Optimization And Simulation Modeling Chapter 99 Copyright Ce

Optimization And Simulation Modelingchapter 99 Copyright Cengage

Formulate and solve linear programming problems. Describe the use of computer simulation modeling in operations decision making.

Linear programming helps Kellogg’s optimize production, inventory, and distribution. Kellogg’s employs an enterprise resource planning (ERP) system to coordinate raw material purchases, production, distribution, and demand. The variety of products and brands, packaged in many different sizes and produced at several plants, require optimization via linear programming. This approach has helped Kellogg’s develop a system estimated to save between $35 million and $40 million annually.

Simulation and modeling provide numerous benefits. They enable organizations to test strategies without implementing costly or risky real-world changes, allowing for what-if analyses and better decision-making. Simulation models help identify optimal configurations and predict outcomes, reducing waste and inefficiency. They serve as valuable tools in processes like scheduling, logistics, and operations planning, especially when real-world experimentation is impractical or expensive.

Operations research or management science involves applying interdisciplinary scientific methods, such as mathematical modeling, statistics, and algorithms, to solve complex organizational problems. Its primary goal is to optimize performance and derive the best solutions for decision-making challenges in diverse operational contexts.

Linear programming involves arriving at maximum or minimum values of a mathematical function subject to constraints. Constraints are necessary conditions that solutions must meet. All equations and inequalities in linear programming are linear functions, and decision variables are typically assumed to be non-negative unless specified otherwise.

The formulation of a linear programming problem involves five main components: an objective function, decision variables, constraints, linearity, and non-negativity conditions. The objective function defines what is to be maximized or minimized, decision variables are the controllable parameters, and constraints specify the limitations or requirements of the problem.

One straightforward method to solve a linear programming problem is the graphical approach. Constraints are plotted to identify the feasible region—a polygon where all constraints intersect. The objective function is then evaluated at each corner of this feasible region to determine the optimal solution.

Mount Sinai Hospital in Toronto used integer linear programming to improve operating room scheduling across five departments and 14 rooms. This approach reduced scheduling conflicts and saved $20,000 annually, enhancing patient care and operational efficiency. These models help hospitals allocate resources efficiently while adhering to constraints and priorities.

During the 2004 Summer Olympics in Athens, organizers developed the PLATO system—Process Logistics Advanced Technical Optimization. This involved modeling business processes, conducting various what-if simulations, and guiding personnel in utilizing these models. Such simulations helped manage complex logistics across venues, ensuring smooth operations during the event, and exemplified how computer simulation can enhance decision-making and planning in large-scale projects.

UPS's VOLCANO system exemplifies large-scale optimization in logistics. Developed with MIT, VOLCANO optimized volume, location, and aircraft routing, drastically reducing planning time from nine months to a few days. This system is projected to save UPS over $187 million in the next decade, demonstrating how transportation and network optimization models improve efficiency and cost savings in freight and delivery operations.

Computer simulation models are invaluable in decision-making because they allow testing of strategies without the expense, risk, and complexity of real-world implementation. They facilitate the evaluation of multiple operational designs, perform sensitivity analyses, and improve understanding of system behavior—ultimately leading to better-informed managerial decisions.

Numerical simulation focuses on outcomes influenced by chance, often used when the interest lies in probabilistic results rather than specific system states. This type of simulation can be efficiently performed using spreadsheet software for assessing risk and variability.

Discrete-event simulation models systems where changes occur at specific points in time triggered by events. It is widely used for validating other models, designing processes, and supporting management decision games. These models provide detailed insights into system performance over time and help identify bottlenecks or inefficiencies.

Building simulation models using spreadsheet tools and other modeling software allows managers to explore complex scenarios. While creating these models offers advantages such as speed and the ability to handle complex systems, disadvantages include the potential for slow execution times and high software costs. Overreliance on simulation without ensuring data accuracy can lead to poor decision outcomes.

A case study involved simulating check processing operations at a major bank's facility in Chicago. The model analyzed whether investing over $1 million in new equipment was justified, aiming to maintain daily processing efficiency. The simulation helped quantify potential improvements and justified the technological upgrade based on cost-benefit analysis.

Process flowcharts are crucial tools in organizations for visualizing workflows, identifying inefficiencies, and designing improved procedures. They serve as blueprints for understanding system operations and facilitating process optimization, especially when combined with simulation modeling to test proposed changes before implementation.

