Fuzzy linear fractional goal programming applied to refinery operations planning

Abstract

Chemical process plant operations planning in an oil refinery has been modelled as fuzzy linear fractional multiple goal programming problem. A variant of the fuzzy linear fractional goal programming model of Dutta et al. [Fuzzy Sets and Systems 52 (1992) 39–45] has been developed and used in the present study to solve the problem which has two fuzzy fractional goals and 22 crisp constraints. Linear membership functions have been assumed and min operator has been used as the aggregator. Linguistic variable has been taken as “ close” throughout the paper, following Dutta et al. (1992). A software has been developed in TURBO C to implement the model. The software takes the parameters defining the fuzziness and crisp data from the input field and solves the crisp equivalent to the fuzzy linear fractional goal programming problem. The parameters defining fuzziness are subjectively chosen by the user/decision maker. The software finally outputs satisfying decision variables, satisfying fuzzy fractional goal values, optimal values of the profit (numerator) and the capacities of the primary unit and cracker (denominators) which are involved in the fuzzy fractional goals. The results indicate that the present model yielded a more efficient solution compared to the crisp solution of Allen [British Chem. Eng. 16 (1971) 685–691] as far as the fractional objectives are concerned. This demonstrates the efficacy of the present model. However, a paltry decrement of 1.3% in the profit is noticed in the present study, in comparison to the crisp solution of Allen (1971).