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