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## Re: [Help-glpk] MIP - Simple? Problem

 From: Eric Winter Subject: Re: [Help-glpk] MIP - Simple? Problem Date: Fri, 11 Mar 2016 12:20:41 -0500

Sure,

My intro text was... a bit terse I'll agree, but hopefully the the code explains it.

A possible metaphor for the model is a worker who comes in for three hours a few days a week.
- the worker can arrive at 1,2 or 3 o'clock
- must work 3 sequential hrs in a workday
- the worker can come in on whatever day he wants but is paid most if it is 3 days since he last worked
- the worker must work 6 hours total in a 5 day period.
var Y represents when the worker is present where the row is the day, and the column is the hour of that day.

The optimization problem I'm trying to solve is like a distance optimization. In my case I have a two dimensional binary array (Y) which has 1's in some rows(working), and not in others (not working). I want a cost function based on the distance between rows having data (distance between days worked). So, for example in the code I show an array have 1's in row 0 and 3, this might have a value of 1.0, whereas if the data were in row 1 and 3 the cost should be lower. What is not clear to me is how to use MathProg to weight based on the difference in the row index.

The other part was how to use MathProg to generate a specific pattern within a row in a binary array. In my trivial example I'm saying my worker must work 3 sequential hours, so in my case a the array is a 5x5, a row has 5 element and my pattern happens to be 3 sequential ones so
1 1 1 0 0, 0 1 1 1 0, or 0 0 1 1 1 would all be valid rows

My program succeeds in requiring that there are 3 1's in a given row (3 hours worked in a day), but I can't think of a way of writing a constraint to enforce that only the three candidates above would be feasible (i.e. that the workers hours are sequential).

Is that clearer?

Thanks,

Eric

On Fri, Mar 11, 2016 at 11:32 AM, Andrew Makhorin wrote:

> I have what seems like a simple problem, but I'm not quite sure how to
> I have complex model that I've simplified below. Basically I have a
> MIP problem where I would like to have
>  - three elements in a row and
>  - I would like the non-zero rows optimally spaced.
>