Linear programming is one of the very famous techniques that helps solve the optimization problems when the objectives and constraints are expressed in a linear function. This technique was developed by George B. Denting in 1947. Though initially, its use was thought to be restricted to the activities of the Second World War but sooner, it gained prominent significance in the corporate world.
It is a quantitative technique that helps in the optimal allocation of the resources, but the fact is that it only operates under conditions of certainty (A.E. Anieting, 2013). The aim of linear programming is to optimize the variables for output by manipulating the variables for decision while considering the constraints. This means that in order to apply Linear Programming in a corporate situation, the manager must be fully aware of all the possible constraints and be sure of the exact relationship between all the variables of output and decision (Lawrence & Klimberg, 2010). So, in the situation where the production manager of Cincinnati is not certain about the constraints as well as the variables of decision making as well as the output, he is right about saying that Linear Programming is not applicable in his situation. The manufacturing firm is subject to highly uncertain conditions due to various reasons, whether it will be a global competitive pressure or the fluctuating demand in the industry. Linear programming is that technique which operates on the assumption that all relationships are linear and this is not the case when the situation is uncertain, so this technique is not applicable under conditions of uncertainty. Linear programming technqiues are only applicable in scenarios where all constraints are explicitly defined like the demand and production etc. In the manufacturing industry, even if the potential resources are explicitly known, the demand remains uncertain. Hence, I believe that the statement given by the production manager does have merit.
With rising globalization and the elimination of geographical boundaries, the manufacturing firms in particular have been facing drastic competitive pressures from companies that can easily acquire cheap labor and cut their costs. Moreover, as information exchange has become easier, there is no restriction to limit manufacturing in a single country. When need arises, the manufacturing can be shifted or outsourced; at times, the manufacturing process is outsourced to several countries and then final assembling takes place elsewhere. Hence, the working conditions for a manufacturing firm are highly uncertain. The production manager is not aware and cannot predict the variables for output and decision making that are required and further, cannot fully predict the possible constraints for his company. As linear programming only applies in scenarios where the variables have a linear relations and all the variables involved are explicitly defined, the manager cannot apply this method due to the fact that he cannot predict the output in uncertain conditions. This is why he is so sure that Linear Programming is not the most suitable technique to be applied in his firm.
References
A.E. Anieting, A. (2013). Application of Linear Programming Technique in the Determination of Optimum Production Capacity. IOSR Journal Of Mathematics, 5(6), 62-65. http://dx.doi.org/10.9790/5728-0566265
Lawrence, K., & Klimberg, R. (2010). Advances in business and management forecasting. Bingley: Emerald.
