Blog >> Optimised way of having trading in Singapore

When Singapore was marked as one of the busiest port for trading, there was an extensive discussion between the panel consisting of great minds, how to reduce the congestion by optimising the traffic. The traders were not satisfied because their freights had to wait for days on the shore such that they can de board their goods on the port and as we all know, each hour delay is inversely proportional to the chance you get to do the business with same entity again.

So with the adverse effect of the traffic in my mind , researchers were given task to give the optimised value such that it can be told to the logistic company earlier such that, there won't be any traffic as such in future.

While undergoing the study, it was understood that the trade of crude oil was the important factor for which port traffic was a major issue of concern. So the primary objective was to optimise the trade of crude oil.

Scientist named Uchiyama.T wrote a paper from which he formulated an empirical formula which gave the relationship between the cost and the Size if refinery and tankers

The equation was verified and was ready to solve, to solve a multi-variable non-linear equation there are many methods to solve, but the problem arises what to choose, because the each method is problem centric. If we choose a wrong method, there is a chance for infinite looping or cycling in lay man's word which may not yield in the answer required.

Thus with intense analysis in this this blog I have showed two methods

Cost = 12.5+0.5+0.9+((2.09*10000*B2^0.3017)/360)+((1.064*1000000*0.2*B2^0.4925)/(52.47*A2*360))+((4.242*10000*0.2*B2^0.7952+1.813*0.1*7000*(2*B2+1.2*A2)^0.861)/(52.47*(A2)*360))+((4.25*1000*0.2*(2*B2+1.2*A2))/(52.47*A2*360))+((5.042*1000*(A2)^0.1899)/360)+((0.1049*(A2)^0.671)/360)

 

Simplex method Algorithm:

1. The iteration was initialised by guessing three vertices of the triangle i.e. (120000, 181865), (110000, 110000), (130000, 110000).

2. The least required vertices was found out, that is the coordinate which has the highest cost.

3. The centroid with the two remaining vertices using the formula was calculated

 Xbar = (X1 + X2)/2

4. Reflection process: Found out the new vertices by the formula

 X4 = Xbar + (Xbar - X high)

5. Now the least required vertices will be replaced by the new vertices.

6. From Step 1, the process was repeated

7. To terminate the cycle:

 

Xnew = X centroid + alpha (Xcentroid-Xhigh)

Alpha was varied from 0.9 to 0.1 until the cost was decreased.

8. From step 1 the process was repeated with new alpha

9. The iteration was stopped when any other value of q and t gave higher C value.

 

 

Result:

Cauchy's method Algorithm:

 

1. Starting point of iteration was guessed which was (110000, 275000)

2. The direction of the search is determined by (dcdt, dcdq), negative because the objective is to minimise the cost. (Steepest decent).

3. The formula used to find dcdq:

 

(-56.33*0.2*B2^0.4925/A2^2)-(2.246*0.2*B2^-0.7952/A2^2)-(0.06718*((417*A2+5000*B2)/(332.7*A2^2*(6*A2+10*B2)^0.139)))-(0.0899*B2/A2^2)-(2.66*A2^-1.1899)+(0.0001955*A2^-0.329)

Dcdt:

(-17.51*B2^-1.3017)+ (5.548*B2^-0.5075)/A2+ (0.3571*B2^-0.2048)/A2+ (0.0899/A2)

4. The step size was calculated by solving the quadratic equation formulated by

 

f(x+a) - f(x), where a, is the magnitude of the step size

5. Step size multiplied with direction gave term to be added to get the new point.

6. Then from step 1 the process was repeated again.

 

Result: 

From both the results we can say:

The optimum tanker size = 485272.3 KL

The optimum refinery capacity = 185762.3 bbl /day

The minimum cost = 17.88 $/KL

- Written By

Shravan Muthukrishnan