There was a time when the only source of transportation for humans was on foot. But the invention of the wheel changed the game, as it allowed them to cover longer distances than before without expending as much energy. Further inventions such as steam locomotives and airplanes have only expanded this distance limit. And now, with the advent of rockets, spacecraft, and rovers, we have begun to explore other planets in our solar system that are millions of kilometers away!
On a higher level, we can understand that our world-class engineers are in the business of expanding our horizons. However, on a much deeper level, they are indeed grappling with the challenges like improving the conversion efficiency of fuel energy into mechanical energy, refining engine designs, and developing better materials.
For example, consider the example of steam engines. When these engines were invented, they marveled the world with their ability to perform mechanical work using water. However, this process had limitations in terms of efficiency due to significant heat loss during the boiling of water to produce steam. Later, internal combustion engines addressed this limitation by utilizing a fuel and air mixture instead of water. This innovation ensured minimal heat loss and improved overall efficiency.
In essence, we can visualize this process as striving to overcome a limitation (like efficiency), resulting in the desired outcome of pushing the boundaries (like distance limit). This concept bears a resemblance to the expansive domain of operations research, where mathematical techniques are employed to solve similar problems.
While operations research doesn't directly deal with the intricacies of thermodynamics to enhance conversion efficiency, its main focus lies in allocating the finite resources at our disposal to achieve some form of advancement.
Let us divert from the boring engineering language and enter the risky profession of theft for now.
Imagine that you have devised an intricate plan to carry out a heist on an antique store, intending to rob it under the cover of darkness. You have your trusty backpack ready to hold the stolen goods. After successfully breaking in and deftly disabling the alarms and security cameras, you realize the store is brimming with valuable items just waiting to be taken. It's as if you're a child in a candy store. In an ideal world, you could empty the entire store and make your escape without a trace. However, the reality is not perfect. You lack a getaway van and an infinite-capacity backpack. Consequently, your only option is to snatch as much as you can, cram it into your backpack, and sprint like a crazed dog being chased, knowing that the police might appear at any moment. But be cautious, overloading the backpack beyond its capacity will cause it to tear apart, leading your entire mission to go down the drain.
Therefore, there is a weight limit imposed on the items that your backpack can accommodate, let's say 5 kilograms for now.
You have these items that you could readily grab and run:
| Serial Num | Item | Weight (kg) | Value (grand) |
|---|---|---|---|
| 1 | Antique lamp | 0.5 | 6 |
| 2 | Porcelain figurine | 1.5 | 5 |
| 3 | Antique clock | 0.4 | 4 |
| 4 | Vintage Painting | 1 | 4 |
| 5 | Vintage music player | 1.1 | 3 |
| 6 | Decorative art piece | 1.6 | 4 |
| 7 | Retro typewriter | 0.8 | 1 |
Now, which of these items would you choose to pack in your backpack? Unfortunately, you cannot steal all of them since their combined weight (6.9 kg) exceeds the backpack's capacity of 5 kg. Since your objective is to maximize the profit from selling the stolen goods, you wouldn't want to randomly grab whatever you can.
Here, you decide to take out the calculator, compute the value unit weight of each item holds, and make a decision based on that.
| Serial Num | Item | Weight (kg) | Value (grand) | Value/Weight |
|---|---|---|---|---|
| 1 | Antique lamp | 0.5 | 6 | 12 |
| 2 | Porcelain figurine | 1.5 | 5 | 3.33 |
| 3 | Antique clock | 0.4 | 4 | 10 |
| 4 | Vintage Painting | 1 | 4 | 4 |
| 5 | Vintage music player | 1.1 | 3 | 2.73 |
| 6 | Decorative art piece | 1.6 | 4 | 2.5 |
| 7 | Retro typewriter | 0.8 | 1 | 1.25 |
Based on these numbers, you decide to carry the first five items and leave the decorative art piece and retro typewriter at the store. You make a huge profit of 22 grand later by selling these items, which enables you to sleep peacefully at night with a feeling of accomplishment.
But what if I told you that you could have made an extra grand if you left out the vintage music player in favor of the decorative art piece?
Operations research (OR) suggests that the optimal solution for this heist is to seize items 1, 2, 3, 4, and 6, which would result in a total profit of 23 grand.
OR is all about making one or more decisions to hit that sweet spot in terms of our objective. And when we say an objective, we don't always need to think about maximizing the profit. Sometimes, we could slightly tweak the scenario to look at the problem from a different direction.
Let's continue with the previous example, imagine that you aim to steal items that would generate a profit of at least 20 grand. However, considering the possibility of a police chase, you prioritize minimizing the weight of the backpack to lighten your load. Therefore, our objective is to minimize the backpack's weight while ensuring a constraint on the minimum required profit.
Mathematically speaking, this objective is captured by an 'objective function'. The choice between a maximization objective (such as profit) or a minimization objective (such as weight or cost) is entirely situational and depends on the specific scenario and your priorities.
In a similar vein, the restrictions you imposed on the backpack weight and minimum profit mirror the finite resources found in the real world. These limitations are captured by the "constraints" component in the mathematical formulation.
And this problem originated because you had to choose among the seven available items. Mathematically, this can be represented by seven binary decision variables, where each variable corresponds to an item (1 indicating chosen and 0 indicating not chosen).
Now, let's shift our focus to the entirely unrelated realm of business, where each day presents you with numerous decisions to make. These decisions are akin to the question of "Which items should I steal?" in the previous example. A decision made without the support of a systematic approach like OR can lead to a solution that deviates significantly from the optimal one. At times, this difference can be crucial in determining whether your company faces bankruptcy or emerges as a leading player in its industry.
OR is an extensive field that already has a significant impact on various aspects of our lives. Therefore, understanding how to formulate real-life decision-making problems into OR problems can be a valuable skill.
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