Introduction to Management Science

Definition The application of the scientific method to solving managerial decision problems  Usually involves a mathematical or a computer model

Historical Background Roots in military services during World War II  Allocation of resources  Tracking submarines After the war, applied to business applications  Refinery scheduling  Distribution  Inventory  Portfolio management Development of non-profit applications  Health care  Criminal justice  Education

Historical Background Mathematical techniques  The simplex method  Queueing theory  Inventory theory  Decision theory  Simulation modeling Current widely used applications  Yield management in airlines  Plant scheduling  Multi-echelon inventory analysis  Personnel scheduling  Credit scoring  Financial engineering

The Management Science Process Management science process includes:  Observe and formulate the problem  Build a model that represents the problem’s essence  Validate that the model’s conclusions are true for the underlying system  Modify and verify by experimentation  Solve the model  Conduct sensitivity analysis Try and take a global viewpoint (of the whole system)  Objectives of the whole organization  Avoid 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 Problem Parker 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:$48 Unit Selling Price:$65 The overhead costs associated with this product are as follows: Sales Force Salary:$9,000 Fixed 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$ ^ 0.5  For 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 Format