International Journal of Industrial Mathematics
Volume:15 Issue: 2, Spring 2023

This study proposes a method for solving mixed integer multi-objective fractional signomial geometric programming (MIMOFSGP) problems. A few methods have been applied in the recent past to convert a fractional signomial objective function into a non-fractional signomial objective function to find the optimal solution by use of some common mathematical programming techniques. In this paper, at first a multi-objective fractional signomial programming is converted into a non-fractional multi-objective signomial programming problem by a new convenient reformulation strategy. A convex relaxation is used to reach global solution and then fuzzy programming technique is applied to find the optimal compromise solution. A mixed integer compromise optimal solution of the convex programming problem can finally be found by use of nonlinear branch and bound algorithm. Then 0n using the Spacial branch and bound algorithm, we find a solution that has the shortest distance from the solution of original problem. Finally two illustrative examples are included to demonstrate the correctness and efficiency of the proposed strategy and compare the results with the other solutions obtained by the other methods.

In this research, two-stage networks are considered in which there are common resources between both stages. Also, there are links between the first and second stages that are undesirable for the first stage. Two models are rendered, the first is a model for calculating the efficiency of the mentioned two-stage processes under the non-convex technology and the second model is an inverse model for calculating output values through input changes. The changes are such that efficiency values remain constant. Actually, at first, a non-radial network free disposal hull (FDH) model is planned to evaluate the entire and stage efficiencies of two-stage processes with shared resources. The introduced framework is a mixed integer nonlinear programming plan and is computed using a heuristic approach. Then, an inverse two-stage FDH approach is presented to determine outputs related to two stages for perturbing inputs of each stage while the efficiency values remain unchanged. To clarify the proposed models, an application from the literature is used.

Border points of the production possibility set (PPS) have particular importance in data envelopment analysis (DEA). The present study aims to provide a method to find weak defining hyperplanes of DEA models by the anchor points. Anchor points are an important subset of the set of extreme efficient points of the PPS in DEA. They are directly related to weak defining hyperplanes in the production possibility set. Therefore, we used this feature and offered a practical algorithm to find weak defining hyperplanes of PPS. Eventually, we illustrate our algorithm using two numerical examples.