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