I need at least 500 words Initial Post. 250 words for each question. No Plagiarism. Due in 12 hours. I will also attached the replies of other students once they are available. I need 0.5 page for each reply. I will attached the reply document later.
The development of linear programming is perhaps among the most important scientific advances of the mid-20th century. Today, it is one of the standard tools that has saved many millions of dollars for most companies and enterprises.
Identify at least two reasons for the importance of linear programming in an enterprise of your choice and describe the impact that linear programming has had in that enterprise in recent decades. Provide a specific example of a linear programming model related to the enterprise that you have selected and interpret the slack variables of your example. Describe how the information obtained about the slack variables of your example can be used by the decision-making sector of that enterprise. (You do not have to write a mathematical formulation of your example. Simply mention the objective, the decision variables, and a few possible constraints to describe your model example).
In your two replies to classmates, compare and contrast the similarities and differences between their model and your model.
Linear Programming in Care Pathways
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A hospital is a machine with a lot of moving parts. When you think about everything that goes into the care of a patient: the staff (often in the thousands at a time), the complex equipment, random supplies (my unit used to have a more than 75 different types of bandages on the floor at all times), and ancillary departments (food service, radiology, laundry, housekeeping), it’s not surprising that it takes a lot of work to keep it all running smoothly. Luckily, linear programming can be used to study how all the moving parts work together as well as the effects that insufficiencies in one place can have in another.
Practicing healthcare also comes with a lot of constraints. For those of use who’ve watched a few medical dramas, I think we picture a risky treatment with a small probability of making a full recovery (and depending on the show their attractiveness may or may not seem to have something to do with their outcome). While that does happen (minus the attractiveness part), I decided to focus instead on the broad risk of just walking into a hospital.
If the moving parts of a hospital was a model, risk would be a constraint. However, these constraints can be studied by creating their own linear model. The the model of risk constraints would have it’s own constraints, such as patient satisfaction (it’s a two-edged sword), budget, and patient rights (necessary, but still a constraint), to name a few.
I found a really great article that outlines the process behind creating a linear model that represents the risk of being in a hospital. It’s broken out into a lot of different parts, but it’s pretty easy to follow. It’s probably important to note that defining the variables is most of the battle. For example, falls are one of the most common harm incidents for hospitals. Any hospital will have a set of risk factors for falls, or variables that make a patient statistically more likely to harm themselves falling. This fall risk is often put in a patient’s chart, or even displayed visibly in the room. There’s a large amount of research on what makes a patient a fall-risk. In the same way, every variable of the model needs to be clearly defined before it’s included.
From a broad sense, a linear model for patient safety would attempt to take into account all possible risk factors. The model in my study was created by breaking different types of risk into different variables and then creating a linear model designed to be a predictor of all risk. Their model included the following variables:
x21: number of patients who needed protection from domestic accidents
x22: number of patients who should be protected from theft
x23: number of patients who should be protected from kidnapping
x24: number of patients who should be protected from mistakes
the equation then became:
If you have the time to read through the article, it’s pretty interesting and I think it does a good job of breaking down the process of creating a complex multivariate linear model.
Agaranca, M. C., & Olokunde, T. O. (2015, June 1). Optimization of Healthcare Pathways in Covenant University Health Centre Using Linear Programming Model. Retrieved March 18, 2020, from http://eprints.covenantuniversity.edu.ng/5478/1/HEALTHCARE%20PATHWAY%20PAPER%5B1%5D
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Linear Programming in Manufacturing
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Linear programming (LP) is used in many aspects of business because it allows users to break down a variable such as manufacturing costs into smaller components in order to identify where the biggest drivers are to save money or maximize profits. It “helps businesses optimize complex operations by depicting the various solutions in a simplified way” (Pondent, 2018). I think the biggest advantage to using LP is that there is really no limit on the number a variables your equation can factor in. A manufacturing company could source 1,000s of raw materials all at different costs but with an organized spreadsheet, you could still create an equation to minimize the cost.
Another huge benefit to LP is that you can also have numerous (infinite?) constraints. Looking at the manufacturing sector again, this is important because it may not always be a dollar constraint, it may be time-sensitive or limited to certain machinery. Manufacturing takes raw materials and turns them into viable products that can earn the company revenue. However, if any bottlenecks exist, they must be addressed urgently to build the most efficient model (Dotson, 2018). A real-world example of this exists in the manufacturing of medical devices because not only are raw materials and costs a constraint, the finished goods must also be sent to a sterilizer before they can be packaged and sold. It’s often expensive to have your own sterilizer so many companies outsource this to other facilities. Yet there’s risk if all the products are going to the same company to be sterilized… what if there’s a hurricane that shuts down the business? What if they can’t keep up with demand and start developing longer lead times?
This equation would ultimately be designed to maximize profits while minimizing risk and manufacturing costs. Another important term to understand is slack. Slack is basically the unused inputs of the equation (Evans, 2013). For instance, if we had purchased $10,000 in raw materials and spent another $5,000 in labor/processing to produce 100 units that were sent to the sterilizer but not able to get sterilized, the slack here would be $15,000 in unsalvageable product. Obviously the business would want to minimize this as well.
Dotson, D. (2018, May 21). Five Areas of Application for Linear Programming Techniques. Retrieved from:
Evans, J. (2013). Statistics, Data Analysis, and Decision Modeling (5th ed.). Upper Saddle River, NJ.
Pondent, C. (2018, December 4). Limitations & Advantages of Linear Programming. Retrieved from:
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