Hello,

I need four responses of at least 200 words each for the below students discussions for this week. Also in the bold below are the questions the students at answering.

**Instructions:**

**The production manager of a large Cincinnati manufacturing firm once made the statement, â€œI would like to use LP, but itâ€™s a technique that operates under conditions of certainty. My plant doesnâ€™t have that certainty; itâ€™s a world of uncertainty. So LP canâ€™t be used here.â€ Do you think this statement has any merit? Why or why not? Explain why the manager may have said it and then further substantiate his argument or compose a rebuttal.**

Student one:

I do not think that the statement has any merit. Uncertainty will exist in any area of business and our daily life. Manufacturing units are bound to have uncertainty. Using LP could help the company plan and organize processes as per requirement and time specified. In return, this will help with organization, time, and finances as well. Resources to be allocated could be the machinery being used, labor, warehouse space, and other raw materials. Linear programming provides a method to optimize operations within certain constraints. It is used to make processes more efficient and cost-effective. Some areas of application for linear programming include food and agriculture, engineering, transportation, manufacturing and energy. So apart from uncertainty factors LP is helpful in many other aspects. Using linear programming requires defining variables, finding constraints and finding the objective function, or what needs to be maximized. In some cases, linear programming is instead used for minimization, or the smallest possible objective function value. Linear programming requires the creation of inequalities and then graphing those to solve problems. While some linear programming can be done manually, quite often the variables and calculations become too complex and require the use of computational software. Manufacturing requires transforming raw materials into products that maximize company revenue. Each step of the manufacturing process must work efficiently to reach that goal. For example, raw materials must past through various machines for set amounts of time in an assembly line (Dotson, 2018). To maximize profit, a company can use a linear expression of how much raw material to use. Constraints include the time spent on each machine. Any machines creating bottlenecks must be addressed. The amount of products made may be affected, in order to maximize profit based on the raw materials and the time needed.

Dotson, D. (2018), Five Areas of Application for Linear Programming Techniques, Retrieved from: https://sciencing.com/five-application-linear-programming-techniques-7789072.html

Student two:

I would hope that I’m not the owner of the large company with a manager who believes they cannot use linear programming to help aid production decisions in a manufacturing plant. If I heard the manager state this, I would believe they are either needing training on how to use the program or are just being lazy when it comes to their work. Linear programming most definitely can be used in a variety of ways in a manufacturing plant. By definition, LP is a method to achieve the best outcome (such as maximum profit or lowest cost) in a mathematical model whose requirements are represented by linear relationships. The problem before any manager is to select only those alternatives which can maximize the profit or minimize the cost of production (Kalpana, n.d.). There are several instances in a plant that can use the LP method, such as workforce, parts, warehouse space, just to name a few. According to the manager, the plant is full of uncertainty , which is true in almost all companies. This is the only part of the statement made, that is true. When this condition needing to be checked, instead of using the LP, the sensitivity analysis could be used. Sensitivity analysis is the study of how the uncertainty inn the output of a mathematical model or system can be divided and allocated to different sources of uncertainty in its inputs. Sensitivity analysis has a place for allowable increases and decreases. This is where one can input the uncertainty. Someone should should the manager this analysis. I’m sure improvements would be found in this manufacturing plant that would benefit everyone.

Reference:

Kalpana, R. (n.d.).* Linear Programming: Meaning, Characteristics, Assumption and Other Details.* Business Management Ideas. Retrieved from: businessmanagementideas.com/business-management/linear-programming-meaning-characteristics-assumption-and-other-details/537

Student three:

This statement is revealing. It is obvious that the manager has a very limited understanding of linear programming. His outright dismissal is unfortunate as it deprives his company from using what Higle and Wallace have called “one of the greatest successes to emerge from operations research and management science” (Higle, Wallace 2003).

The manager is correct in that linear programming shines when dealing with certainties. However, the manager is either unaware of, or has completely dismissed the fact that sensitivity analysis is an option with linear programming. By applying a sensitivity analysis linear programming look to his factory he and his team may be able to account for the variables the factory faces and develop a plan that not only supports the factory’s current efforts, but one that leverages the factory’s abilities and improves on current practices.

I believe that if the manager input the known information and used a range for the unknown, for example, if customer demand is the unknown, he can use historical information to determine what high demand , low demand and moderate demand has looked like and can then use those numbers in the linear programming analysis to compare the different scenarios, out comes and develop the appropriate plan of action. (Hegle, Wallace 2003)

References

Render, B., Stair, R. M., Hanna, M. E., & Hale, T. S. (2015). Quantitative Analysis for *Management*(12th ed.). Boston, MA: Pearson.

Higle, J. L., & Wallace, S. W. (2003). Sensitivity Analysis and Uncertainty in Linear Programming. *Interfaces*, *33*(4), 53â€“60. doi: 10.1287/inte.33.4.53.16370

Student four:

I am not in agreement with the managerâ€™s statement about linear programming (LP) models needing certainty to function properly.

First of all, Linear programming is a mathematically modeling technique that is used for planning and decision making in relation to the allocation of resource (Render, Stair,

Hanna, & Hale, 2015).).

In a situation where the manager claims his plant does not have certainty, that can easily be fixed by simply varying the values of the variables. The manager could combine different scenario planning. LP models can still be used in situations where uncertainty exists. All that needs to be done is to build a range of optimal solutions based on the conditions.

If the plantâ€™s goal is to figure out a way to reach maximum profit for example, it is important to figure out the constraints, the decision variables, and develop mathematical relationships for the constraints. In a situation where exact values and variables are not known, a simple solution will be to vary them by coming up with numbers closest to those the plant actually uses.

So, Mr. Cincinnati Manager, the LP model can be used at your manufacturing firm and your statement has no merit. I do however think the manager made the statement because he did not fully understand the function of the LP model. When dealing with the LP model, certainty simply means that parameters and relevant input data are known. Some certainties are needed to develop the model, but it doesnâ€™t mean that all properties of the linear program must be present and all assumptions met.

As long as the manager can understand the managerial problem the plant is facing, identity the constraints, and define decision variable mathematical expressions can be written. Therefore, the LP model can be used at his firm.

References

Render, B., Stair, R. M., Hanna, M. E., & Hale, T. S. (2015). Quantitative Analysis

for Management (12th ed.). Boston, MA: Pearson. Chapter:7

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