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MIS655 Woodlands University Nonlinear Optimization Problems Discussion

MIS655 Woodlands University Nonlinear Optimization Problems Discussion

Question Description

Please answer the following questions using a minimum of 250 words for each question. Each question should include at least one reference.

Topic 3 DQ 1

Description:

Before computers were widespread, almost all risk analysis was done without simulation. Therefore,

only a handful of scenarios could be formulated to understand the risk of a decision. Typically, a

best-case and worst-case scenario was determined and decisions were based on these two

scenarios. What are some of the drawbacks of this decision-making approach? Specifically, how

does the capability to summarize 1,000s of simulated scenarios improve the approach?

Topic 3 DQ 2

Description:

By definition, simulations require a distribution to be specified (e.g., normal, Poisson). Many times,

the exact distribution to be used is unknown, so it must be assumed. One argument against using

simulations to perform risk analysis is that there is no real benefit because the set of assumptions is

simply shifted from assumed parameter values to assumed distributions of parameters. Comment on

this argument and justify your opinions with reasons, facts, and examples.

Topic 4 DQ 1

Description:

Many times, linear optimization is used to maximize an objective function because profit, productivity,

or efficiency is the outcome of interest. Provide two examples where the goal is to optimize a process

by minimizing an objective function. In your examples, identify the outcome and any constraints that

would need to be met.

Topic 4 DQ 2

Description:

When many constraints are present in a linear optimization problem, there is a greater chance that a

redundant constraint exists. Assume you are trying to maximize an objective function and you have

two decision variables, X1 and X2. If a redundant constraint exists, does the constraint become

necessary if you try to minimize (instead of maximize) the same objective function? Why? Do you

need an objective function to determine if a constraint is redundant? Explain.

Topic 5 DQ 1

Description:

Many linear optimization problems can be solved by finding a graphical solution, but there are some

problems that require more advanced spreadsheets and software to find an optimal solution.

Describe an optimization problem in which finding a solution would be impossible using the

feasible-region approach. Discuss the attributes the problem would have to make it impossible to

solve using the feasible-region approach.

Topic 5 DQ 2

Description:

Optimization techniques are used in many applications. For example, when customers order products

from an online store, the shipper has to determine the optimal way to get the product delivered to the

customer. The delivery path that is chosen is the path that minimizes shipping costs while

simultaneously satisfying these constraints:

The product must arrive by a promised date.

The shipper must deliver a finite set of items.

The product must originate from one of several warehouse hubs across the country.

Discuss whether there can be multiple solutions (i.e., more than one path to get the product to your

house). Explain why. Is there a guarantee that a solution always exists? Explain.

Topic 6 DQ 1

Description:

Most transshipment network modeling problems assume the costs are constant. For example, the

costs of shipping a product from one city to another are assumed fixed. This can change over time if

fuel costs change. If you knew the distribution of fuel costs, how could the distribution of fuel costs be

incorporated into the transshipment problem? Discuss the benefits of employing this approach.

Topic 6 DQ 2

Description:

Minimum spanning trees were initially design to solve electrical grid problems but now have many

more applications such as computer networks, transportation networks, and supply networks.

Describe a business problem where minimum spanning trees can be used to find a solution.

Topic 7 DQ 1

Description:

Can linear and nonlinear optimization problems use the same approach to find a solution? For

example, if the GRG algorithm is used to solve a nonlinear optimization problem, will it work to solve

a linear optimization problem? Discuss whether or not the GRG algorithm will always find a corner

point similar to the feasible-region approach.

Topic 7 DQ 2

Description:

Nonlinear optimization problems can have multiple solutions, and a solution can be local or global.

Can there be multiple local solutions? Explain your answer. Can there be multiple global solutions?

Explain our answer.

Topic 8 DQ 1

Description:

Betamax (or Beta) was a video recording format developed by Sony in the 1970s. Sony conducted

research and found that consumers wanted a high-quality picture when using a Beta cassette with

their home recording equipment. Sony developed the technology with video quality in mind and, as a

consequence, limited the recording time to only 60 minutes.

At the same time, JVC developed the Video Home System (VHS) but without much consumer

research. JVC was more interested in developing a unified standard for broadcast operations.

Consequently, they focused more on extending the recording time for their VHS cassettes at the

expense of picture quality.

In the end, the VHS format won by eventually squeezing the Beta format out of the market. Discuss

the approaches these two companies took in the good decisions/good outcomes context.

Topic 8 DQ 2

Description:

Suppose you received two job offers when looking for a job, one from Company A and one from

Company B. To make a decision, what type of methodology would you use: probabilistic or

nonprobabilistic? Whichever you choose, describe the items to consider and the decision rules you

would use before deciding which job offer to accept.


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