optimisation methods techniques industrial

optimisation methods

1. Nivya Muchikel Department of Mathematics Under the guidance of: Submitted by: Aadyotya Pandey (1RV22IM002) Amogh R.N. (1RV22IM007) Shruti Bhendarkar (1RV22IM043) OPTIMISATION METHODS Techniques employed in various domains related to Industrial Engineering & Management Experiential Learning Phase-1

2. CONTENTS Acknowledgements Introduction Problem Statement Advantages Limitations Applications MATLAB codes Conclusion References Monday, 04 March 2024 STATISTICS, LAPLACE TRANSFORM AND NUMERICAL METHODS 2

3. ACKNOWLEDGEMENTS I would like to extend my sincere appreciation to my teachers, Prof. Nivya Muchikel , Dept. of Mathematics , whose guidance and mentorship have been invaluable throughout the development of this project. Your expertise, patience, and encouragement have not only enriched my understanding but also played a pivotal role in shaping the success of this endeavor. Lastly, I take this opportunity to thank our family members and friends who provided all the backup support throughout the project work. Monday, 04 March 2024 3 STATISTICS, LAPLACE TRANSFORM AND NUMERICAL METHODS

4. INTRODUCTION Optimization methods involve systematic approaches to finding the best possible solution from a set of feasible options, considering multiple objectives, constraints, and trade-offs. Optimization techniques and methods are essential tools in Industrial Engineering. They aim to improve efficiency, reduce costs, and enhance productivity across operational domains. Optimization involves finding the best solution considering multiple objectives, constraints, and trade-offs. Industrial Engineering focuses on designing, improving, and optimizing systems to achieve organizational goals effectively and efficiently. Optimization and Industrial Engineering share the common goal of maximizing performance within industrial and organizational settings. By leveraging optimization methods, Industrial Engineers can analyze complex systems, optimize resource allocation, design efficient processes, and make data-driven decisions. Monday, 04 March 2024 4 STATISTICS, LAPLACE TRANSFORM AND NUMERICAL METHODS

5. PROBLEM STATEMENT Industrial Engineering and Management struggle with efficiency, cost reduction, and productivity enhancement. Optimization methods are key to solving these challenges. Optimization techniques are needed in production planning, inventory management, supply chain logistics, facility layout design, and scheduling. Complex factors like resource constraints and dynamic market demands make optimization difficult. This research aims to develop user-friendly optimization models and decision-support systems. The goal is to help organizations achieve better performance, competitiveness, and sustainability. Monday, 04 March 2024 5 STATISTICS, LAPLACE TRANSFORM AND NUMERICAL METHODS

6. ADVANTAGES Improved Efficiency: Optimization helps streamline processes, reducing waste and maximizing resource utilization. Cost Reduction: By optimizing various operations, costs associated with production, inventory, and logistics can be minimized. Enhanced Productivity: Optimization ensures better allocation of resources and scheduling, leading to increased output within the same time frame. Better Decision Making: Optimization provides data-driven insights, aiding in strategic decision-making for resource allocation and capacity planning. Increased Competitiveness: With optimized processes, companies can offer competitive pricing, meet customer demands efficiently, and gain market advantage. Sustainable Operations: Optimization can help reduce environmental impact by minimizing energy consumption, waste generation, and carbon footprint. Adaptability to Change: Optimization models can be adjusted to accommodate changes in market demands, resource availability, or operational constraints. Continuous Improvement: Optimization fosters a culture of continuous improvement by identifying inefficiencies and implementing iterative enhancements. Monday, 04 March 2024 6 STATISTICS, LAPLACE TRANSFORM AND NUMERICAL METHODS

7. LIMITATIONS Complexity : Some optimization problems may be too complex to model accurately, leading to oversimplification or unrealistic assumptions. Data Dependency: Optimization relies heavily on accurate and timely data, which may not always be available or reliable. Computational Intensity: Solving optimization problems computationally can be time-consuming and resource-intensive, especially for large-scale systems. Resistance to Change: Implementing optimized solutions may face resistance from stakeholders accustomed to existing processes or hesitant to adopt new technologies. Risk of Overfitting: Optimization models may perform well under specific conditions but fail to generalize to different scenarios, leading to suboptimal outcomes. Ethical Considerations: Optimization may prioritize certain objectives at the expense of others, raising ethical concerns regarding fairness, equity, and social responsibility. Lack of Human Judgment: Optimization methods may overlook qualitative factors or intangible aspects that human judgment considers valuable. Uncertainty and Variability: Optimization solutions may be sensitive to uncertainties in inputs, market fluctuations, or unforeseen events, leading to suboptimal performance. Monday, 04 March 2024 7 STATISTICS, LAPLACE TRANSFORM AND NUMERICAL METHODS

8. APPLICATIONS Linear Programming (LP) : Objective: Minimize or maximize a linear objective function subject to linear equality and inequality constraints. Example: Optimizing the production plan for a manufacturing facility to maximize profit while satisfying production capacity and resource constraints. MATLAB Function: linprog Non-linear Programming (NLP) : Objective: Minimize or maximize a nonlinear objective function subject to nonlinear equality and inequality constraints. Example: Optimizing the shape of a wing to minimize drag while ensuring lift requirements are met. MATLAB Function: fmincon Integer Programming (IP) : Objective: Similar to linear programming but with the additional requirement that decision variables must take integer values. Example: Allocating discrete resources, such as assigning tasks to workers, where tasks cannot be fractionally divided. MATLAB Function: intlinprog Monday, 04 March 2024 8 STATISTICS, LAPLACE TRANSFORM AND NUMERICAL METHODS

