Introduction to Management Science

Definition

The application of the scientific method to solving managerial decision problemsUsually involves a mathematical or a computer model

Historical Background Roots in military services during World War II

Allocation of resourcesTracking submarines

After the war, applied to business applicationsRefinery schedulingDistribution InventoryPortfolio management

Development of non-profit applicationsHealth careCriminal justiceEducation

Historical Background Mathematical techniques

The simplex methodQueueing theory Inventory theoryDecision theorySimulation modeling

Current widely used applicationsYield management in airlinesPlant schedulingMulti-echelon inventory analysisPersonnel schedulingCredit scoringFinancial engineering

The Management Science Process

Management science process includes:Observe and formulate the problemBuild a model that represents the problem’s essence Validate that the model’s conclusions are true for the

underlying systemModify and verify by experimentationSolve the modelConduct sensitivity analysis

Try and take a global viewpoint (of the whole system)Objectives of the whole organizationAvoid suboptimization

An Example Where Modeling Can be Illustrated

Make or Buy?

Power Notebooks, Inc. is a manufacturer of notebook computers. They are trying to decide whether to purchase the LCD screens for their computers from an outside supplier or to manufacture the screens in-house.

The screens cost $100 each from the outside supplier. To set up the assembly process required to produce the

screens in-house would cost $10,000. They could then produce each screen for $75.

For what range of production volume is each alternative best?

An Illustration of the Management Science Approach

An Advertising ProblemParker Sisters is a manufacturer of children’s toys and games. One of their hottest selling toys is a remote-control “Walking–Talking Barney”. Some data for this product are as follows:

Unit Variable Cost: $48Unit Selling Price: $65

The overhead costs associated with this product are as follows:

Sales Force Salary: $9,000Fixed Overhead: $23,000

Parker Mothers has analyzed past data for talking Barney (and other similar toys), and determined that sales are affected by a number of factors:

(1) the season (e.g., more at Christmas, more at the start of the new TV season of Barney, less during summer repeats, etc.),(2) the size of the sales force devoted to the product,(3) the level of advertising.

Question: What should the advertising budget for “Walking–Talking Barney” be? (Proposal: $10,000)

Spreadsheet for Quarter 1

Trial Solutions

The Excel Solver

When the Solver add-in is installed, it is available under the “Tools” menu.

The Optimized Solution

Four Quarters Spreadsheet

Four Quarters (Solver Optimized)

Class Example You have started a small business and from prior industry

experience, conclude your yearly sales are related to advertising by the following relationship:Sales = 1.1 * Last year’s Sales + This Year’s Adv$ ^

0.5For year 1 assume last year’s sales were 10,000

Your overhead costs are 100,000 per year plus advertising costs and your initial year 1 variable costs per unit are $50. Assume in year 1 you can sell each unit at $65.

Construct a model to find optimal advertising expenditures for the years 1 through 5 assuming overhead, price, and variable costs are fixed at year 1 values.

Spreadsheet Example FormatInitial Conditions

Fixed 100,000.00$ Price 65.00$ Variable cost 50.00$ Year 0 Sales 10,000 Sales growth Factor 1.1

Year 1 Year 2 Year 3 Year 4 Year 5Advertising $

Sales Volume

RevenuesCost of salesGross Margin

OverheadTotal Fixed Costs

Profit

Present Value of Profits: