CA5103 PRELIMS

objective function

is the function that needs to be optimized (either maximized or minimized). Examples are profit functions and cost functions

constraint

is a limitation on the resources (such as materials and labor) or a requirement that must be complied (such as laws or material specification).

linear programming problem

consists of a linear objective function to be maximized or to be minimized subject to certain constraints in the form of linear equations or inequalities

sensitivity or post-optimality analysis

is the analysis of the effect of change in one or more parameters (change in the objective function coefficient or right-hand side) defining a linear programming model.

profit contribution

refers to the objective function coefficient c1 and c2 .

total profit contribution

refers to the objective function value Z

the optimal solution to the original linear programming problem has been obtained

analysis does not begin until

no effect on the feasible region, it only changes the slope of the objective function line

Changes in the OFC (c1 and c2) have

range of optimality

a range for each OFC (c1 and c2 ) where the current optimal corner point (or optimum solution) remains optimal is callled

a different corner point will become optimal

If the slope changes beyond the Range of Optimality and the OFC (c1 or c2) changes beyond that range

binding constraint

constraints where the left-hand side and the right-hand side are equal upon substituting the optimum solution (x1 , x2 ) to the constraint expression

slope of the objective function line is between the slope of the two binding constraints

the solution is kept optimal as long as the

less negative and the slope increases

Rotating the objective function line counterclockwise causes the slope to become

more negative and the slope decreases

Rotating the objective function line clockwise causes the slope to become

the extreme point to be nonoptimal

Any further counterclockwise or clockwise rotation of the objective function line will cause

non-binding constraint

a constraint where no optimal solution is on the line for the constraint.

binding constraint

if a constraint whose rhs or resources are fully consumed, it is a

nonbinding constraint

if a constraint whose rhs or resources are not fully consumed, it is a

positive

the shadow price/dual value of a maximization problem is generally assumed to be

negative

the shadow price/dual value of a minimization problem is generally assumed to be

Profit new - Profit old/Cost new - Cost old

formula for shadow price

shadow price/dual value

change in the value of the optimal solution per unit increase in the right-hand side of the constraint

range of feasability

the range over which the shadow price/dual value is applicable. (or allowable increase or decrease in the constraint)

worsen, improve

Tightening the binding constraints can _______ the objective function value & loosening it can __________ the objective function value.

non-zero, zero

a binding constraint always has a _________ value of shadow price while a non-binding constraint has a value of __________

negative shadow price

indicates that the objective function will not improve if the RHS is increased

only one coefficient changes assuming all other coefficients remain

sensitivity analysis information in computer output is based on the assumption that

summation of proposed change/allowable change of OFC or RHS

what is the formula of the 100% rule

simultaneous changes, changes in constraint coefficients, and non-intuitive dual values

three limitations of classical sensitivity analysis

vertex or corner point

If a linear programming problem has a solution then it must occur at a

optimized at every point on the line segment joining these vertices

if the objective function 𝑍 is optimized (either maximized or minimized) at two adjacent vertices of 𝑆, then it is

both maximum and minimum value on S

If S is bounded, then 𝑍 has

minimum value on S provided that constraint defining S include nonnegativity constraints

If S is unbounded and both 𝑎 and 𝑏 are nonnegative, then 𝑍 has

no solution

If S is the empty set, then the linear programming problem has

infinitely many solutions given by the points on the line segment

If two adjacent corner points satisfy the objective, then there are

right-most

For maximization problems, the ____________ corner point intersected by the isoprofit line is the optimal solution

left-most

For minimization problems, the ____________ corner point intersected by the isocost line is the optimal solution.

infinitely many solutions given by the points on the line segment

If an objective function line coincides with the rightmost (leftmost) line segment, not just a corner point, then there are

-c1/c2

Assuming an objective function Z=C1x+C2y, then the slope of the objective function is

Constraints

the uncontrollable restrictions, requirements, or regulations

input-output (technology) variables

indicate the rate at which a given resource is depleted or utilized

capacities (availability) of the various resources

usually expressed as some upper or lower limit, can also express minimum requirements

limits to the decision variables

positive, negative, unrestricted

maximization of expected return or minimization of risk.

