Linear Programming Project

Below are some samples of Linear programming projects that portray real-life challenges and problem-solving by mathematical strategies. Strategies of linear programming apply to a variety of industrial contexts and problem scenarios. Modern-day companies make the most of LP models to plan the manufacturing course of, schedule personnel, maximize office space, guarantee timely supply of products, optimize shelf space, and so on.

Activity-based learning gives a dependable resolution for enhancing student engagement. Linear programming is a simplification downside that seeks to switch an advanced mathematical expression. A typical case relies on three main factors.

First, the simplification relationships ought to comply with a straight line. Therefore, the term linear.

Second, all values should be subject to constraints, which can be in numerical or in phrases or properties.

Third, the answer has to optimize (i.e., maximize or minimize, relying on the issue) the amount of a given variable.

Definitions you should be familiar with,

Decision variables: These variables decide the output and categorical the ultimate solution. For occasion, the variety of items of various automobiles manufactured by an automobile firm (represented as x items of Automotive A and y items of Automotive B).
Objective function: It lays down what you need to obtain in a particular problem. For instance, growing profit, reducing lead time, and so on. You’d usually encounter the usage of Z for the whole profit operate.
Constraints: These are limitations or restrictions posed on the choice variables, such because the production capacity of machines, availability of inputs, and so on.
Non-negativity: As a rule, LPP choice variables take non-negative values, which means that they’re always greater than or equal to 0.

#1 Profit optimization for business plan

Each enterprise wants financial sources to get things began and maintain over time. Furthermore, buyers and credit providers normally ask for detailed analyses of profitability. And LPP will be immensely useful in clearly explaining the viability of a enterprise.

Allow us to suppose that you simply need to make a professional B-plan. In the beginning, you’ll have to outline your problem utilizing different variables, constraints, and the objective function. Then, you’ll clear up the LPP utilizing an acceptable method, say a graph. Lastly, you’ll consider your outcomes and present your resolution to the parties.:

Constraints (manufacturing capability, the proportion of input requirement, price of products, and so on.)
Calculation worksheets
Coding examples

#2 Project on supply chain management

This downside relates to warehousing and the switch of manufactured products. Right here, you would want to attenuate the price of transporting items with respect to the resources (motor vehicles and workforce) accessible within the storage facility and at each depot.

You possibly can take up a undertaking to showcase the feasibility of linear programming in improving supply chain modeling. Contemplate an industrial case that determines the best transportation schedule throughout the given limits and establishes a integrated supply chain.

#3 On-time delivery example

For delivery services firms (FedEx, Blue Dart, and such), figuring out the shortest path to ship packages to their respective destinations forms a core job. This kind of distance optimization saves fuel and time and helps these logistics corporations in bettering customer experience.

Linear programming can assist select the precise path if a delivery person has to take six packages in a day from the warehouse (located at point X) to 6 different destinations (cities, namely L, M, N, O, P, and Q). You’ll need an goal operate and linear inequalities subject to sure constraints.

#4 Applications on diet-based or nutritional problems

A number of linear programming undertaking concepts incorporate optimization issues into diet plans. Such functions will be associated to any of the next functions:

Food aid
National food programs
Individual-specific dietary guidelines
As for the constraints, your research can embrace limits primarily based on vitamin, cost, ecological points, or acceptability. You might design a built-in framework protecting the domains of dietary quality, financial feasibility, and environmental sustainability. A linear programming model is a perfect software for this undertaking because it means that you can fulfill a number of restrictions without delay.

In case you are simply beginning with LP modeling, you may attempt your hand at a chart with solely two constraints (per gram nutrient content material and unit prices). Your resolution ought to reduce the price of the food regimen and checklist the optimum amount of various meals gadgets you may have in a day. The plan will be such that you simply eat a minimum of 300 energy with 75 grams of protein, 65 grams of fats, and 300 grams of carbohydrates.

5. Linear programming projects on automobile

production

Take the instance of an organization that has a product combine of 4 forms of cars – for instance, luxurious, sedan, minivan, and compact vehicle. The manufacturing amenities have a restrict on the whole annual manufacturing capability. Moreover, the corporate has to adjust to fuel consumption requirements beneath varied vitality insurance policies and nationwide legal guidelines.

The main points concerning the revenue margins, market share, and fuel effectivity can be found for all of the models. Now, think about a situation the place the highest administration desires to maximise the earnings under these restrictions. It could be difficult to depict a technique with out simplifying the issue.

You possibly can try an identical linear programming project primarily based on the secondary data of any automaker. With this research, you may go a step additional to research the implications of presidency insurance policies on profitability. It’s a distinctive means of manufacturing planning issues that usually revolve round ERP data.

**I will be very happy to discuss your projects individually if you feel the need!

Below is the information verbatim from your Course Assignment Section for Week 8 for your convenience,

Linear Programming Project
Overview
For this assignment, your instructor will assign a linear programming project based on the following specifications:

It will be a problem with at least three constraints and at least two decision variables.
The problem will be bounded and feasible. It will also have a single optimum solution (in other words, it won’t have alternate optimal solutions).
The problem will also include a component that involves sensitivity analysis and the use of the shadow price.
Instructions
You will be turning in two deliverables, a short writeup of the project, and the spreadsheet showing your work.

Writeup
Your writeup should introduce your solution to the project by describing the problem.

Correctly identify what type of problem this is. For example, you should note if the problem is a maximization or minimization problem, as well as identify the resources that constrain the solution.
Identify each variable and explain the criteria involved in setting up the model. This should be encapsulated in one or two succinct paragraphs.
After the introductory paragraph, write out the LP model for the problem. Include the objective function and all constraints, including any non-negativity constraints. Then, you should present the optimal solution, based on your work in Excel. Explain what the results mean.
Finally, write a paragraph addressing the part of the problem pertaining to sensitivity analysis and shadow price.
Spreadsheet
Please set up your problem in QM for Windows or Excel and find the solution using Solver.

Clearly label the cells in your spreadsheet.
You will turn in the entire spreadsheet, showing the setup of the model, and the results.
This course requires the use of Strayer Writing Standards. For assistance and information, please refer to the Strayer Writing Standards link in the left-hand menu of your course. Check with your professor for any additional instructions.

The specific course learning outcome associated with this assignment is:

Determine an approach to a problem that uses a linear programming model.