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### TheManagement Science Approach

Problem Definition

What is Management Science?

- Scientific approach applied to decision making
- “Mess management”-- Early developer of MS
- “The use of logic and mathematics in such a way as to not to interfere with common sense”
- “The results should look, feel and taste like common sense” -- Prominent MS Consultant
- “The use of [mathematical and statistical] techniques, mathematical programming, modeling, and computer science [to solve complex operational and strategic issues]. -- US Army

Definition ofManagement Science

- Art of mathematical modeling
- Science of the solution techniques for solving mathematical models
- Ability to communicate results

Management Science Objective

- Given a limited amount of personnel, resources and material, how do we use them most effectively to:
- Maximize -- Profit, Efficiency
- Minimize -- Cost, Time
- Management Science is about doing the best you can with what you’ve got -- OPTIMIZATION

Management Science Applications

- Linear Programming Models

Using of scare resources to achieve maximum profits when there are constant returns to scale.

- Steelcase scheduling monthly production desks, cabinets, and other office furniture to maximize profit by assigning workers and utilizing the steel, wood, and other resources that are available.
- Texaco blending various grades of raw crudes to maximize profits while meeting production targets.
- Integer Linear Programming Models

Determining integer quantities (such as people, machines, airplanes, etc.) that maximize profits.

- American Airlines assigning planes, crews, and support personnel on a daily basis.
- McDonald’s assigning workers throughout the day.

Management Science Applications

- Network Models

Using specialized linear models to determine routes of shortest distance, connections that tie points together of minimum length or finding a maximum flow (through a series of pipes)

- UPS scheduling deliveries in a fleet of trucks.
- United Van Lines determining the least costly route between a pickup and delivery point.
- Project Scheduling Models

Scheduling of the various tasks that make up a project in order to minimize the time or cost it takes to complete the entire project.

- William Lyon Homes scheduling the construction of a new tract of homes in Orange County.
- CalTrans supervising the reconstruction of the Golden State Freeway after the devastating earthquake in the 1990’s.

Management Science Applications

- Decision Models

Making decisions about the best course of action when the future is not known with certainty.

- Fidelity Investments making mutual fund decisions given the uncertainty of the company performance, and the markets.
- The International Olympic Committee making site decisions given uncertain weather patterns and changing international conditions.
- Inventory Models

Determining how much of a product to order and when to place the order to minimize overall total costs.

- Macy’s making merchandising decisions for the season.
- See’s Candies producing goods for their own stores.

Management Science Applications

- Queuing Models

Analyzing the behavior of customer waiting lines to determine optimal staffing policies.

- Disneyland designing waiting lines and policies for rides at the amusement park.
- United States Postal Service determining staffing levels and type of waiting line at different branch offices.
- Simulation Models

Analyzing a variety models whose forms do not meet the assumptions or are too complex to be solved by other specialized techniques.

- United States Army evaluating tactical combat situations.
- Conagra Foods evaluating “what-if” situations in their food production processes.

Management Science Team Approach

- Most management science models, particularly in larger companies are developed by “teams” of professionals.
- Expertise from various specialists is integrated into building a good mathematical model
- Engineers, accountants, economists, marketing analysts, production personnel, etc. are just some of the specialists that can be utilized in the model building process.

Parts of a Management Science Study

- Problem Definition
- Building Mathematical Models
- Solving/Refining Mathematical Models
- Communication of Results

Types of Management Science Problem Definitions

- How Do We Get Started?
- Evaluation of new operations and/or procedures
- Can We Do Better?
- Ongoing operations may be performing well, but perhaps they could improve
- Help!
- Situations where the company is clearly in trouble – “mess management”

Problem Definition Approach

- Observe Operations
- Try to view problem from various points of view within the organization.
- Ease into complexity
- Do a lot of listening; ask simple questions; initially build a simple, common sense model that can be made more complex later.
- Recognize political realities
- Managers will not usually supply evidence showing his/her failures – there can be a “blame game” for failures.
- Decide what is really wanted -- the goal/objective
- Managers can have a fuzzy or a definitive idea as to the objective; this can be at odds with the global objective.
- Identify constraints
- With input from various sources seek the factors that will limit the firm’s ultimate objective; include only relevant factors.
- Seek continuous feedback
- The management science team must solve the “right” problem; seek, share and document frequent input with decision makers.

Updating The Problem Definition

- Once the problem has been defined it is time for the modeling/solution phase.
- But results from this phase may result in a re-evaluation of the problem definition.
- The model may be “infeasible”
- The model may not provide “good enough results”
- The model may highlight heretofore unobserved or unanticipated constraints
- The model may result in a set of optimal or at least “good” possible courses of action allowing the decision maker to look at secondary objectives.

Review

- Management science seeks to do the best you can with what you’ve got.
- It involves modeling, solution approaches, and communication.
- The process consists of:
- Problem definition
- Mathematical modeling
- Solving the mathematical model
- Communication/implementation of results.
- Approaches/pitfalls associated with the problem definition step.

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