Analytics 2321

profit

(selling price per unit)(# of units) - (fixed cost) - (variable cost per unit)(# of units)

criterion of realism

- a compromise of pessimism and optimism approaches to decision making under uncertainty - uses the weighted average - a is between 0 and 1, 0 being pessimistic and 1 being optimistic - (a)(maximum payoff for alternative) + (1-a)(minimum payoff for alternative)

maximin

- a pessimistic approach to decision making under uncertainty - finds the alternative that maximizes the minimum payoff over all decision alternatives

linear programming models

- all problems seek to maximize or minimize some quantity (usually profit or cost) - goal is to find an optimal solution that achieves the best value for the objective function while abstaining to all constraints - which limit the degree to which an objective function can be obtained - must be alternatives available - all mathematical relationships are linear

decision analysis

- an analytic and systematic way to tackle problems - good decisions = based on logic - bad decisions = do not consider all alternatives

equally likely

- an approach to decision making under uncertainty that finds the decision alternative that has the highest average payoff - calculate the average payoff for each decision and then pick the alternative with the maximum average payoff

minimax regret

- an approach to decision making under uncertainty that is based on opportunity loss (regret) - finds the alternative that minimizes the maximum opportunity loss

maximax

- an optimistic approach to decision making under uncertainty - selects the decision alternative that maximizes the maximum payoff over all alternatives

right hand side value of a constraint

- changes in these values could affect the size of the feasible region, becomes smaller if this is decreased in a binding (<=) constraint - increasing this in a nonbinding (<=) constraint does not affect the optimality of the current solution - the location of the optimal corner point changes if this changes in a binding constraint - usually represent the amount available of the resource (<=) or the minimum satisfaction level needed (>=) and are likely to have uncertainty, therefore are studied under sensitivity analysis

constraint coefficients

- coefficients for the decision variables in model's constraints (many times represent design issues) - not usually known to have uncertainty and therefore are not usually studied by sensitivity analysis

decision making under certiantity

- decision makers know for sure the payoff for every decision alternative - typically only one outcome for each alternative

sensitivity analysis

- involves examining how sensitive the optimal solution is to changes in profits, resources, or other input parameters - determines how the solutions will change with a different model or input data

decision node

- lines originating from this on a decision tree denote all decision alternatives available to the decision maker at that point, and the decision maker must then select only one alternative - begins a decision tree - at each one, we choose the alternative that yields the better expected payoff

outcome node

- lines originating from this on a decision tree denote all outcomes that occur at that point, of these, only one will occur - at each one, we compute the EMV, using the probabilities of all the outcomes at that point and the payoffs associated with them

deterministic

- models that assume that all relevant input data values are known with certainty, that is, they assume that all of the information needed for modeling a decision making problem is available with fixed and known values - most common technique is LP

expected value of perfect information

- places an upper bound on what to pay for any information - EVwPI - maximum EMV

objective function

- represents the motivation for solving a problem - goal is either to maximize or minimize

shadow price

- the change in the objective function value for a one-unit increase in a constraints RHS value - valid only for a certain range of change in a constraints RHS value (allowable increase and allowable decrease) - value for a nonbinding constraint = 0

expected opportunity loss

- the cost of not picking the best solution - the weighted average of all possible regrets for that alternative, where the weights are the probabilities of the different outcomes - will always result in the same decision as the maximum EMV

decision making under risk

- the decision makers have some knowledge regarding the probability of occurrence of each outcome - decision makers attempt to identify the alternative that maximizes their expected payoff - expected monetary value, expected opportunity loss and expected value of perfect information

reduced cost

- the difference between the marginal contribution of a variable and the marginal worth of the resources it uses - the minimum amount by which the OFC of a variable should change in order to affect the optimal solution

expected value with perfect information

- the expected payoff if we have perfect information before a decision has to be made - choose the best payoff for each outcome and multiply it by the probability of occurrence of that outcome

break even point

- the number of units sold that will result in total revenue equaling total cost - fixed cost / (selling price per unit-variable cost per unit)

feasible region

- the overlapping area on our graph that satisfies all the constraints at the same time - the optimal solution to an LP model must lie at one of the corner points of this (to solve for the coordinates of the corner points, use the substitution method for the two intersecting constraints) - often unbounded in minimization problems - if the size increases, the optimal objective function value could improve

decision making under uncertianty

- the probabilities of the various outcomes are unknown to the decision makers - maximax, maximin, criterion of realism, equally likely oe minimax regret

decision variables

- the unknown entities in a problem - the problem is solved to find values for these - different ones in the same model can be measured in different units

objective function coefficient

-the coefficients for the decision variables in the objective function - changes in these values do not affect the size of the feasible region but a new corner point could possibly become optimal - usually unit profits or costs, and therefore are likely to have uncertainty and are studied under sensitivity analysis

steps of decision making

1) clearly define the problem 2) list all possible decision alternatives 3) identify the possible future outcomes for each alternative 4) identify the payoff for each combination of alternatives and outcomes (use payoff tables) 5) select one of the decision analysis modeling techniques, apply it, and make your decision

linear programming assumptions

1) conditions of certainty exist 2) proportionality exists in the objective function/constraints 2) the total of all activities equals the sum of the individual activities (additivity) 3) divisibility exists (solutions need not be in whole numbers)

steps of linear programming

1) formulating a problem scenario in terms of simple mathematical expressions 2) solving mathematical expressions to find values for the variables 3) perform a sensitivity analysis to answer "what-if" questions regarding a problems solution

problems with decision modeling

1) real-world problems are not always easily identifiable 2) the problem needs to be examined from multiple viewpoints, and these may conflict with one another 3) all inputs must be considered 4) incorrect beginning assumptions 5) solution can become outdated during the process and be useless by the time its over

expected monetary value

the weighted average of possible payoffs for each alternative

formulation, solution, and interpretation

three steps to decision modeling

variable

a measurable quantity that is subject to change

parameter

a measurable quantity that usually has a known value

decision modeling

a scientific approach to decision making

infeasibility

can occur if constraints conflict with one another

redundant constraint

does not affect the feasible solution region

interpretation

final step in the decision modeling process that involves analyzing the results, conducting a sensitivity analysis and then implementing the results (closely monitored)

break even point $

fixed cost + variable costs x BEP

binding

means the constraint is exactly satisfied and the RHS = LHS

probabilistic

models that assume that some input data values are not known with certainty, that is, they assume that the values of some important variables will not be known before decisions are made

formulation

most challenging step in decision modeling process that involves defining the problem, developing a model (physical, scale, schematic or mathematical) and then acquiring input data (GIGO)

qualitative factors

pending state and federal legislation, technological breakthroughs, the outcome of an upcoming election, etc.

product mix

problems that use linear programming to decide how much of each product to make, given a series of resource restrictions

quantitative factors

rates of return, financial ratios, cash flows, etc.

constraints

represent restrictions on the values the decision variables can take

solution

step in the decision modeling process that involves solving mathematical expressions created by the formulation and then testing our answers

opportunity loss

the difference between the optimal payoff and the actual payoff received