Skip to main content

Posts

Questions based on dynamic programming

Q.1 The owner of a chain of four grocery stores has purchased six crates of fresh strawberries.The estimated probability distribution of potential sales of the strawberries before spoilage differ among the four stores.The following table gives the estimated total expected profit at each store, when it is allocated various numbers of crates:                                                                     Store                                                                  1          2          3            4              ...

THE UNINVITED (Indian After Partition)

I never gave thought on how drastically people are changing. The only way I can see humanity being defined is CART FULL OF HUSK ­­­­ – dry, emotionless, and ignite into blazes by spark of information which can be fully or partially true or by one which has nothing to do with the truth. Last night’s event shook me from within. “Who bought her here?”-Shouted a women shrieking voice, enough to make people near-by go deaf. Pitch high enough to give complex to an Opera singer. “I am here to attend my best friend’s marriage. She invited me.” Said the girl in low defensive voice. By now, people gathered around the two. “Don’t you understand my daughter invited you out of courtesy? You yourself should not have come here. You have Lung Cancer and it is highly communicable, especially for those who breathe in same air.” I saw people covering their nose and stepping back muttering among themselves that how insensitive and careless she is towards other member of society. My glance fle...

Graphical Method to Solve a Linear Programming Problem

The graphical method is applicable to solve the LPP involving two decision variables x 1 , and x 2 , we usually take these decision variables as x, y instead of x 1 , x 2 . To solve an LPP, the graphical method includes two major steps: a)   The determination of the solution space that defines the feasible solution.  Note that the set of values of the variable x 1 , x 2 , x 3 ,....x n which satisfy all the constraints and also the non-negative conditions are called the feasible solutions of the LPP. b)   Finding the optimal solution from the feasible region. a)To determine the feasible solutions of an LPP, we have the following steps: Step 1: Consider only the first quadrant of xy-coordinate plane(because both the variables x 1 and x 2 are non-negative). Step 2: Each equation is of the form ax+by≤c or ax+by≥c. Draw the line ax+by=0. For each equation, the line divides the first quadrant into two region...

PARTITION OF INDIA

It was mid-night. I was done crying and cursing myself for opting here to get some “adventure” in final year of my graduation. Before me were lying  Saapadu and a mug of coffee, both completely untouched. Finally I decided to pack my bags and return to my hometown, my people...Delhi. I was in  Karumathampatti , a suburb of Coimbatore city in the state of Chennai. My summer internship was in BHEL and was scheduled in May. I was given an option to join the company’s zonal office which was in my hometown but I chose to go to some place far, where I would be able to discover myself, my shortcomings, someplace where I can live free and breathe free. Actually it had been so long since last I stepped out of Delhi so I found it to be best opportunity to flee from mind-numbing daily routine. Scorching heat of summers welcomed me from airport. I was ready for my voyage but the only problem I was able to see till now was language problem. South Indian cuisine was something I cheri...

Finding MYSELF through partition of INDIA

It was mid-night. I was done crying and cursing myself for opting here to get some “adventure” in final year of my graduation. Before me were lying  Saapadu and a mug of coffee, both completely untouched. Finally I decided to pack my bags and return to my hometown, my people...Delhi. I was in  Karumathampatti , a suburb of Coimbatore city in the state of Chennai. My summer internship was in BHEL and was scheduled in May. I was given an option to join the company’s zonal office which was in my hometown but I chose to go to some place far, where I would be able to discover myself, my shortcomings, someplace where I can live free and breathe free. Actually it had been so long since last I stepped out of Delhi so I found it to be best opportunity to flee from mind-numbing daily routine. Scorching heat of summers welcomed me from airport. I was ready for my voyage but the only problem I was able to see till now was language problem. South Indian cuisine was something I cheris...

Big-M Method and Two-Phase Method

Big-M Method The Big-M method of handling instances with artificial  variables is the “commonsense approach”. Essentially, the notion is to make the artificial variables, through their coefficients in the objective function, so costly or unprofitable that any feasible solution to the real problem would be preferred, unless the original instance possessed no feasible solutions at all. But this means that we need to assign, in the objective function, coefficients to the artificial variables that are either very small (maximization problem) or very large (minimization problem); whatever this value,let us call it Big M . In fact, this notion is an old trick in optimization in general; we  simply associate a penalty value with variables that we do not want to be part of an ultimate solution(unless such an outcome is unavoidable). Indeed, the penalty is so costly that unless any of the  respective variables' inclusion is warranted algorithmically, such variables will ...

SIMPLEX METHOD

Simplex method is an iterative procedure that allows to improve the solution at each step. This procedure is finished when it isn't possible to improve the solution. Simplex method is based on the following property: if objective function, F, doesn't take the max value in the A vertex, then there is an edge starting at A, along which the value of the function grows. You should take care about Simplex method only works with "≤" type inequality and independent coefficients higher or equal to zero, and you will have to standardize the restrictions for the algorithm. Case after this procedure "≥" o "=" type restrictions appear (or not modified) you should try other ways, being Two-Phase Simplex method the best choice. Model of the problem is prepared to adapt it to the Simplex Method This is the standard way of the model: Objective function: c 1 ·x 1  + c 2 ·x 2  + ... + c n ·x n Subject to: a 11 ·x 1 ...