Exam 12: Advanced Optimization Applications

The interpretation of the dual price for nonlinear models is different than the interpretation of the dual price for linear models.

The logic of a DEA model is to determine whether _________ facility can achieve the same or more output than ________ facility while requiring less input.​

Native Customs sells two popular styles of hand-sewn footwear: a sandal and a moccasin.The cost to make a pair of sandals is $18,and the cost to make a pair of moccasins is $24.The demand for these two items is sensitive to the price,and historical data indicate that the monthly demands are given by S = 400 − 10P₁ and M = 450 − 15P₂ ,where S = demand for sandals (in pairs),M = demand for moccasins (in pairs),P₁ = price for a pair of sandals,and P₂ = price for a pair of moccasins.To remain competitive,Native Customs must limit the price (per pair)to no more than $60 and $75 for its sandals and moccasins,respectively.Formulate this nonlinear programming problem to find the optimal production quantities and prices for sandals and moccasins that maximize total monthly profit.

List several industries in which revenue management has been applied and list several different types of decisions being made with the aid of the methodology.​

Skooter's Skateboards produces two models of skateboards,the FX and the ZX.Skateboard revenue (in $l,000s)for the firm is nonlinear and is stated as (number of FXs)(5 − 0.2 number of FXs)+ (number of ZXs)(7 − 0.3 number of ZXs).Skooter's has 80 labor-hours available per week in its paint shop.Each FX requires 2 labor-hours to paint and each ZX requires 3 labor-hours.Formulate this nonlinear production planning problem to determine how many FX and ZX skateboards should be produced per week at Scooter's.

The overall goal of portfolio models is to create a portfolio that provides the best balance between

Nonlinear programming algorithms are more complex than linear programming algorithms.

A feasible solution is a global optimum if there are no other feasible points with a better objective function value in the feasible region.

The function f (x,y)= x ² + y ² has a single global minimum and is relatively easy to minimize.

Explain the logic of a DEA model.On what basis can the facility being evaluated be judged as relatively inefficient?​

Revenue management methodology was originally developed for the banking industry.

Revenue management methodology enables an airline to maximize the number of full-fare seats it sells on each flight.

The objective for the Markowitz portfolio model is to minimize portfolio return variance.

The output shows the solution to a DEA model where facilities in Seaview (S),Farmington (F),Lewiston (L),and San Domingo (D)are compared.The inputs,in order,are number of machines,size of work force,and goodness of location.The outputs,in order,are production,quality rating,and on-time completion percentage.The model examines the efficiency of Lewiston. OPTIMAL SOLUTION Objective Function Value = 0.510 $\text { Min } 0 \mathrm {~S} + 0 \mathrm {~F} + 0 \mathrm {~L} + 0 \mathrm { D } + 1 \mathrm { E }$ S.T. 1) $1 \mathrm {~S} + 1 \mathrm {~F} + 1 \mathrm {~L} + 1 \mathrm { D } = 1$ 2) $5 \mathrm {~S} + 22 \mathrm {~F} + 36 \mathrm {~L} + 15 \mathrm { D } - 36 \mathrm { E } < 0$ 3) $400 \mathrm {~S} + 1500 \mathrm {~F} + 3150 \mathrm {~L} + 1060 \mathrm { D } - 3150 \mathrm { E } < 0$ 4) $24 \mathrm {~S} + 13 \mathrm {~F} + 32 \mathrm {~L} + 17 \mathrm { D } - 32 \mathrm { E } < 0$ 5) $800 \mathrm {~S} + 2900 \mathrm {~F} + 1860 \mathrm {~L} + 1700 \mathrm { D } + 0 \mathrm { E } > 1860$ 6) $95 \mathrm {~S} + 92 \mathrm {~F} + 83 \mathrm {~L} + 94 \mathrm { D } + 0 \mathrm { E } > 83$ 7) $83 \mathrm {~S} + 85 \mathrm {~F} + 90 \mathrm {~L} + 91 \mathrm { D } + 0 \mathrm { E } > 90$ Variable Value Reduced Cost S 0.000 0.385 F 0.167 0.000 L 0.000 0.490 D 0.833 0.000 E 0.510 0.000 Constraint Slack/Surplus Dual Price 1 0.000 1.365 2 2.208 0.000 3 474.479 0.000 4 0.000 0.031 5 40.000 0.000 6 10.667 0.000 7 0.000 -0.021 a.Is the Lewiston plant efficient? Why or why not? If not,which plants should it emulate in order to improve? b.How much more production does the composite facility provide than the Lewiston site? c.What is the quality rating for the composite facility?

Provide several examples of both nonlinear objective functions and nonlinear constraints.​

In the case of functions with multiple local optima,most nonlinear optimization software methods can get stuck and terminate at a local optimum.