BSAD 30 Chapter 1 & Appendix A

Steps of Problem Solving (1-7)

1. Define the problem. 2. Identify alternatives. 3. Determine the criteria. 4. Evaluate the alternatives. 5. Choose an alternative. (Decision) 6. Implement the selected alternative. 7. Evaluate the results to determine whether a satisfactory solution has been obtained.

Steps of Decision Making

1. Define the problem. 2. Identify the alternatives. 3. Determine the criteria. 4. Evaluate the alternatives. 5. Choose an alternative. (Decision)

Excel Function: COUNTIF

=COUNTIF(range, condition)

Excel Function: IF

=IF(condition, result if condition is true, result if condition is false)

Excel Function: VLOOKUP

=VLOOKUP(arg1,arg2,arg3,arg4) where arg1 is the value to search for in the first column of the table, arg2 is the table location, arg3 is the column location in the table to be returned, and arg4 is TRUE if looking for the first partial match of arg1 and FALSE for looking for an exact match of arg1. We will explain the difference between a partial and exact match in a moment. VLOOKUP assumes that the first column of the table is sorted in ascending order. The VLOOKUP function for student Choi in cell E16 is as follows: =VLOOKUP(D16,B6:D10,3,TRUE)

Feasible Solution

A decision alternative or solution that satisfies all constraints.

Infeasible

A decision alternative or solution that violates one or more constraints.

Deterministic Model

A model in which all uncontrollable inputs are known and cannot vary.

Stochastic/Probabilistic model

A model in which at least one uncontrollable input is uncertain and subject to variation; stochastic models are also referred to as probabilistic models.

Iconic Model

A physical replica, or representation, of a real object.

Single-criterion decision problems

A problem in which the objective is to find the "best" solution with respect to just one criterion.

Multicriteria decision problems

A problem that involves more than one criterion; the objective is to find the "best" solution, taking into account all the criteria.

4. A firm recently built a new plant that will use more than 50 production lines and machines to produce over 500 different products. The production scheduling decisions are critical because sales will be lost if customer demand is not met on time. If no individual in the firm has had experience with this production operation, and if new production schedules must be generated each week, why should the firm consider a quantitative approach to the production scheduling problem?

A quantitative approach should be considered because the problem is large, complex, important, new, and repetitive. Some of the reasons why a quantitative approach might be used in the decision-making process include the following: 1. The problem is complex, and the manager cannot develop a good solution without the aid of quantitative analysis. 2. The problem is critical (e.g., a great deal of money is involved), and the manager desires a thorough analysis before making a decision. 3. The problem is new, and the manager has no previous experience from which to draw. 4. The problem is repetitive, and the manager saves time and effort by relying on quantitative procedures to automate routine decision recommendations.

Model

A representation of a real object or situation.

Constraint

A restriction or limitation imposed on a problem.

Analog Model

Although physical in form, an analog model does not have a physical appearance similar to the real object or situation it represents.

Reasons for Quantitative Approach:

Complex, Critical, New, Repetitive

Mathematical Model

Mathematical symbols and expressions used to represent a real situation.

6. Suppose a manager must choose between the following two mathematical models of a given situation: (a) a relatively simple model that is a reasonable approximation of the real situation and (b) a thorough and complex model that is the most accurate mathematical representation of the real situation possible. Why might the model described in part (a) be preferred by the manager?

Saves time and wouldn't have to re-do a complex model if something changed. Quicker to formulate, easier to solve, and/or more easily understood

Decision

The alternative selected.

Controllable Inputs/Decision Variables

The decision alternatives that can be specified by the decision maker.

Uncontrollable Inputs

The factors that cannot be controlled by the decision maker.

Objective Function

The mathematical expression that defines the quantity to be maximized or minimized.

Fixed Cost

The portion of the total cost that does not depend on the volume; this cost remains the same no matter how much is produced.

Variable Cost

The portion of the total cost that is dependent on and varies with the volume.

Decision Making

The process of defining the problem, identifying the alternatives, determining the criteria, evaluating the alternatives with respect to each criterion, and choosing an alternative.

Problem Solving

The process of identifying a difference between the actual and the desired state of affairs and then taking action to resolve the difference.

Marginal Cost/Revenue

The rate of change of the total cost/revenue with respect to volume.

Optimal Solution

The specific decision variable value or values that provide the "best" output for the model.

Breakeven Point

The volume at which total revenue equals total cost.

Excel Function: Relative vs. Absolute References

When copying in Excel, one can use a relative or an absolute address. When copied, a relative address adjusts with the move of the copy, whereas an absolute address stays in its original form. Relative addresses are of the form C7. Absolute addresses have $ in front of the column and row, for example, $C$7. How you use relative and absolute addresses can have an impact on the amount of effort it takes to build a model and the opportunity for error in constructing the model. $A1 Allows the row reference to change, but not the column reference. A$1 Allows the column reference to change, but not the row reference. $A$1 Allows neither the column nor the row reference to change.

3. Discuss the different roles played by the qualitative and quantitative approaches to managerial decision making. Why is it important for a manager or decision maker to have a good understanding of both of these approaches to decision making?

When using a quantitative approach, an analyst will concentrate on the quantitative facts or data associated with the problem and develop mathematical expressions that describe the objectives, constraints, and other relationships that exist in the problem. Then, by using one or more mathematical methods, the analyst will make a recommendation based on the quantitative aspects of the problem. Although skills in the qualitative approach are inherent in the manager and usually increase with experience, the skills of the quantitative approach can be learned only by studying the assumptions and methods of management science. A manager can increase decision-making effectiveness by learning more about quantitative methodology and by better understanding its contribution to the decision-making process. A manager who is knowledgeable in quantitative decision-making procedures is in a much better position to compare and evaluate the qualitative and quantitative sources of recommendations and ultimately to combine the two sources to make the best possible decision.

8. Max 10x, 5x <=40, x>=0 Suppose the firm in this example considers a second product that has a unit profit of $5 and requires 2 hours for each unit produced. Assume total production capacity remains 40 units. Use y as the number of units of product 2 produced.

a- max 10x + 5y, 5x+2y <= 40, x=>0, y=>0 b- Controllable inputs: x and y Uncontrollable inputs: profit (10, 5), labor-hours (5, 2), and labor-hour availability (40) c- d- x=0, y=20, profit = $100 (by trial and error) e- deterministic model