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Sensitivity analysis plays a crucial role in multiobjective linear programming (MOLP), where understanding the impact of parameter changes on efficient solutions is essential. This work builds upon and extends previous investigations. In this paper, we introduce a novel approach to sensitivity analysis in MOLP, designed to be computationally feasible for decision-makers studying the behavior of efficient solutions under perturbations of objective function coefficients in a two-dimensional variable space. This approach classifies all MOLP problems in $S \subset \mathbb{R}^{2}$ by defining an equivalence relation that partitions the space of linear maps$-$comprising all sequences of linear forms on $\mathbb{R}^2$ of length $K \geq 2-$into a finite number of equivalence classes. Each equivalence class is associated with a unique subset of the boundary of $S$. For any MOLP with $K$ objective functions belonging to the same equivalence class, its set of efficient solutions corresponds to the associated subset of the boundary of $S$. This approach is detailed and illustrated with a numerical example.

In this paper, we introduce an algorithm designed to solve a Multilevel MOnoObjective Linear Programming Problem (ML(MO)OLPP). Our approach is a refined adaptation of Sinha and Sinha's linear programming method, incorporating the development of an "interval reduction map" that precisely refines decision variable intervals based on the influence of the preceding level's decision maker. Each construction stage is meticulously examined. The effectiveness of the algorithm is validated through a detailed numerical example, illustrating its practical applicability in resource management challenges. With a specific focus on vaccination planning within long-term care facilities and its relevance to the COVID-19 pandemic, our study addresses the optimization of resource allocation, placing a strong emphasis on the equitable distribution of COVID-19 vaccines.

In this paper, we present a new geometric approach for sensitivity analysis in linear programming that is computationally practical for a decision-maker to study the behavior of the optimal solution of the linear programming problem under changes in program data. First, we fix the feasible domain (fix the linear constraints). Then, we geometrically formulate a linear programming problem. Next, we give a new equivalent geometric formulation of the sensitivity analysis problem using notions of affine geometry. We write the coefficient vector of the objective function in polar coordinates and we determine all the angles for which the solution remains unchanged. Finally, the approach is presented in detail and illustrated with a numerical example.

This paper is a follow-up to a previous work where we defined and generated the set of all possible compromises of multilevel multiobjective linear programming problems (ML-MOLPP). In this paper, we introduce a new algorithm to solve ML-MOLPP in which the adaptive method of linear programming is nested. First, we start by generating the set of all possible compromises (set of all non-dominated solutions). After that, an algorithm based on the adaptive method of linear programming is developed to select the best compromise among all the possible compromises achieved. This method will allow us to transform the initial multilevel problem into an ML-MOLPP with bounded variables. Then, apply the adaptive method which is the most efficient to solve all the multiobjective linear programming problems involved in the resolution process instead of the simplex method (It should be noted that the adaptive method is more efficient than the simplex method). Finally, all the construction stages are carefully checked and illustrated with a numerical example.

In this paper, an algorithm is developed to solve a multilevel mono-objective linear programming problem (ML(MO)LPP), where the constructive adaptive method of linear programming is nested. This procedure is the modified version of the SB. Sinha and S. Sinha's linear programming approach. First, we build a map that reduces the ranges of decision variables that are over control of the previous level's decision maker, depending on the chosen approach, called the range reduction map. Then, we use it to define a new sub-optimality estimate of the adaptive method for the problem under consideration. All the construction stages are carefully checked and illustrated with a numerical example.

In this paper, we present a novel method for solving multiobjective linear programming problems (MOLPP) that overcomes the need to calculate the optimal value of each objective function. This method is a follow-up to our previous work on sensitivity analysis, where we developed a new geometric approach. The first step of our approach is to divide the space of linear forms into a finite number of sets based on a fixed convex polygonal subset of $\mathbb{R}^{2}$. This is done using an equivalence relationship, which ensures that all the elements from a given equivalence class have the same optimal solution. We then characterize the equivalence classes of the quotient set using a geometric approach to sensitivity analysis. This step is crucial in identifying the ideal solution to the MOLPP. By using this approach, we can determine whether a given MOLPP has an ideal solution without the need to calculate the optimal value of each objective function. This is a significant improvement over existing methods, as it significantly reduces the computational complexity and time required to solve MOLPP. To illustrate our method, we provide a numerical example that demonstrates its effectiveness. Our method is simple, yet powerful, and can be easily applied to a wide range of MOLPP. This paper contributes to the field of optimization by presenting a new approach to solving MOLPP that is efficient, effective, and easy to implement.