MSIS final exam

Excel Functions to Avoid in Linear Optimization

-ABS -IF -MIN and MAX -INT -ROUND COUNT

what is the default integer tolerance in excel solver?

5%

descriptive model of total cost

= Fixed Cost + Variable Cost * Quantity Produced •Also written as C=F+VQ

descriptive model of variable cost

= Unit Variable Cost * Quantity Produced

Solver

An add-in application that manipulates variables based on constraints to find the optimal solution to a problem.

general integer variables

Decision variables that are forced to be integers

Variable Cost of Production

Logic suggests that variable cost is the unit variable cost times the quantity of item produced.

one way data tables

Multiple outputs may be evaluated using ______________-examples include profit and revenue

which type of decision variables are used to model yes-or-no decision?

binary variables

Balance Constraints

essentially state that input = output and ensure that the flow of material or money is accounted for at locations or between time periods.

all nonlinear optimization models have nonlinear constraints

false

in predictive modeling, verification refers to how well a model represents reality

false

rectilinear distance is the measure of a distance as a straight line between two points

false

to find the guaranteed optimal integer solution, integer tolerance must be set to 1

false- must be set to zero

quadratic optimization model

has a quadratic objective and all constraints are linear.

optimal solution

includes any set of decision variables that optimizes the objective function. To guarantee finding an optimal solution, some type of systematic mathematical solution procedure is necessary.

infeasible problem

is one for which no feasible solution exists—that is, when there is no solution that satisfies all constraints simultaneously.

Cash budget

is the process of projecting and summarizing a company's cash inflows and outflows expected during a planning horizon, usually 6 to 12 months. also shows the monthly cash balances and any short-term borrowing used to cover cash shortfalls

unique optimal solution

it means that there is only one solution that will result in the maximum (or minimum) objective.

spreadsheet models

often called spreadsheet engineering, is part art and part science. Spreadsheets need to be accurate, understandable, and user friendly

Proportional Relationship constraints

often found in problems involving mixtures or blends of materials or strategies.

problem statements such as production must be sufficient to meet promised customer orders, would be categorized as a_________________ constraint

requirement

alternative optimal solutions

the objective is maximized (or minimized) by more than one combination of decision variables, all of which have the same objective function value exists when any of the allowable increase or allowable decrease values for changing cells are zero.

Constraints in an Optimization Model

these are limitations, requirements, or other restrictions that are imposed on any solution, either from practical or technological considerations or by management policy

a quadratic optimization model is one that has a quadratic objective and all linear constraints

true

absolute value functions in optimization models, result in non smooth functions

true

decision variables that we force to be integers are called general integer variables

true

integer linear optimization models are simply linear models with added constraints on variables to ensure that they are integer valued (that is whole numbered)

true

many optimization models require binary variables, which are variables that are restricted to being either 0 or 1

true

requirements involve the specifications of minimum levels of performance

true

supply chain optimization is one of the broadest applications of integer optimization and is used extensively today as companies seek to reduce logistic costs and improve customer service in tough economic environments

true

the feasible region is the set of points that satisfy at least one constraint

true

nonlinear optimization model.

which the relationship among variables in a model is not linear

Solving a linear optimization model can result in four possible outcomes

•A unique optimal solution •Alternative (multiple) optimal solutions •An unbounded solution •Infeasibility

what is the spreadsheet model for profit is revenue minus variable cost minus fixed cost

•Profit = Revenue - Variable Cost - Fixed Cost

feasible solution•

•a set of values for the decision variables that satisfy all of the constraints. Linear programs generally have an infinite number of feasible solutions. The feasible region is the set of points that satisfy all constraints simultaneously

Constraints

•are expressed as algebraic inequalities or equations, with all variables on the left side and constant terms on the right. Look for key words in word statements of constraints: "cannot exceed"= _<_ "at least"= _>_ "must contain exactly"= "=" •All constraints in optimization models must be one of these three forms.

binary variables

•are variables that are restricted to being either 0 or 1.

Simple Bound constraints

•constrain the value of a single variable.

Two-way data tables

•evaluate only one output variable. To evaluate multiple output variables, you must construct multiple two-way tables.

Predictive Decision Models

•focus on understanding the future. •usually involve multiple time periods. •incorporate the uncertainty element.

Demand

•has an influence on profit by predicting how many units of a product will be sold. Quantity produced is a decision option typically based on __________.

unbounded

•if the value of the objective can be increased or decreased without bound (that is to infinity for a maximization problem or negative infinity for a minimization problem) without violating any of the constraints. This generally indicates an incorrect model, usually when some constraint or set of constraints have been left out.

default Integer Tolerance value

•in Excel solver is 5%. The value of Integer Tolerance should be zero in order to find the guaranteed optimal integer solution?

Requirement constraints

•involve the specification of minimum levels of performance.

Optimization models

•is the most important tool in prescriptive analytics. •the process of selecting values of decision variables that minimize or maximize some quantity of interest. •used extensively in operations and supply chains, finance, marketing, and other disciplines. •Objective function is the quantity that is to be minimized or maximized.

Integer Tolerance

•is the parameter that specifies when the Solver algorithm will terminate an optimization process with integer constraints.

Verification

•is the process of ensuring that a model is accurate and free from logical errors.

Solver Answer Report

•provides basic information about the solution, including the values of the original and optimal objective function and decision variables.

integer linear optimization model

•some or all of the variables are restricted to being whole numbers.

Limitation constraints

•usually involve the allocation of scarce resources.

data validation feature

•which allows you to define acceptable input values in a spreadsheet and provides an error alert if an invalid entry is made. This can help you avoid inadvertent user errors.