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    <p>Maybe you can use a genetic algorithm. This has the advantage that you can do really crazy stuff (if you have set up the basics), e.g. you could also say that a carer should optimally visit a service user he used to visit before, or minimize the distance between visits :)</p> <p>Doing it like that every service user gets a carer even if there is no available schedule. The algorithm just tries to create a optimal solution..</p> <p>Probably it's a bit overkill, but it's an interesting topic.. :) I wanted to mention it because it may be a new way to tackle your problem. At least worth a thought ;)</p> <p>Some Links: <a href="https://stackoverflow.com/questions/509173/genetic-algorithm-resource">Genetic Algorithm Resource</a>, <a href="http://geneticalgorithms.ai-depot.com/Tutorial/Overview.html" rel="nofollow noreferrer">Genetic Algorithm Tutorial</a>, <a href="http://en.wikipedia.org/wiki/Genetic_algorithm" rel="nofollow noreferrer">Wikipedia</a></p> <hr> <p><strong>Edit</strong>: More concrete explanation of genetic algorithms.</p> <p>A genetic algorithm consists of modelling the theory of evolutionary development. Evolutionary development needs a population of certain creatures. Then you simulate the development of the population using certain biological effects like mutation, selection, crossing etc.. Like darwin found out a few years ago :)</p> <p>Now you have to map your problem to such a creature (or a DNA). This means every creature represents a solution in your problem space (every DNA is a solution to your problem).</p> <p>So the phrase "survival of the fittest" just means "I get a solution to my problem which might be optimal" (not guaranteed though).</p> <p>A mapping from your problem to such a DNA can be done very differently. First you need an array to represent your DNA. You can specify for example this:</p> <p>You create chunks of 42 elements for every service user (6 slots per day, 7 days a week). Then your first entry in the array is the "AM"/Mon slot for service user 1. Your second entry the "Lunch"/Mon slot for service user 1. Your 43th entry is the "AM"/Mon slot for service user 2. This defines the DNA of your creature. Then you let them hump each other so they can develop :)</p> <p>In order to find out which creature is well fitted, you also need a formula which calculates the fittness. You create a formula which has a DNA as input and a number as output. This is depending on your rules. For example you can give some plus or minus points if there are certain rules holding or not. If a carer is used for two different service user at the same time you give some minus points, if a carer has actually time for a slot and he is really scheduled for a service user you can give plus points.</p> <p>You can also say: A genetic algortihm tries to find out how to maximize this formula using a genetic approach.</p> <p>Very short introduction to genetic algorithms..if you have enough time and if you're also interested in the topic it's really worth digging into it.. you can some really cool stuff with it. But keep in mind, it can get also messy and complicated :)</p>
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    1. COHmm, I've never heard of genetic algorithms before. It sounds a bit overkill but I will definitely take a look. I can't seem to find much documentation on them though, could you point me in the right direction?
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    2. COAdded in the answer, however, I'm not sure whether they are suitable, if you've never heard of it. Tell me if you need some more hints..
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    3. COAs interesting as GA's are I feel that it is most definitely overkill and probably not going to solve the problem. GA's can be useful in a domain with an unknown solution eg its not immediately obvious how to solve the problem. In this scenario there is an algorithm for how to solve teh problem (its complex but it has a set of well defined rules. A GA here would be an unnecessary complication.
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