Question

Address one of the following questions.

1. Discuss how the assumptions of certainty, non-negativity, proportionality, and divisibility are necessary to solve linear programming models?

2. What are the strengths and weaknesses of network models?

Then, please respond to a student who answered a different question than the one you addressed. Your answer should be 3-4 paragraphs (150-200 words). Responses to other students should be one paragraph (about 50-75 words). Repeating the question does not count as a paragraph.

Answer 1

The Linear Programming problems is formulated to determine the optimum solution by selecting the best alternative from the set of feasible alternatives available to decisions maker. An assumption is a simplifying conditions taken to hold true in the system being analysed in order to render the model mathematically tractable.  

The linear programming problems are based on four mathematical assumptions i.e., certainty, non - negativity, proportionality, and divisibility.  

Proportionality means that each decision variable must appear with a constant coefficient. In the objective function, it implies that marginal rate of contribution to objective is assumed to remain constant while in constraints, it implies that resources per variable is assumed constant throughout the entire operational range of problem.  Non- Negativity or Additivity means that variable are added or subtracted together, never multiplied or divisible by each other. In objective function , it implies that contribution of variable to objective is assumed to be sum of their individual weighted contributions while in constraints it implies that total resources usage is likewise sum of individual resource usage per variable. Divisibility means that variable can take on fractional values. If production is conceived of as a continuous process, divisibility is usually not an obstacle. Fractional values can be taken often as work in progress to finished on next production period.  Certainity means a problem is asaumed to have no probabilistic elements whatsoever. This is technically never true in real world, some degree of uncertainty is always is always present. Longer term problems have aspects involving pronounced uncertainty.  

It can be concluded from the above that to solve the linear programming problems , the assumptions of certainty, non-negativity, proportionality and divisibility. If proportionality and additivity cannot be assumed to hold, the problem would call for non-linear programming solutions problem.