Questions & Answers on Assignment #2, LP Formulation:

Date: Mon, 26 Jan 1998 21:22:10 -0500 (EST)
From: Jiangbin Yang 

> I have question about the assignment #2 (Linear Programming).  In question
> #2, we are asked about the portions of each cargo in each compartment.
> I am just wondering if I am suppose to take the amount in proportions or
> in tons.
> By proportions I mean--- Let x1f(15) from cargo1 is put in the front
> compartment.  
> By amount in tons I mean the weight x1f tons from cargo is put in the
> front compartment.  

You can do it in either way. But, using absolute tons
is more straightforeward than using relative proportions.
Don't confuse Q#2 with Q#1.
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Date: Tue, 27 Jan 1998 15:13:09 -0500 (EST)
From: Jiangbin Yang 

> 	Hi, I am a student in MIE 165S and I have a question with
> assignment #2; When solving Linear Programming Problems(reference to
> question#2), are we allowed to use 2 sets of variables....The only way I
> can solve question two is by using at least 7 variables, which seems like
> too many.  Thanks for your help!

You can use as many variables as they are needed in LP problems,
and all of them consist of 1 set. You don't need 2 sets.
As in Q#2, you will need MORE THAN 7 variables. Think about that
EACH cargo can be distributed among the THREE compartments, then
you can figure out how many necessary decision variables are needed.
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Date: Wed, 28 Jan 1998 12:14:27 -0500 (EST)
From: Jiangbin Yang 

>    I have some questions regard with the second assignment. The major
> problem is to find the variables. I chose the proportion of each alloy as
> the variable for the first question, then I chose the amount of each cargo
> stored in different compartments as variables for the second queation. 
> But I am not sure about it, would you give me some idea?

You are right in defining the decision variables in both q#1
and q#2. Think about how many variables you need in q#2.
Find the objectives correctly, and don't miss any constraint.
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Date: Wed, 28 Jan 1998 12:17:55 -0500 (EST)
From: Jiangbin Yang 

> I did not understand the bonus part of question 2.  Could you please
> send me an explanation for this particular question?  

Total amount of all cargos in each compartment
is proportional to 
the weight capacity in that compartment.
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Date: Wed, 28 Jan 1998 12:27:23 -0500 (EST)
From: Jiangbin Yang 

> 	In question #1, I assigned each alloy with a decision variable 
> (i.e. X1, X2, etc). Then I assigned within each decision variable the 
> percentage of lead, zinc, and tin (i.e. X1 = 20 lead + 60 zinc + 20 
> tin). Is this correct? 
> 	In question #2, I assigned each cargo to have three variable for 
> the front compartment, the centre and the rear (i.e. X1F = portion of 
> cargo 1 in the front compartment, X1C = portion of cargo 1 in the centre 
> compartment, and X1R = portion of cargo 1 in the rear compartment). 
> Would this be correct?

You got right decision variables in q2.
But, you have gone too far in q1.
In q1, you need a decision variable for the proportion of each alloy 
(so, altogether how many?), and you DON'T need any more.
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Date: Wed, 28 Jan 1998 18:42:07 -0500 (EST)
From: Jiangbin Yang 

> I need more explanation about the question.I want some clues to start
> writting constraints.It could be more helpful if you point some starting
> constraints for the problem number two.

First, you'd better find the decision variables you need.
As for the constraints, actually they are stated pretty
clearly in the question. Think about these capacity limits
and the availability of cargos.
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Date: Wed, 28 Jan 1998 21:30:35 -0500 (EST)
From: Jiangbin Yang 

> 	As I understand Problem #2 in Assignment#2 (and as Prof. Jardine
> understands it), if you accept, say, 13 tons of cargo 1, you may put
> it wherever you wish, ie the cargo does not have to be all in the same
> compartment. Therefore, to solve question 2 I only needed four variables,
> x1,x2, x3, and x4 where each represents the number of tons of cargo
> 1,2,3,and 4 taken. With these four variables I believe it is impossible to
> complete the bonus question as it says "Using the decision variables from
> problem 2, add the constraint...." Is something wrong with my
> understanding of the problem and if so, what? 

... "the cargo does not have to be all in the same compartment",
absolutely right. Therefore, to solve BOTH question 2 AND the Bonus 
question, your four variables are DEFINITELY NOT ENOUGH!
Yo must consider the amount of EACH cargo distributed to EACH
compartment.
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Date: Wed, 28 Jan 1998 21:39:12 -0500 (EST)
From: Jiangbin Yang 

> In the second question, there seems to be two possible ways to set up the
> weight constraints. They both seem correct to me and I was just wondering
> if it matters which way we set them up.  
> 
> The variables are as follows:
> x1 = tons of cargo 1 in front
> x2 = tons of cargo 1 in centre
> x3 = tons of cargo 1 in back
> x4 = tons of cargo 2 in front
> x5 = tons of cargo 2 in centre etc etc (up to x12)
> 
> The first way is:
> 15x1 + 9x4 + 18x7 + 10x10 <= 8
> 15x2 + 9x5 + 18x8 + 10x11 <= 12
> 15x3 + 9x6 + 18x9 + 10x12 <= 7
>  (The constraints on the weight capacity of the compartments as well as
> the constraints on the maximum weight of each cargo are together in one
> equation for each compartment)
> 
> 
> 
> The second way is:
> x1 + x4 + x7 + x10 <= 8       x1 + x2 + x3 <= 15
> x2 + x5 + x8 + x11 <= 12      x4 + x5 + x6 <= 9
> x3 + x6 + x9 + x12 <= 7       x7 + x8 + x9 <= 18 
> 			      x10 + x11 + x12 <= 10 				
> 
> (constraints on weight capacity of compartments and on weight of each
> cargo are separate)
>  
> 
> Is there a difference between these two ways of setting up the
> constraints?  Are both ok?	

The 1st way is wrong.  The 2nd way is perfectly right.
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