Decision Science Chapter 1 Intoduction

Introduction We face numerous decisions in life & business. Such as in: - Production Planning - Project Planning - Capital Budgeting - Inventory Analysis - Marketing Planning - Scheduling We can use computers to analyze the potential outcomes of decision alternatives.

The Decision Science Approach Decision Science uses a scientific approach to solve different types of problems in a variety of organizations by using mathematical models.

The Modeling Approach to Decision Making Models are usually simplified and accurate versions of things they represent Types of models: Mental (arranging furniture) Visual (road maps, architecture drawing) Physical/Scale (architecture design of building, Car models) Mathematical (what we’ll be studying) Everyone uses models to make decisions.

Example of a Mathematical Model Profit = Revenue - Expenses or Profit = f(Revenue, Expenses) Y = f(X1, X2)

A Generic Mathematical Model Y = f(X1, X2, …, Xn) Where: Y = Objective or output) Xi = Inputs f(.) = function defining the relationship between the Xi and Y

The Decision Science Process

Steps in the Decision Science Process Observation - Identification of a problem that exists (or may exist in an organization. Definition of the Problem – Clearly defining problem’s variables, objective, constraints or boundaries and their interactions. Model Construction - Development of the functional mathematical relationships that describe the decision variables, objective function and constraints of the problem. Model Solution – Solving the developed model using decision science techniques. Model Implementation - Actual use of the model or its solution.

Example of Model Construction (1 of 3) Information and Data: Business firm makes and sells a steel Vase Each Vase costs $5 to produce Each Vase sells for $20 Each Vase requires 4 pounds of steel to make Firm has 100 pounds of steel Business Problem: Determine the number of units to produce to make the most profit, given the limited amount of steel available.

Chapter 1- Management Science Example of Model Construction (2 of 3) Decision Variable: X = number of Vases to produce Z = total profit (in $) Objective Function Z = $20X - $5X Resource Constraint 4X = 100 lb of steel Model: maximize Z = $20X - $5X subject to 4X = 100 Chapter 1- Management Science

Example of Model Construction (3 of 3) Model Solution Consider the constraint equation: 4x = 100 or x = 25 units Substitute this value into the profit function: Z = $20x - $5x = (20)(25) – (5)(25) = 500 – 125 = $375 (Produce 25 Vases, to yield a profit of $375)

Benefits of Modeling Economy - it is less costly to analyze decision problems using models. Timeliness – it delivers needed information more quickly than their real-world situations Feasibility - models can be used to do things that would be impossible. Models give us insight & understanding that improves decision making.

Good Decisions vs. Good Outcomes Good decisions do not always lead to good outcomes... If sunny weather is predicted you may (rightly) decide to your umbrella at home. If it rains unexpectedly you may get wet (a bad outcome), but that doesn’t mean you made a bad decision. A structured, modeling approach to decision making helps us make good decisions, but can’t guarantee good outcomes.

Chapter 1- Management Science