Goal Programming

Posted: August 27th, 2021

Discussion 2

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Discussion 2

Goal Programming

It entails an extension of linear programming whereby formulated targets are specified in a particular set of constraints. Two models in goal programming are pre-emptive (lexicographic) and the Archimedean model. In lexicographic models, goals are arranged according to their priorities, with the highest to the least priority (Mohammed & Hordofa, 2016). Additionally, under this model, goals at a particular level are considered more important than the next level. On contrarily, in the Archimedean model, weights are given to specific goals, and penalties are imposed for not achieving the set targets (Steffen & Naujokat, 2016). Furthermore, in the Archimedean model, one attempts to reduce the weighted sum of the stipulated goals to avoid underachievement. Hence, goal programming is crucial and applicable in real life, as discussed below.

            Goal programming is performed using theXPRSgoal (GOAL) command syntax, where the goals are constructed in the optimizer either from objective functions (N rows) or constraints. Similarly, when the constraints are employed to construct the goals, they are set to constraints’ violation. Thus, the set objectives areachieved when stipulated constraints are satisfied. Additionally, the primary objective of the lexicographic model is to accomplish the maximum number of goals possible. On the other hand, in the Archimedean case, the objective is to minimize the penalties’ weighted sum for failure to meet each goal. Besides, where the goals are constructed on N-rows in the lexicographic model, every N-row’s target is set on the optimal value done by the N-rows’ absolute deviation (Mohammed & Hordofa, 2016). However, the Archimedean model’s problem develops to multi–objectives linear programming where the weighted sum should be minimized (Steffen & Naujokat, 2016). Therefore, a company can achieve its objectives using pre-emptive or Archimedean models, as explained below.

            In the pre-emptive model, the objectives are arranged from the most to the least important. Likewise, the company will achieve the most important goals first with the maximum number of solutions. For instance, in the below example, the company will satisfy the goal (i) achieved by  and. However, this does not satisfy goals (ii) and (iii), and the solution for goal (ii) while trying to satisfy goal (i)is  and. We repeat the process for goal (iii) as the solution does not fulfill it.

Goals;

            Further, inArchimedean models, the objective would be to minimize the goals as shown below;

Goals;

The solution would be;

Subject to;

References

Mohammed, G. T., & Hordofa, B. G. (2016). The modified sequential linear goal programming

Method for solving multiple objectives linear programming problems. Pure and Applied    Mathematics Journal, 5, 1-8.

Steffen, B., & Naujokat, S. (2016). Archimedean points: the essence for mastering change. In Transactions on Foundations for Mastering Change I (pp. 22-46). Springer, Cham.