Decision Making: Deterministic and Probabilistic Models

• Decisions are classified by degree of certainty: deterministic models (complete certainty, unique payoff) and probabilistic models (probability measure attached to payoffs).
• The scale of assumed certainty ranges from complete certainty to complete uncertainty.
• Decision making under certainty (DMUC) and decision making under uncertainty (DMUU) are at opposite ends of the scale.
• Decision-making under risk (DMUR) is the region between the extremes and relates to probabilistic models.
• Most decision-making problems fall under decision making under risk, where degree of certainty is one aspect.
• Classifications also considers linear/non-linear behavior, static/dynamic conditions, and single/multiple objectives.
• Decision theory addresses decision making under conditions of risk and uncertainty.
• Quantitative decision models help managers identify optimal or the best actions.
• Before exploring decision theory, it is important to consider questions such as "What is a decision?" and "Why must decisions be made?".

What is a Decision?

• A decision concludes a process to weigh utilities or merits of options, for selecting the best action for implementation.
• Decision-making involves selecting the best choice to satisfy a desired goal or objective.
• The decision-making process encompasses goals, priorities, methods to enumerate alternatives, and a system for identifying the most favorable option.
• Decisions are sequential; selecting an alternative prompts further questions (e.g., what quantity is needed?).

Why Decisions Must Be Made

• Management's core involves making decisions that commit resources to achieve organizational goals.
• Decision theory aids in making choices that best meet needs when resources are limited.
• Decisions facilitate achieving goals and objectives.

Decision and Conflict

• Individual behavior and mentality within a group in an organization may spark conflicts.
• Departments in an organization may have conflicting objectives subordinate to an organizational goal.
• Decision makers must balance factors to minimize conflicts between departments to achieve the overall objective.

Phases of Decision-Making Process

• Decision theory has an important position due to contributions of diverse disciplines.
• Two phases of the decision-making process:
  • Formulating goals/objectives, enumerating constraints, identifying strategies, and projecting payoffs.
  • Choosing the optimal strategy given objectives, strategies, and payoffs.

Classifications of Decisions

• Strategic decisions relate to an organization's external environment.
• Administrative decisions structure resources.
• Operational decisions address day-to-day problems.
• Programmed decisions solve repetitive, well-structured problems.
• Non-programmed decisions solve non-routine problems.
• Decisions can be divided as individual and managerial based on scope, complexity, and the number of people involved.
• Decisions can be divided as static (requiring one decision for the planning horizon) and dynamic (requiring a series of decisions) based on the sphere of interest.

Decision Theory Approach Steps

• List viable alternative strategies for the decision.
• List future events that can occur called "states of nature".
• Construct a payoff table for each alternative course of action and state of nature combination.
• Choose the criterion that yields the largest payoff.

Decision Making Under Certainty (DMUC)

• Relies on deterministic models with complete knowledge, stability, and no ambiguity.
• Managers must understand strategies and their unique certain payoffs.
• Decision-making can have single or multiple objectives.

Decision Making Under Risk (DMUR)

• Each strategy results in multiple outcomes/payoffs, with probability measures attached.
• The probability distribution of outcomes is known/assumed.
• Key assumptions:
  • Availability of multiple strategies.
  • Existence of multiple states of nature.
  • Knowledge of relevant outcomes.
  • Probability distribution of outcomes.
• The optimal strategy exhibits the highest expected utility or value.

Decision Making Under Uncertainty

• Formulated like decision making under risk, except no probability to each strategy is assigned.
• Components: states of nature and strategies with utilities or payoffs.
• Characteristics:
  • More than one state of nature.
  • Multiple column matrix.
  • Uncertain outcomes.
• Optimal strategy identified using number of criteria.

Criterion of Optimism

• Determine the best possible outcome in each strategy, and then to identify the best outcome to select the optimal strategy.
• The process is also known as Maximax.

Criterion of Pessimism

• Applied to solve problems under uncertainty, determine the worst possible outcome/row minimum in each strategy and the best of the worst outcome to select the optimal strategy.
• Maximin assumes complete pessimism.

Criterion of Regret

• Determine the regret matrix/opportunity loss matrix by subtracting all column elements from the column's highest element.
• The select such a strategy whose opportunity loss is zero (zero regret).

Equal Probability Criterion

• If no objective evidence of probability distribution, use equal probabilities for each state of nature.
• Known as Laplace criterion or criterion of insufficient reason.

Decision Making Under Conflict and Competition

• Two rationale competitors are required to select optimal strategies .
• Strategies of each party are known to both opponents and both opponents choose their strategies simultaneously.
• Two opponents are considered as two players, we adopt the convention that a positive payoff will mean a gain to the row player A or maximizing player, and a loss to the column player B or minimizing player.

Hurwicz Criterion (Criterion of Realism)

• Compromise between maximax and maximin criteria.
• Assign weights to the best and the worst outcomes by degree of optimism or pessimism.
• To select the alternative that maximizes the sum of weighted payoffs.

Decision Trees

• A schematic representation of a decision problem.
• Single-stage problems (data isn't revised).
• Multistage problems (the outcome of one decision affects subsequent decisions).
• Decision trees has two types of nodes: decision node (represented by a square) and chance node, plus branches, estimates of probability, and payoffs.
• Decision branches: strategy or course of action.
• Chance branch: chance determined event with respective probabilities.
• Terminal branch: end of a decision tree without another decision or chance node.
• Negative or possitive payoffs are associated with decision branch or a chance branch.
• Decision trees can be deterministic or probabilistic (stochastic).
• Can represent a single-stage (one decision) or a multistage (a sequence of decisions) problem.