Maximize Production Capacity with Prescriptive Analytics

Management Science is an approach to decision making based on the scientific method that makes extensive use of quantitative analysis. In today’s world, many use the terms management science, operations research, optimization, prescriptive analytics, decision science interchangeably.

One of the most significant management science applications developed by the operation research (OR) group came about as a result of the deregulation of the airline industry in late 1970. Consequently, a number of low-cost Airlines were able to move into the market by selling seats at a fraction of the price charged by established carriers such as American airlines. OR group suggested offering different fare classes (discount and full fare) and, in the process, created a new area of management science. The OR group was able to achieve this by using forecasting and optimization techniques to determine how many seats to sell at a discount and how many seats to hold for full fare.

Let us understand what decision making is and what are the two approaches by which we can take decisions.

Problem-solving can be defined as the process of identifying the difference between the actual and desired situation and then taking action to resolve the difference. In contrast, Decision making is the term generally associated with the first five steps of the problem-solving process. Thus, the first step of decision making is to identify and define the problems.

Decision making ends with the choice of an alternative, which is the act of making the decisions. An example of decision making can be a student who needs to decide which job to choose based on job evaluation data that leads to decision-making problems.

Making a choice from the available alternatives is difficult. If the student decides that salary is the only criteria, then his decision will be referred to as single criteria decision making if he selects multiple options along with salary, like location and potential advancement then his decision will be multi-criteria decision-making.

And in the real world, it becomes even more complex to solve. This leads to two approaches, called the Qualitative approach and Quantitative approach.

The Qualitative Approach is based primarily on your judgment and experience. It includes your intuitive “feel” for the problem and is more of an art than science. A simple example is a manager taking decision for his company based on his experience.

The Quantitative Approach is followed when the problem is complex, then Quantitative Analysis of the problem can be an important consideration for your final decision.

Using the quantitative approach, an analyst will concentrate on the quantitative facts or data associated with the problem and develop mathematical expressions that describe the objective, constraint, and relationships.

Linear programming is used when the objective function and the constraints of the problem can be expressed as linear equations of decision variables. Such comes under prescriptive analytics, which helps in providing the optimal solution to a problem. Traditionally, Operations Research (OR) techniques are used for finding the optimal solution to a problem. Many machine learning algorithms use optimization techniques such as gradient descent while solving a problem.

Based on the above understanding, let us try to solve a product mix problem that comes under linear programming.

“Maximize production capacity of a Manufacture”

Suppose two products need to be manufactured: Tables and Chairs.

To manufacture a product requires two resources:  budget ($) and labor (man-hours) The resources required to manufacture each product and the total available amounts of each resource are given in the table below:
Such Linear/Integer programming problems can have a significant influence on the profitability of organizations. Modern-day issues can have several millions or billions of decision variables and are solved using sophisticated software tools such as IBM CPLEX and FICO Xpress, GAMS. Such problems can also be solved using R (library ROI, lP solver, optimx), Python (library pulp), and even excel using solver.

While experimenting on various tools like GAMS, Excel Solver, R, and Python, we identified optimal solution is 3 tables and 6 chairs. When using the Branch and Bound algorithm, there could be a scenario where multiple optimal solutions exist. We then leverage a qualitative approach in decision making.

Reference:

  • An Introduction to Management Science by Anderson Sweeney Williams Martin
  • Business Analytics by Prof U Dinesh Kumar

 

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