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Edexcel D2 Transportation Problem

Hi, I am self-teaching D2 and am having trouble grasping how to obtain an improved solution using the stepping-stone method. The question gives a table of costs, and I have firstly used the north-west corner method of getting an initial solution. I have calculated improvement indices, but do not know how to pick a loop in order to improve my solution.

The original question, and my initial solution are shown in the picture, and I have calculated improvement indices
I 1,2 = 2
I 1,3 = 0
I 3,1 = -1
I 3,2 = 2

I'm slightly stuck how to carry on, and any help would be really great, thanks!
d2pic1.bmp423.9KB
Reply 1
Avatar for SsEe
SsEe
13
The index on (3,1) is negative so you want to send goods along that route.

Use the stepping stone method. There's only one possibility: in the initial solution, add x to box (3,1), subtract x from box (2,1), add x to box (2,3) and subtract x from box (3,3). Then pick x to be as large as possible so as to not make any of the boxes in the new solution negative. Then re-test for optimality.
That's really great help, but how do you know which squares you can use? I don't quite understand the rules for the stepping stone method. Thanks :smile:
Reply 3
Avatar for SsEe
SsEe
13
Try to think about what exactly it is you're doing when you use the stepping stone method.
You want to add x items to the route with negative index (that's row 3, column 1). In order to keep the total demand on column 1 in check you need to also subtract x from somewhere in column 1. Similarly, you need to subtract x from somewhere in row 3. And then you keep doing this until everything adds up again. And don't add or subtract from any unused cells except the one you started with.

Have a look at the wiki: http://www.thestudentroom.co.uk/wiki/Revision_Notes:_Transportation_Algorithm
wow, thank-you so much, that's a great help :smile:

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