Robust fuzzy programming
Robust fuzzy programming (ROFP)
Robust fuzzy programming (ROFP) is a powerful mathematical programming approach to deal with optimization problems under uncertainty. This approach is firstly introduced by Pishvaee, Razmi & Torabi (2012) in the Journal of Fuzzy Sets and Systems. ROFP enables the decision makers to be benefited from the capabilities of both fuzzy mathematical programming and robust optimization approaches. At 2016 Pishvaee and Fazli put a significant step forward by extending the ROFP approach to handle flexibility of constraints and goals. ROFP is able to achieve a robust solution for an optimization problem under uncertainty.
Robust solution
Robust solution is defined by Pishvaee and Fazli (2016) as a solution which has "both feasibility robustness and optimality robustness; Feasibility robustness means that the solution should remain feasible for (almost) all possible values of uncertain parameters and flexibility degrees of constraints and optimality robustness means that the value of objective function for the solution should remain close to optimal value or have minimum (undesirable) deviation from the optimal value for (almost) all possible values of uncertain parameters and flexibility degrees on target value of goals".
Classification of ROFP methods
As fuzzy mathematical programming is categorized into (1) Possibilistic programming and (2) Flexible programming, ROFP also can be classified into (1) Robust possibilistic programming (RPP), (2) Robust flexible programming (RFP) and (3) Mixed possibilistic-flexible robust programming (MPFRP) (see Pishvaee and Fazli, 2016). The first category is used to deal with imprecise input parameters in optimization problems while the second one is employed to cope with flexible constraints and goals. Also, the last category is capable to handle both uncertain parameters and flexibility in goals and constraints.
From another point of view, it can be said that different ROFP models developed in the literature can be classified in three categories according to degree of conservatism against uncertainty. These categories include (1) hard worst case ROFP, (2) soft worst case ROFP and (3) realistic ROFP. Hard worst case ROFP has the most conservative nature among ROFP methods since it provides maximum safety or immunity against uncertainty. Ignoring the chance of infeasibility, this method immunizes the solution for being infeasible for all possible values of uncertain parameters. Regarding the optimality robustness, this method minimizes the worst possible value of objective function (min-max logic). On the other hand Soft worst case ROFP method behaves similar to hard worst case method regarding optimality robustness, however does not satisfy the constraints in their extreme worst case. Lastly, realistic method establishes a reasonable trade-off between the robustness, the cost of robustness and other objectives such as improving the average system performance (cost-benefit logic).
Applications
ROFP is successfully implemented in different practical application areas such supply chain management, healthcare management, energy planning to handle epistemic uncertainty of input parameters and flexibility of goals and constraints.
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