Chapter 9 Assignment due in 24 hours
Due in 24 hours
1. What benefits can we receive from simulations and modeling? (20 points)
2. What can we use process flowcharts for in companies? (10 points)
Optimization and Simulation Modeling
Chapter 9
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Learning Objectives
Formulate and solve linear programming problems.
Describe the use of computer simulation modeling in operations decision making.
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Linear Programming Helps Kelloggs Optimize Production, Inventory, and Distribution
Kelloggs must manage a highly complex production, inventory control, and distribution system.
Kelloggs employs an enterprise resource planning (ERP) system to coordinate its raw material purchases, production, distribution, and demand.
The many different varieties of products and brands, packaged in many different sizes and produced at several different plants, require the use of an optimization approach known as linear programming.
The innovative use of optimization techniques has allowed the company to develop a system that is estimated to save between $35 million and $40 million annually.
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Discussion Starter
What benefits can we receive from simulations and modeling?
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Operations Research
or Management Science
Operations research or management science: the use of interdisciplinary scientific methods such as mathematical modeling, statistics, and algorithms that aid decision making for complex real-world problems of coordination and execution of the operations in an organization
The goal is to derive the best possible solution to a problem or to optimize the performance of the organization.
Source: Image Source/Corbis
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Linear Programming
Optimization: arriving at a maximum or minimum point of a mathematical function
Constraints: the necessary conditions that must be met when a mathematical function is being optimized
Linear programming: a special formulation of an optimization problem in which all equations and inequalities are linear
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Formulation of a
Linear Programming Problem
Five main components of a linear programming
problem:
Objective function: A mathematical formulation of the criterion by which all decisions should be evaluated.
Decision variables: The parameters that can be changed by the decision makers to achieve a higher or lower value of the objective function.
Constraints: The necessary conditions that must be met when a mathematical function is being optimized
Linearity: When formulating linear programming problems, all mathematical equations or inequalities are represented as straight lines.
Non-negativity: Each decision variable within a linear programming formulation is assumed to take only nonnegative values, although this is not essential.
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Solution of a Linear Programming Problem by a Graphical Method
A simple linear programming problem can be solved by using a graphical method.
Because all the equations within a linear programming problem are either straight lines or inequalities, the constraints are first plotted to find the region that satisfies all conditions.
Once that region is identified, the researcher evaluates the objective function at each corner of the feasible region.
Source: Image Source/Corbis
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Mount Sinai Hospital: Scheduling Operating Rooms by Integer Linear Programming
Mount Sinai Hospital in Toronto, Canada, has 14 operating rooms and five departments using the OR.
To address the problem of scheduling operating rooms effectively, Mount Sinai Hospital now uses a constrained-optimization model know as integer linear programming.
Since implementing this approach, the hospital has seen a reduction in the number of conflicts in scheduling operating room times and saves $20,000 annually.
In the end, a better schedule means more effective care for Mount Sinai Hospitals patients.
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PLATO Helps Athens Win Gold During 2004 Summer Olympic Games
During the 2004 Olympic Games in Athens, over the course of 16 days, more than 2,000 athletes participated in 300 events in 28 different sports across 36 venues located across the city.
The events were watched by 3.6 million spectators in the stadiums, 22,000 journalists, and 2,500 members of the international committees.
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PLATO Wins Gold!
The organizing team for the Athens Olympics developed PLATO, the Process Logistics Advanced Technical Optimization approach.
The PLATO project:
Developed business process models for the various venues.
Developed computer simulation models that enabled managers to conduct a variety of what-if analyses.
Developed software that guided the Olympic Committee personnel in using the business process and simulation models.
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VOLCANO Saves $187 Million for UPS
UPS carries more than 13 million packages to more than 8 million customers in more than 200 countries daily.
UPS, along with a team of researchers from MIT, developed and implemented Volume, Location and Aircraft Network Optimization (VOLCANO), an optimization-based planning system that is transforming the business process within UPS.
The VOLCANO system is an interactive transportation modeling and optimization approach.
Prior to VOLCANO, it used to take planners up to nine months to develop a single transportation plan for UPS airline operations manually.
VOLCANO is expected to save more than $189 million for UPS within the next decade.
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Simulation Modeling
Computer simulation models are used in decision making because testing proposed new operating procedures in an actual operation is expensive, complicated, and risky.
Computer simulation models allow the user to try out different strategies without actually implementing them in practice.
Simulation models allow managers to evaluate multiple operations designs and perform what-if types of analyses.
Simulation replaces the wasteful and unreliable practice of testing managers ideas through trial-and-error methods.
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Numerical Simulation
Numerical Simulation: simulating outcomes that are controlled by chance, but where the state of the system at specific times is not of interest
Numerical simulations can typically be performed in computer-spreadsheet software.
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Discrete-Event Simulation
Discrete-event simulation: a type of simulation that is applicable when the state of a system over time is the major concern; the term discrete event describes the nature of such systems, where the system changes at discrete times when particular events occur
Three major uses:
Validating other models
Process design
Management decision-making games
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Building Simulation Models
Spreadsheet-Based Models
Simulation-Modeling Tools
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Advantages and Disadvantages
of Simulation-Modeling
Advantages:
The ability to create complex discrete-event models without programming knowledge
The speed at which models can be created by experienced modelers
Disadvantages:
A slow speed of execution
The cost of the software
can be in the tens of thousands of dollars per copy
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More Disadvantages?
Simulation, like an quantitative-decision aid, is dependent on accurate data.
Because simulation models are relatively easy to create, simulation is often overused.
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Computer Simulation
of Check Process Operations
One of the largest commercial banks in the U.S. asked one of the authors of this text to develop a simulation model of the upgrade and redesign plan for its check processing operations at its central check processing facility in Chicago.
The objective of the project: Was it worthwhile to spend more than $1 million for new equipment for check process operations?
It was essential that the check processing operation complete its daily work in a timely manner so that customer accounts could be posted and online balance information updated for branch operations.
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Discussion Starter
What can we use process flowcharts for in companies?
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Figure 9.10: Check
Processing Workflow Schematic
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Computer Simulation of
Check Processing Operations
The reject repair and balancing process is used to manually process any check that the automatic sorter is not able to read.
Animated simulation models were developed to understand the old and new reject repair processes.
A model is only an abstraction of reality. Therefore, models should include all essential and relevant elements of the real system and leave the nonessential elements out.
Simulation can be used to model the effects of such new technology.
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Figure 9.11: Old Check Reject
Repair Process Simulation Model
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Figure 9.12: New Check Reject
Repair Process Simulation Model
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Tables 9.9 and 9.10: Summarized Simulation Results for Current and New Process
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