programming modeling approach has a lot of scope in dealing with the transportation planning decision problems. This paper presents a model for transportation problem with multiple fractional objectives involving uncertain parameters. In order to make the model more realistic, we have considered the case when there exists more than one fractional objective. All the parameters involved in the proposed model viz. objective function coefficients, availabilities and demands are assumed to be uncertain. Moreover, an equivalent deterministic model is also presented. Fuzzy goal programming approach is discussed as the solution approach for reaching the compromise solution. A numerical example is also given to illustrate the model more clearly

Carbon footprint based multi-objective supplier selection problem with uncertain parameters and fuzzy linguistic preferences

In this paper, we have studied supplier selection Problem (SSP) with reference to carbon footprint associated with the activities of each supplier. Carbon footprint in the proposed model is considered as one of the crucial dimension for the evaluation and selection of the suppliers.. In the problem, primary objectives are minimization of the total cost, minimization of rejection, minimization of the late deliveries along with minimization of carbon footprint. These objectives are subjected to some realistic constraints concerning customers’ demand, supplier's capacity, flexibility, allocated budget and accepted amount of carbon footprint. Some parameters in the proposed model are considered to be uncertain values. The proposed multi-objective supplier selection problem with uncertain parameter is solved using fuzzy concept based goal programming approach. The main focus of the proposed model is to deal with human subjectivity by applying the linguistic preference-based method and analyzed the operational effects of supplier selection in terms of environmental efficiency. We have adopted the Expected Constraint programming technique given by Liu (2007) to convert the uncertain parameters into a deterministic one. For the applicability and effectiveness of the model, an illustration has been given in the end