The objective function of financial problems usually is

conduct the survey so as to meet the client's needs at a minimum cost.

The marketing research firm's objective is to

Problem formulation or modeling

is the process of translating a verbal statement of a problem into a mathematical statement.

art

Formulating models is an _________ that can only be mastered with practice and experience.

unique features, but most problems also have common features.

Every LP problem has some

time-series

sequence of observations on a variable measured at successive points in time or over successive periods of time

horizontal, trend, seasonal, trend & seasonal, cyclical

types of patterns and trends in time series

horizontal pattern

data fluctuates around a constant mean

stationary time series

time series whose statistical properties are independent of time

horizontal pattern with a shift

changes in conditions that result in a shift to a new level

trends

show gradual shifts or movement over a long period of time

seasonal pattern

recognized by recurring patterns over successive periods of time

seasonal pattern

repeated behavior in the data that occurs at regular intervals

cyclical pattern

shows alternating sequence below or above the trend line of points that lasts more than a year

cyclical

the series follows an up-and-down movement with no regular intervals

random pattern

This pattern has no distinct crests and troughs. There could be a general trend but variation is __________

irregularities

strange dips or jumps that may occur due to a one-off event

naive forecasting method

simplest of all forecasting methods

naive forecasting method

uses the most recent observations in the time series as the forecast for the next period

forecast error

difference between the forecast and actual demand at the same time period

positive, negative, and forecast bias

types of forecast errors

positive forecast error

it indicates that forecasting method underestimated the actual value

negative forecast error

it indicates that forecasting method overestimated the actual value

forecast bias

it refers to the persistent tendency for forecasts to be greater or less than the actual values of the time series

mean absolute error (MAE), mean squared errors (MSE), and mean absolute percentage error (MAPE)

types of measures of forecast accuracy

mean absolute error (MAE)

obtained by getting the average of the absolute values of the forecast errors

mean squared error (MSE)

obtained by getting the average of the squared forecast errors

mean absolute percentage error (MAPE)

obtained by getting the average of the absolute value of the percentage forecast errors

demand, economic, and technology

major areas of forecasting

demand forecasting

predicts the timing and quantity of demand of a firm's commodities

technology forecasting

predicts possible technological advancements in the future

economic forecasting

predicts the future business condition with reference to economic factors

causal models

quantitative forecasting models wherein the variable forecasted is influenced by or correlated with other variables

regression analysis

the purpose of this analysis is to understand the relationship between two variables and to predict the value of one based on the other

correlation analysis

this analysis is used to measure the strength of the linear relationship between two variables

p<0.05

What should be the p-value in order to reject the null hypothesis H0?

time-series models

these are quantitative forecasting models that attempt to predict future values by using historical data

qualitative models

these are forecasting models based on judgmental or subjective factors

delphi method, jury of executive opinion, sales force composite, and consumer market survey

types of qualitative forecasting models

delphi method

this model allows experts in different places to make forecasts

jury of executive opinion

this forecasting method uses the opinions of a small group of high-level managers

sales force composite

it is a forecasting approach where salespersons estimate what sales will be in the district and national levels

consumer market survey

this forecasting method solicits ideas from customers or potential customers in order to modify or create products

demand, economic, and technology forecasting

major areas of forecasting

define the problem

determine the set of alternative solutions

determine the criteria for evaluating alternatives

evaluate the alternatives

choose an alternative

implement the decision

evaluate the results

seven steps in problem solving

decision making process

Steps 1-5 in problem solving are considered as __________

structuring the problem and analyzing the problem

two classifications of the decision making process

step 1-3

steps included in structuring the problem

4-5

steps included in analyzing the problem

single-criterion decision problems

refer to problems in which the object is to find the best solution with respect to one criterion

multicriteria decision problems

refer to problems that involve more than one criterion