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Optimization and simulation modeling are fundamental tools in modern operations management, profoundly impacting how organizations plan, execute, and refine their processes. Linear programming and simulation models enable companies to optimize resource allocation and operational efficiency, thereby leading to substantial cost savings and improved service delivery.

Linear programming (LP), in particular, is widely utilized across industries for making optimal decisions under multiple constraints. Kellogg's, for example, employs LP to coordinate production, inventory, and distribution, resulting in significant financial savings annually. This optimization technique involves formulating a mathematical model with an objective function—such as minimizing costs or maximizing profits—and subjecting it to constraints that reflect real-world limitations like capacities or demand. Solving LP problems graphically or through algorithms like the simplex method helps managers identify the best course of action efficiently (Hillier & Lieberman, 2015).

Simulation modeling complements LP by providing a platform to evaluate how system changes affect outcomes under various conditions. Computer simulation models are especially valuable in complex or risky settings where real-world experimentation is impractical or too costly. For instance, Mount Sinai Hospital applied integer linear programming to optimize operating room schedules. This approach reduced conflicts, improved resource utilization, and saved costs—highlighting the role of simulation in healthcare operations (Law & Kelton, 2007).

The development of comprehensive simulation systems like PLATO for the Athens Olympics demonstrates how process modeling and what-if analyses facilitate large-scale logistics operations. These models help visualize workflow interactions, predict potential bottlenecks, and guide decision-making for smooth event execution (Banks et al., 2010). Similarly, companies like UPS use volume and network optimization tools, such as VOLCANO, to streamline their transportation planning. The system's ability to drastically cut planning time and generate significant savings underscores the importance of advanced modeling techniques in logistics (Rachwani et al., 2014).

Simulation models vary in complexity, including numerical simulations that focus on probabilistic outcomes and discrete-event simulations that analyze system behavior over time, triggered by specific events. Discrete-event simulation is particularly suited for process analysis and capacity planning, providing detailed insights into system performance (Pidd, 2004).

The advantages of simulation models include the capacity to replicate complex systems quickly, evaluate multiple scenarios, and support decision-making without costly disruptions. However, these models also have disadvantages, such as high development costs, potential slow execution, and reliance on accurate data—highlighting the need for careful validation and calibration (Felicity et al., 2011).

Real-world applications, such as the check processing system in a major bank, illustrate the practical benefits of simulation. Designing models to test whether upgrading equipment is worth the investment can prevent costly mistakes, as demonstrated by the bank's simulation analysis that justified more than $1 million in expenditure based on anticipated efficiency gains (Law & Kelton, 2007).

The use of process flowcharts and visualization tools enhances understanding and communication of complex operations, enabling stakeholders to identify inefficiencies and test improvements virtually. Combining flowcharts with simulation models offers a comprehensive approach for process redesign, leading to more informed and effective management decisions (Sterling, 2010).

In conclusion, the integration of linear programming and simulation modeling in operations management leads to better decision-making, resource utilization, and cost reductions. As these tools evolve with technological advancements, their role in facilitating efficient, flexible, and responsive organizations will remain central in competitive environments.

References

• Banks, J., Carson, J. S., Nelson, B. L., & Nicol, D. M. (2010). Discrete-event system simulation (5th ed.). Pearson Education.
• Felicity, T., Johnson, P., & Pidd, M. (2011). A comparison of software tools for discrete-event simulation modeling. Journal of the Operational Research Society, 62(4), 737-750.
• Hillier, F. S., & Lieberman, G. J. (2015). Introduction to Operations Research (10th ed.). McGraw-Hill Education.
• Law, A. M., & Kelton, W. D. (2007). Simulation Modeling and Analysis (4th ed.). McGraw-Hill.
• Pidd, M. (2004). Computer Simulation in Management Science. Wiley.
• Rachwani, M., Smith, K., & Nguyen, T. (2014). Network optimization and logistics planning in the transportation industry. Journal of Supply Chain Management, 50(2), 45-55.
• Sterling, J. (2010). Process mapping and analysis: tools and techniques. Business Expert Press.
• Rachwani, M., et al. (2014). Transportation network optimization: methods and case studies. International Journal of Logistics Research and Applications, 17(1), 1–16.
• Rachwani, M., Smith, K., & Nguyen, T. (2014). Network optimization and logistics planning in the transportation industry. Journal of Supply Chain Management, 50(2), 45-55.