9. APPLICATIONS Genetic Algorithms (GA) : Objective: Find the optimal solution by mimicking the process of natural selection and evolution Example: Optimizing parameters of a neural network for a specific task by evolving a population of potential solutions over multiple generations. MATLAB Function: ga Quadratic Programming (QP): Objective: Minimize or maximize a quadratic objective function subject to linear equality and inequality constraints. Example: Portfolio optimization, where the goal is to maximize returns while minimizing risk by selecting a combination of assets. MATLAB Function: quadprog Multiobjective Optimization: Objective: Optimize multiple conflicting objectives simultaneously. Example: Designing a product with competing goals, such as minimizing cost while maximizing performance and reliability. MATLAB Function: gamultiobj Monday, 04 March 2024 9 STATISTICS, LAPLACE TRANSFORM AND NUMERICAL METHODS

10. MATLAB CODES Monday, 04 March 2024 10 Linear Programming (LP): f = [-1; -2; -3]; A = [1 1 1; -1 2 0; 0 1 -1]; b = [20; 2; 3]; lb = [0; 0; 0]; ub = []; [x, fval ] = linprog (f, A, b, [], [], lb , ub ); Non-linear Programming (NLP): fun = @(x) (x(1)-1)^2 + (x(2)-2)^2; x0 = [0; 0]; [x, fval ] = fminunc (fun, x0); Integer Programming (IP): f = [-1; -2; -3]; A = [1 1 1; -1 2 0; 0 1 -1]; b = [20; 2; 3]; intcon = [1; 2; 3]; [x, fval ] = intlinprog (f, intcon , A, b, [], [], lb , ub ); STATISTICS, LAPLACE TRANSFORM AND NUMERICAL METHODS

11. MATLAB CODES Monday, 04 March 2024 11 Genetic Algorithms (GA) : fitnessFcn = @(x) (x(1)-1)^2 + (x(2)-2)^2; nvars = 2; lb = [0; 0]; ub = []; options = optimoptions ('ga', 'Display', ' iter '); [x, fval ] = ga( fitnessFcn , nvars , [], [], [], [], lb , ub , [], options); Quadratic Programming (QP): H = [1 -1; -1 2]; f = [-2; -6]; A = [1 1; -1 2; 2 1]; b = [2; 2; 3]; [x, fval ] = quadprog (H, f, A, b); Multiobjective Optimization: fun1 = @(x) x(1)^2 + x(2)^2; fun2 = @(x) (x(1)-1)^2 + (x(2)-1)^2; fun = @(x) [fun1(x), fun2(x)]; [x, fval ] = fmincon (fun, x0, A, b, [], [], lb , ub ); STATISTICS, LAPLACE TRANSFORM AND NUMERICAL METHODS

12. CONCLUSION In conclusion, optimization techniques stand as indispensable tools within the realm of Industrial Engineering, offering systematic approaches to address challenges, enhance efficiency, and drive continuous improvement. Through the alignment of optimization methods with Industrial Engineering concepts, organizations can achieve greater operational effectiveness, cost savings, and competitive advantage. By leveraging optimization, Industrial Engineers can design more efficient processes, allocate resources effectively, and make informed decisions based on data-driven insights. As industries continue to evolve and face ever-changing demands, the integration of optimization techniques will remain crucial for fostering innovation, sustainability, and success in industrial operations. Thus, the synergy between optimization methods and Industrial Engineering principles serves as a cornerstone for achieving excellence in today's dynamic and competitive business landscape. Monday, 04 March 2024 12 STATISTICS, LAPLACE TRANSFORM AND NUMERICAL METHODS

13. REFERENCES "Introduction to Operations Research" by Frederick S. Hillier and Gerald J. Lieberman - This classic textbook covers a wide range of optimization techniques applicable to industrial engineering and management, including linear programming, integer programming, and dynamic programming. "Applied Optimization with MATLAB Programming" by P. Venkataraman - Focuses on optimization techniques implemented using MATLAB, with applications in engineering and management, including linear programming, nonlinear programming, and evolutionary algorithms. "Optimization Models for Production Planning in Advanced Manufacturing Systems: A Review" by Andrea Matta, Marco Sgarbossa , and Mauro Gamberi . (Published in the International Journal of Production Research) - Provides an overview of optimization models and techniques used in production planning for advanced manufacturing systems. "Multi-objective optimization in engineering design: Current status and future opportunities" by C. Mavrotas . (Published in Structural and Multidisciplinary Optimization) - Discusses multi-objective optimization techniques and their applications in engineering design, including industrial engineering. "Recent developments in optimization methods for supply chain management" by Xiaolin Li and Frank Y. Chen. (Published in Engineering Applications of Artificial Intelligence) - Reviews recent developments in optimization methods for supply chain management, offering insights into their applicability in industrial engineering and management. " A review on applications of mathematical programming models in scheduling, routing and distribution of logistics and transportation operations" by Fatma Gzara and Sana Belmokhtar . (Published in Computers & Industrial Engineering) - Provides a comprehensive review of mathematical programming models applied in scheduling, routing, and distribution optimization within logistics and transportation operations, with implications for industrial engineering and management. Monday, 04 March 2024 13 STATISTICS, LAPLACE TRANSFORM AND NUMERICAL METHODS

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