The purpose of this study is to achieve a novel and efficient method for treating the interval coefficient linear programming (ICLP) problems. The problem is used for modeling an uncertain environment that represents most real-life problems. Moreover, the optimal solution of the model represents a decision under uncertainty that has a risk of selecting the correct optimal solution that satisfies the optimality and the feasibility conditions. Therefore, a proposed algorithm is suggested for treating the ICLP problems depending on novel measures such as the optimality ratio, feasibility ratio, and the normalized risk factor. Depending upon these measures and the concept of possible scenarios, a novel and effective analysis of the problem is done. Unlike other algorithms, the proposed algorithm involves an important role for the decision-maker (DM) in defining a satisfied optimal solution by using a utility function and other required parameters. Numerical examples are used for comparing and illustrating the robustness of the proposed algorithm. Finally, applying the algorithm to treat a Solid Waste Management Planning is introduced.

Multi-dimensional transportation problems denoted as multi-index are considered as the extension of classical transportation problems and are appropriate practical modeling for solving real–world problems with multiple supply, multiple demand, as well as different modes of transportation demands or delivering different kinds of commodities. This paper presents a method for detecting the complete nondominated set (efficient solutions) of multi-objective four-index transportation problems. The proposed approach implements weighted sum method to convert multi-objective four-index transportation problem into a single objective four-index transportation problem, that can then be decomposed into a set of two-index transportation sub-problems. For each two-index sub-problem, parametric analysis was investigated to determine the range of the weights values that keep the efficient solution unchanged, which enable the decision maker to detect the set of all nondominated solutions for the original multi-objective multi-index transportation problem, and also to find the stability set of the first kind for each efficient solution. Finally, an illustrative example is presented to illustrate the efficiency and robustness of the proposed approach. The results demonstrate the effectiveness and robustness for the proposed approach to detect the set of all nondominated solutions.