Every organizations create decisions to pursue their goals on a regular basis: Whether they want to maximize profits, cutting costs or maintaining particular level of threshold, these decisions made is crucial. Operations Research is a scientific approach for decision making by utilizing mathematical models such that they represent the situation of system. These models are usually formed as optimization models and consist of three main components: objective function(s), decision variables and constraints.
Objective function(s) are the equations we want to optimize, whether it is maximization or minimization. For example, a small coffee shop wants to maximize daily revenue from two of their most popular products, americano and cappuccino, with the price of 5 Euro and 3 Euro respectively. Hence, the objective functions would be:
max đ„0 = 5đ„đ + 3đ„c
đ„0 represents revenue (objective function value), đ„đ serves as the number of americano sold and đ„đ means the number of cappuccinos sold. đ„đ and đ„đ are called decisions variables: controllable variables and impact the objective functions value. The goal of Operations Research is determining value of these variables to optimize the objective functions.
Constraints are equations that restrain decision variables value because of certain reasons. Back to our example, let say the owner could only afford 2 kilogram of coffee beans each day. If each americano needs 150 grams of beans and cappuccino needs 100 grams of beans, then the constraint would be:
150đ„đ + 100đ„đ †2000
This equation tells us that the weights of beans required for both products are prohibited to exceed 2000 grams. Hence, this equation indirectly restricts the number of decision variables value to a certain threshold. Note that this example is just one of many methods in Operations Research and some approaches have different representation for some problems.
According to Operations Research: Applications and Algorithms (Winston,1987), solving a problem with Operations Research requires to follow this seven-step procedure:
(1) Formulate the problem
(2) Observe the system
(3) Formulate the mathematical model of the problem
(4) Verify the model and use the model for prediction
(5) Select a suitable alternative
(6) present the result and conclusion to the organization
(7) Implement and evaluate recommendations
These steps assure that the problem-solving process is structured and scientific while still aligned with the organizationsâ objectives and goals.
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