Multi Criteria Decision Models
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New York Institute of Technology, Manhattan *
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Industrial Engineering
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Feb 20, 2024
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Uploaded by AgentExploration19827
MULTIPLE CRITERIA DECISION MODEL REPORT
RHEA AVLAR: 1318653
DHARA VADERA: 1313086
PURVA THAKKAR: 1312893
KRISHNA GABANI: 1301884
UNDER THE GUIDANCE OF PROFESSOR: SHAYA SHEIKH
CONTENTS
Introduction
Objectives
Data Collection and Presentation
Problem and Solution
Manufacturing of the Washing Machine data
Solver Parameters
Drawbacks of Linear Programming
Conclusion
References
INTRODUCTION
Multiple criteria decision models are used to make decisions in situations where multiple objectives or criteria need to be considered. These models involve the use of mathematical and statistical tools to analyze and evaluate the options available based on various criteria.
Optimization is a key topic in multiple criteria decision models. It involves finding the best solution to a problem based on a set of constraints and objectives. There are various types of optimization techniques, such as linear programming, nonlinear programming, and dynamic programming. Given a set of constraints, these techniques can be used to find the optimal solution to a problem.
Integer and binary programming are also important topics in multiple criteria decision models. These techniques are used when the decision variables take integer or binary values. Integer programming is used when the decision variables take integer values, while binary programming is used when the decision variables take binary values (either 0 or 1). These techniques can be used to solve a wide range of problems, such as scheduling, resource allocation, and network optimization.
Decision analysis is another important topic in multiple criteria decision models. It involves using decision trees and other tools to analyze decision problems and evaluate the options available. Decision analysis can be used to identify the best course of action, given the available information and the preferences of the decision-maker.
Goal programming is another important topic in multiple criteria decision models. It involves the use of mathematical programming techniques to find solutions that satisfy multiple goals or objectives. Goal programming can be used to solve a wide
range of problems, such as resource allocation, project scheduling, and portfolio optimization.
Overall, multiple criteria decision models provide a powerful set of tools for analyzing complex decision problems and identifying the best course of action, given the available information and the preferences of the decision-maker.
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OBJECTIVES:
The main objectives of this project are:
To analyze the current state of the supply chain and identify potential areas for improvement.
To apply decision analysis methods to develop a supply chain management strategy that will optimize the production and distribution of components.
To provide recommendations based on the results of the analysis that will improve the overall efficiency of the supply chain.
DATA COLLECTION AND PRESENTATION
The data used for this analysis were collected from a web source of financial magazine. The data consists of several tables containing information on the starting
node, ending node, product, period, and initial flow of each transaction. The data also includes information on the various components used to produce the products, as well as the inventory levels of each supplier.
PROBLEM AND SOLUTION
In today's highly competitive business world, businesses aim to maximize earnings
by utilizing existing resources as efficiently as possible. Jonas Co. is a renowned producer of washing machines that provides its clients with a variety of models. However, with limited hours of labor, elastic hosing, and drums available, the firm will face substantial resource limits in the following manufacturing cycle. In today's highly competitive business world, businesses aim to maximize earnings by
utilizing existing resources as efficiently as possible.
Jonas Co. must identify the ideal number of units to produce for each washing machine model given the available resources to overcome these limits and
maximize earnings. The profitability of the firm is directly proportional to the number of units produced and sold for each model, as well as the cost of production. Jonas Co. has thorough information on the profit margins and manufacturing needs for each washing machine model, allowing them to make educated judgments about the future production run.
This project depicts Jonas Co.'s issue in calculating the appropriate production levels for each washing machine model to maximize profitability while guaranteeing 100% of output is sold. We will utilize mathematical models to calculate the most lucrative production levels for each model based on the information supplied.
A SUMMARY OF WASHING MACHINE MANUFACTURING
TOP LOAD
FRONT-
LOAD
WASHER
DRYER COMBO
FULLY AUTOMATIC
TOTAL AVAILABLE
LABOUR
HOURS
25
22
28
29
4800
RUBBER HOSING
8
10
7
9
2540
DRUMS
1
1
1
1
600
PROFIT
350
300
370
400
To solve a linear programming problem, the first step is to create a mathematical model of the business problem. Identifying the decision factors, objective function,
and constraints is required. The decision variables in this scenario are the number of top load front load washer dryer combinations and fully automatic machines manufactured, denoted by X1, X2, X3, and X4, respectively. The goal function is to maximize profit, which is estimated based on the unit's sales price and manufacturing cost. The manufacturing plant's limited production capacity and the minimal demand for each product are the restrictions.
After developing the mathematical model, it may be applied in a spreadsheet using Excel formulae. We can use the spreadsheet model to enter alternative values for the choice variables and compute the resulting profit. We can find the best production levels for each product that will maximize profit within the limitations by using the Solver add-in in Excel.
TOP LOAD
FRONT LOAD
WASHER DRYER COMBO
FULLY AUTOMATIC
Total Av
ailable
0
1000
2000
3000
4000
5000
Labours Hours
Rubber Hosing
Drums
Profits
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The data for this analysis was collected from various sources including the inventory and production records of the suppliers, as well as the transportation records between the suppliers and the production facility.
To prepare the data for analysis, it was first compiled into a single dataset and cleaned to remove any missing or erroneous data. The dataset was then organized by product type and period to facilitate the analysis process.
SOLVER PARAMETERS
Linear programming is a mathematical approach for optimizing a linear objective function that is constrained by linear constraints. The objective function is the quantity that must be maximized or decreased, whilst the constraints are the constraints that must be followed to get an optimum solution. Solver, a Microsoft Excel add-in, is a tool for solving optimization issues in Excel spreadsheets, including linear programming problems.
