Integrating a Weighted Additive Multiple Objective Linear Model with Possibilistic Linear Programming for Fuzzy Aggregate Production Planning Problems

This study uses an integrated optimization method by applying a weighted additive multiple objective linear model with Possibilistic Linear Programming (PLP) to fuzzy Aggregate Production Planning (APP) problems under an uncertain environment. The uncertainty conditions include uncertainties of operating times and costs, customer demand, labor level, as well as machine capacity. The aim of this study is to minimize total costs of the plan that consist of the production cost and costs of changes in labor level. The proposed hybrid approach minimizes the most possible value of the imprecise total costs, maximizes the possibility of obtaining lower total costs, and minimizes the risk of obtaining higher total costs from PLP as multiple objectives for the fuzzy multiple objective linear model optimization. The outcome of the proposed approach shows that the solution is closer to the ideal solution obtained from Linear Programming than a typical solution obtained from PLP. There is also a higher overall satisfaction value.

Possibilistic Linear Programming Problems involving Normal Random Variables

A new solution procedure of possibilistic linear programming problem is developed involving the right hand side parameters of the constraints as normal random variables with known means and variances and the objective function coefficients are considered as triangular possibility distribution. In order to solve the proposed problem, convert the problem into a crisp equivalent deterministic multi-objective mathematical programming problem and then solved by using fuzzy programming method. A numerical example is presented to illustrate the solution procedure and developed methodology.