Question

(c) What is a blending problem? Briefly discuss the objective function and constraint requirements in a blending problem. Give a real world example of a blending problem.

(d) Explain how the simulation process is used in business analytics models. What are the advantages of using simulation? What are its limitations? How can a simulation model be verified? Give a real world example where using simulation is appropriate.

Answer 1

Ans c)

Blending problems are a typical application of mixed integer-linear programming (MILP). They involve blending several resources or materials to create one or more products corresponding to a demand. Mixed integer-linear programs are linear programs in which some variables are required to take integer values.

Objective function represents how the decision variables affect the cost or value to be optimized (minimized or maximized)

Constraints represent how the decision variables use resources, which are available in limited quantities

Example 1: To determe the optimum amounts of three ingredients to include in an animal feed mix. The final product must satisfy several nutrient restrictions. The possible ingredients, their nutritive contents (in kilograms of nutrient per kilograms of ingredient) and the unit cost are shown in the following table.

The mixture must meet the following restrictions:

• Calcium — at least 0.8% but not more than 1.2%.
• Protein — at least 22%.
• Fiber — at most 5%.

The problem is to find the composition of the feed mix that satisfies these constraints while minimizing cost.

Nutritive content and price of ingredients Ingredient Calcium (kg/kg) Protein (kg/kg) Fiber (kg/kg) Unit cost (cents/kg) Limestone 0.38 0.0 0.0 10.0 Corn 0.001 0.09 0.02 30.5 Soybean meal 0.002 0.50 0.08 90.0

Example 2: Predator-Prey Problem

Ans d)

Business analytic model uses simulation modeling and analysis as mechanisms to introduce and link predictive and prescriptive modeling because managers can't fully assess what will happen in the future, but must still make decisions, the book treats uncertainty as an essential element in decision-making.

Advantages

• It can avoid danger and loss of life.
• Conditions can be varied and outcomes investigated.
• Critical situations can be investigated without risk.
• It is cost effective.
• Simulations can be sped up so behaviour can be studied easily over a long period of time.
• Simulations can be slowed down to study behaviour more closely.

Limitations:

• It can be expensive to measure how one thing affects another, to take the initial measurements and to create the model itself (such as aerodynamic wind tunnels).
• To simulate something, a thorough understanding is needed and an awareness of all the factors involved. Without this, a simulation cannot be created

Following are the ways to perform verification of simulation model −

• By using programming skills to write and debug the program in sub-programs.
• By using “Structured Walk-through” policy in which more than one person is to read the program.
• By tracing the intermediate results and comparing them with observed outcomes.
• By checking the simulation model output using various input combinations.
• By comparing final simulation result with analytic results.

Example:

The popular series Call of Duty and in particular Call of Duty: Modern Warfare 2 provides a glimpse of an immersive environment which parallels many real world scenarios of law enforcement as well as military. Medical: The medical field uses simulations to train practitioners in a multitude of skills and environments.

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