To solve a linear programming issue in Solver, three main components must be defined: the objective cell, the variable cells, and the constraints.
OBJECTIVE CELL
The objective cell is the cell in the mathematical model that reflects the objective function. We wish to maximize or lower the value of the cell. We must indicate the objective cell and whether its value should be maximized or reduced in Solver. This is accomplished by choosing the objective function cell and then selecting the appropriate option in the "Set Objective" section of the Solver Parameters dialog box. In our case, the objective cell is cell F15, which indicates total profit, and we have set "Max" as the goal.
VARIABLE CELLS:
The cells in the spreadsheet that reflect decision variables in the mathematical model are known as variable cells. These are the cells whose values we may adjust to maximize the objective function while keeping the limitations in mind. The variable cells must be specified in Solver by choosing them in the "By Changing Variable Cells" section of the Solver Parameters dialog box.
CONSTRAINTS: Constraints are the constraints that must be followed to get an ideal solution. These
are the linear equations or inequalities that describe the system's constraints. We must specify the constraints in Solver by choosing the rows in the spreadsheet that reflect the constraint functions. Constraints can be of several forms, such as equality and inequity or limits.
-UNCONSTRAINED VARIABLES:
In our example, we specified that the unconstrained variables must be non-
negative, which implies that they must all be larger than or equal to 0. In the Solver
Parameters dialog box, pick the "Make Unconstrained Variables Non-Negative" option. This sets the decision variable bound, which indicates that Solver will not accept negative values for any decision variables.
SOLVER METHOD
Finally, we pick the Solver-solving technique, which is the methodology that Solver will use to discover the best solution. In our case, we used Simplex LP as
the solution technique. A simplex algorithm is a prominent approach for solving linear programming problems, and it is the default method in Solver for solving linear programming problems.
After we've established these critical components in Solver, we can hit the "Solve" button to find the best solution to the linear programming issue. Solver will apply the given solving technique to discover the variable cell values that maximize the objective function subject to the restrictions, and it will display the optimal solution in the spreadsheet.
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DRAWBACKS OF LINEAR PROGRAMMING
Linear programming is one of the optimization approaches available for determining the most effective use of resources. While it is a strong approach with numerous applications, it should only be used to tackle optimization problems with
a single linear objective function and linear constraints that cannot be broken.
There may be instances where linear programming is not the best optimization approach to use. For example, when there are multiple objectives, nonlinear objective functions and/or constraints, or soft constraints (that can be violated) rather than hard constraints (that cannot be violated), other more appropriate optimization techniques such as multiple objective linear programming, goal programming, or nonlinear programming should be used.
ILLUSTRATING ITS VALUE
Linear programming is a sophisticated mathematical approach for optimizing a linear objective function under the limitations of a set of linear constraints. It may be used to a broad variety of real-world challenges involving decision-making under restrictions. Resource allocation, production planning, transportation and logistics, inventory management, and financial portfolio optimization are some examples.
The Solver function in Excel is a built-in tool that uses linear programming methods to discover the best solution to a given issue. It allows users to provide the
objective function, decision variables, and restrictions in a spreadsheet format and provides an intuitive interface for configuring and solving optimization issues.
The goal in the scenario given was to maximize profitability while meeting production and resource restrictions. The quantities of all washing machine models
were the choice variables, while the constraints were manufacturing capacity, labor
hours, and material availability. The total profit created by the production mix of all models was the goal function.
The example shows how linear programming with Solver may give an objective and systematic method to constraint-based decision-making. It aids in avoiding frequent mistakes of intuitive decision-making, such as overlooking practical constraints and trade-offs. The method may be used to a wide range of business challenges and scaled up to handle increasingly complicated scenarios.
Overall, linear programming and Solver are useful tools for accountants and other professionals that make financial and operational decisions. It helps them to make data-driven decisions that consider many elements and restrictions, resulting in superior results and performance.
CONCLUSION
Based on the information provided, the project aims to analyze the current state of the supply chain of Jonas Co. and identify potential areas for improvement. The project's main objectives are to develop a supply chain management strategy that optimizes the production and distribution of components and provides recommendations to improve the overall efficiency of the supply chain. The data for the analysis was collected from various suppliers and their transactions with each other, as well as their inventory levels. The project involves applying decision
analysis methods to develop a strategy that maximizes earnings by utilizing existing resources efficiently. The project aims to identify the ideal number of units
to produce for each washing machine model given the available resources to maximize profitability while guaranteeing 100% of output is sold. Linear programming is the mathematical approach used to solve the problem, and Solver, a Microsoft Excel add-in, is the tool used to solve the optimization problem. The production plan is subject to certain constraints, such as available labor hours, rubber hosing, and drums. By solving the linear programming problem, the project found that the production quantities for each type of washing machine that maximizes profit are as follows: 192 units of top-load, 0 units of front-load, 0 units
of washer-dryer combo, and 0 units of fully automatic. The Best choice on the above analysis would be to choose the production of the top load washing machines and get the maximum profit. This production plan results in a total profit of $67,200.
REFERENCES
Linear Programming Refereed by https://www.britannica.com/science/linear-programming-
mathematics
Simplex Algorithm Refereed by https://optimization.cbe.cornell.edu/index.php?
title=Simplex_algorithm
Excel Solver Referred by https://support.microsoft.com/en-us/office/load-the-solver-add-in-in-
excel-612926fc-d53b-46b4-872c-e24772f078ca
Acuna, M., Sessions, J., Zamora, R., Boston, K., Brown, M., & Ghaffariyan, M. R. (2019). Methods to manage and optimize forest biomass supply chains: A review.
Current Forestry Reports
,
5
, 124-141.
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