Describe the hierarchical method for multi-objective optimization assuming up to 15% of the optimal objective function value can be sacrificed. In terms of preference: Obj1 > Obj2 > Obj 3 > Obj 4. Use the following model.

The planner wants to give the right share of the business to these suppliers. The nature of each criterion is listed below with other constraints:

Formulation:

Objective 1 (Cost ):??? 20000? + 10000? + 18000? + 35000?

Objective 2 (Local welfare):??? 12? + 9? + 5? + 4?

Objective 3 (Pollution):??? 30? + 10? + 20? + 4.5? 5

Objective 4 (Product recovery):??? 0.001? + 0.098? + 0.09? + 0.0009? S.T. ? + ? + ? + ? >= 4 ? + ? ? 2.5 ? + ? ? 5.5

Criteria (score per unit of product] Suppliers Local Welfare Pollution Product Recovery Capability (C2) (C3) (c4)