ManSci Prelims

• Problem solving

  can be defined as the process of identifying a difference between the actual and the desired state of affairs and then taking action to resolve this difference.
• For problems important enough to justify the time and effort of careful analysis, the problem-solving process involves the following seven steps:

  1. Identify and define the problem.2. Determine the set of alternative solutions.3. Determine the criterion or criteria that will be used to evaluate the alternatives.4. Evaluate the alternatives.5. Choose an alternative.6. Implement the selected alternative.7. Evaluate the results to determine whether a satisfactory solution has been obtained.
• can be defined as the process of identifying a difference between the actual and the desired state of affairs and then taking action to resolve this difference.
• Decision making

  is the term generally associated with the first five steps of the problem-solving process. Thus, the first step of decision making is to identify and define the problem. It ends with the choosing of an alternative, which is the act of making the decision.
• Problems in which the objective is to find the best solution with respect to one criterion are referred to as single-criterion decision problems
• Problems that involve more than one criterion are referred to as multicriteria decision problems.
• Qualitative analysis

  is based primarily on the manager's judgment and experience; it includes the manager's intuitive "feel" for the problem and is more an art than a science.
• 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.
• Reasons why a quantitative approach might be used in the decision making process

  • The problem is complex, and the manager cannot develop a good solution without the aid of quantitative analysis
  • The problem is critical (e.g., a great deal of money is involved), and the manager desires a thorough analysis before making a decision
  • The problem is new, and the manager has no previous experience from which to draw
  • The problem is repetitive, and the manager saves time and effort by relying on quantitative procedures to automate routine decision recommendations
• Models

  are representations of real objects or situations and can be presented in various forms.
• In modeling terminology, physical replicas are referred to as Iconic Models
• A second classification includes models that are physical in form but do not have the same physical appearance as the object being modeled. Such models are referred to as analog models.
• • mathematical models A third classification of models—the type we will primarily be studying—includes representations of a problem by a system of symbols and mathematical relationships or expressions.are a critical part of any quantitative approach to decision making.
• Classification of Models

  Iconic Models

  Analog Models

  Mathematical Models
• The purpose, or value, of any model is that it enables us to make inferences about the real situation by studying and analyzing the model.
• constraints a set of restrictions which express limitations on resources.
• The mathematical expression that defines the quantity to be maximized or minimized is referred to as the objective function.
• Factors which can affect both the objective function and constraints are referred to as Uncontrollable Inputs
• Controllable Inputs

  the inputs that are controlled or determined by the decision maker to the model.
• Decision Variables controllable inputs are the decision alternatives specified by the manager.
• Data Preparation

  Another step in the quantitative analysis of a problem is the preparation of the data required.
• Data

  In this sense, refer to the values of the uncontrollable inputs to the model.
• Model Solution

  The analyst attempts to identify the values of the decision variables that provide the "best" output for the model.
• Optimal Solution

  The specific decision-variable value or values that provide the "best" output for the model.
• if a particular decision alternative does not satisfy one or more of the model constraints, the decision alternative is rejected as Infeasible
• Feasible the decision alternative and is a candidate for the "best" solution or recommended decision.
• Fixed Cost

  • is the portion of the total cost that does not depend on the production volume.
  • This cost remains the same no matter how much is produced.
• Variable Cost

  Is the portion of the total cost that depends on and varies with the production volume.
• Marginal Cost is defined as the rate of the total cost with respect to production volume.
• Marginal Revenue is defined as the rate if exchange of total revenue with respect to sales volume.
• The volume that results in total revenue equaling total cost (providing 0 profit) is called the breakeven point
• Linear Programming is a problem-solving approach developed for situations involving maximizing or minimizing a linear function subject to linear constraints that limit the degree to which the objective can be pursued.
• Integer Linear Programming is an approach used for problems that can be set up as linear programs with the additional requirement that some or all of the decision recommendations be integer values.
• Project Scheduling: PERT/CPM

  In many situations managers are responsible for planning, scheduling, and controlling projects that consist of numerous separate jobs or tasks performed by a variety of departments, individuals, and so forth. PERT and CPM help managers carry out their project scheduling and tracking responsibilities.
• PERT

  Program Evaluation and Review Technique
• CPM

  Critical Path Method
• Inventory Models are used by managers faced with the problem of maintaining sufficient inventories to meet demand for goods while incurring the lowest possible inventory holding costs.
• Waiting Line or Queueing Models

  help managers understand and make better decisions concerning the operation of systems involving waiting lines.
• Simulation is a technique used to model the operation of a complex system. This technique employs a computer program to model the operation and perform simulation Computations.
• Decision Analysis

  can be used to determine optimal strategies in situations involving several decision alternatives and an uncertain or risk-filled pattern of future events.