Operation Management Exam Two - Spring 2018

18.5 cups in a 5 pound bag of flour how many cups in 20 pound bag pf flour

18.5/5 = x/20

Product mix example WK7 - track capacity constraint, sweatshirt box is three time larger than T shirt

3(Sweatshirt) + (T-shirt) <= 1200

The slope of a curve at its highest point ___

=0

0 - 1 integer restriction

Binary

refers to the ability of an organization to sell products in a market

Business competitiveness

0 - 1 Integer programming modeling

Capital budgeting Fixed Charge and Facility Location Set Covering

Ps

Change in Z/Change in Q

Right hand side

Changes in constraint constant values

Sensitivity ranges can be computed only for the coefficients of the objective function.

False

is not part of a Monte Carlo simulation.

Finding an optimal solution

Select a Solving Method

GRG Nonlinear

Certainty Hypothesis

Mathematical programming assumes that all parameters are known with certainty - Probability violate this - What we've learned so far does not violate this

A transportation example

Supply <= Demand =

3 types of integer programming

Total X1, X2 >=0 and integer 0 or 1 X1234 = 0 or 1 Mixed

Random numbers are equally likely to occur.

True

Unconstrained optimization model

a nonlinear objective function and NO constraints;

Productivity is

efficiency

The slope of a curve at any point is ______ to the derivative of the curve's function

equal

Rounding down

max

The sensitivity range for an objective function coefficient is the range of values over which the current __________________ will remain optimal.

optimal solution

A company can compete on cost by:

producing standardized products for larger markets

Australian road freight company Linfox uses aerodynamic trucks and trailers to reduce fuel consumption. This is a case of generating higher

productivity

Properties of LP problems

proportionality additivity divisibility certainty

Radom number

uniformly distributed sequence reflect no pattern

Western Clothing Company Excel

(p-12)X1 is the profit of X2 P=price 12=cost X1=#

0.2 0.4 0.2 0.1 0.1

0-19 20-59 60-79 80-89 90-99

Set Covering

City constraint >= 1

Six Sigma is a quality management approach that seeks to identify and remove the causes of problems in the operations process, achieving virtually defect-free production. Which of the following will directly contribute to six sigma quality management process?

Continuous improvement of processes Reduce variance in final output Strictly conforming to standards

A Fixed Charge and Facility Location

Decision Variable: Yi = farm is selected or not ; Xi=potato shipped Objective Function Min shipping and Annual Fixed cost S.t - Harvest constraints (potato shipped to plant <= Projected harvest) - Capacity constraints (potato received form farms equal to plant capacity)

Shadow Price

Defined as the marginal value of one additional unit of resource shadow price is same for right hand side

Sensitivity Analysis

Determine the effect on the optimal solution of changes in parameter values of the objective function and constraint equations

A blend example

Max profit: Selling price - cost

32x - 2x^2 + 50

Max value

Facility Location Nonlinear Model Example

Min total mile D = ΣDi*Ti

Sensitivity Range for an obj function Coefficient

Range of value : Current optimal solution point will remain optimal Ci

Cadbury's chocolate operations in Tasmania does produce greenhouse emissions, but is taking steps to reduce those emissions. This is an example of:

Socially responsible and ethical management

A transportation example - Supply side constraint - Demand side constraint

Supply X1a + X1b + X1c <= Warehouse supply of TV Demand: X1a +X2a +X3a = Retail store demand

Western Clothing Company Problem

Take derivative

Standard Form

Variable on left Numerical on right hand side X3-X1-X2>=0

Mutually Exclusive Constraint

X1 + X2 <= 1 (Sum either equal 0 or 1)

Conditional Constraint

X1 >= X2 (X2 is conditional upon X1) or X1 - X2 >=0 or X2 - X1 <=0 when X2 is selected, X1 also need to be selected, not vice versa X2=1 X1=1 X1=1 X2=0 X2=0 X1=0

Total integer Universal Constraint

X1, X2 >= 0 and integer

An investment example - More should be invested in CDs(x2) and treasury bills(x3) than in municipal bonds(x1) and the growth stock fund(x4), by a ratio of at least 1 to 1.2

X2 + X3 >= 1.2 (X1 + X4)

Mixed integer constraint

X2(Acre of land) >= 0 X1, X3 >=o and integer X1= #condo X3= #bond

Capital Budgeting - The store does not have enough space available to create both a computer department(X4) and a clothing department(X3)

X3 + X4 <= 1 (Mutually Exclusive ) Xi = 0 or 1

if project 2 is selected, project 5 must also be selected

X5 >= X2

If project 2 is selected, project 5 must also be selected (Not Vice versa)

X5 >= X2 ; X2 conditional upon X5

A blend example - oil grade OBJ function ?

Z = Total Rev - Total Cost

Profit Function for real-even analysis

Z=vp - Cf - V*Cv

Surplus

amount over the minimum unit, excess >= subtracted

Constrained optimization model has the same ____ except _____

general form as a linear programming model; except that the OBJ function and the constraints are nonlinear

Optimizing variance in final output can augment

quality

sensitivity range for a right hand side value

range of value over which the quantity value can change without changing the solution variable mix

The Lagrange multiplier reflects the appropriate change in the objective function resulting from an unit change in the ________ of the constraint equation.

right-hand side

A fixed charge and facility location example - minimum total cost, including annual fixed costs and shipping costs is sign of what ?

sign of two type of decision variable Yi:farm is selected or not (0,1) Xij: potatoes shipped from Fram i to plant j

Simulation results will not equal analytical results unless enough trials have been conducted to reach

steady state

Lagrange Multiplier

the dual value of a constraint. Analogous to the shadow price. It reflects the approximate change in the objective function resulting from a unit change in the quantity (right-hand-side) value of the constraint equation.

Random numbers generated by a mathematical process instead of a physical process are pseudorandom numbers.

true

Sensitivity analysis is a way to deal with uncertainty in linear programming models.

uncertainty

Slack

unused resources <= added

For a minimization integer linear programming problem, a feasible solution is ensured by rounding ________ non-integer solution values if all of the constraints are the greater-than-or-equal-to type.

up

Cont - facility location nonlinear model example Di =? Ti=?

where Di = Distance to rescue facility Ti = # annual trips

In a "capital budgeting" problem, if either project 1 or project 2 is selected, then project 5 cannot be selected. Which of the alternatives listed below correctly models this situation?

x1 + x5 ≤ 1, x2 + x5 ≤ 1