Operations Research - A Thought - 'Optimization'

Operations Research is one of my favorite topics in Management Science, I view this subject something as “wisdom from God”, the biblical characters that come to mind immediately are Joseph and Daniel who stood in the courts of Kings and answered in wisdom…essentially saving their kingdoms from great destruction.  Genesis 41 verses 25-33 gives us the account about the exceptional wisdom Joseph displays in advising the Pharaoh:

25 Then Joseph said to Pharaoh, "The dreams of Pharaoh are one and the same. God has revealed to Pharaoh what he is about to do. 26 The seven good cows are seven years, and the seven good heads of grain are seven years; it is one and the same dream. 27The seven lean, ugly cows that came up afterward are seven years, and so are the seven worthless heads of grain scorched by the east wind: They are seven years of famine.  28 "It is just as I said to Pharaoh: God has shown Pharaoh what he is about to do. 29Seven years of great abundance are coming throughout the land of Egypt, 30 but seven years of famine will follow them. Then all the abundance in Egypt will be forgotten, and the famine will ravage the land. 31 The abundance in the land will not be remembered, because the famine that follows it will be so severe. 32 The reason the dream was given to Pharaoh in two forms is that the matter has been firmly decided by God, and God will do it soon.  33 "And now let Pharaoh look for a discerning and wise man and put him in charge of the land of Egypt. 34Let Pharaoh appoint commissioners over the land to take a fifth of the harvest of Egypt during the seven years of abundance. 35 They should collect all the food of these good years that are coming and store up the grain under the authority of Pharaoh, to be kept in the cities for food. 36 This food should be held in reserve for the country, to be used during the seven years of famine that will come upon Egypt, so that the country may not be ruined by the famine."

I have little doubt that Joseph  had the gift of knowledge in operational research. He knew exactly the count of how much needed to be saved for the kingdom to survive in the time of famine.  So what is this to do with operational research; it is to display that this subject though neither fully art nor neither fully science (its mixture of economics, statistics, math, physics, conventional wisdom) managers need to effectively use it for business decisions. So what is operations research? In short it is the discipline of applying advanced analytical methods to help make better decisions or in short wiser decisions. To get you interested in my writings here’s to start off with a problem — An optimization problem?

I have a collection of numbers partitioned in two groups such that the resulting difference in the sums is as small as possible:

7, 10, 13, 17, 20, 22 [The total of these numbers sum up to 89]

They can be split for example into [7, 10, 13, 17] where sum is 47 and [20, 22] where sum is 42 the difference between the two sets is 5.

Can you do better?

Note: The amazing thing about this example as you will find out they all lead to solutions that are under 10, often zero or one. It would be extremely hard to achieve without formal optimization.