Improved two-phase solution strategy for multiobjective fuzzy stochastic linear programming problems with uncertain probability distribution

Abstract

Multiobjective Fuzzy Stochastic Linear Programming (MFSLP) problem where the linear inequalities on the probability are fuzzy is called a Multiobjective Fuzzy Stochastic Linear Programming problem with Fuzzy Linear Partial Information on Probability Distribution (MFSLPPFI). The uncertainty presents unique difficulties in constrained optimization problems owing to the presence of conflicting goals and randomness surrounding the data. Most existing solution techniques for MFSLPPFI problems rely heavily on the expectation optimization model, the variance minimization model, the probability maximization model, pessimistic/optimistic values and compromise solution under partial uncertainty of random parameters. Although these approaches recognize the fact that the interval values for probability distribution have important significance, nevertheless they are restricted by the upper and lower limitations of probability distribution and neglected the interior values. This limitation motivated us to search for more efficient strategies for MFSLPPFI which address both the fuzziness of the probability distributions, and the fuzziness and randomness of the parameters. The proposed strategy consists two phases: fuzzy transformation and stochastic transformation. First, ranking function is used to transform the MFSLPPFI to Multiobjective Stochastic Linear Programming Problem with Fuzzy Linear Partial Information on Probability Distribution (MSLPPFI). The problem is then transformed to its corresponding Multiobjective Linear Programming (MLP) problem by using a-cut technique of uncertain probability distribution and linguistic hedges. In addition, Chance Constraint Programming (CCP), and expectation of random coefficients are applied to the constraints and the objectives respectively. Finally, the MLP problem is converted to a single-objective Linear Programming (LP) problem via an Adaptive Arithmetic Average Method (AAAM), and then solved by using simplex method. The algorithm used to obtain the solution requires fewer iterations and faster generation of results compared to existing solutions. Three realistic examples are tested which show that the approach used in this study is efficient in solving the MFSLPPFI.