Worker Scheduling Algorithm

Question

The Problem

Here\'s the essence of the problem I want to solve. We have workers taking care of children in a nursery for set times during the weekend. There\'s 16 diff

Answer 1

In case anyone comes across a similar problem, here's the solution I went with:

I ended up using a Backtracking Search Algorithm for Constraint Satisfaction Problems. All it does it do a normal backtracking search but checks that all constraints are satisfied as it traverses the tree. Here is the pseudo-code:

function BACKTRACKING-SEARCH(csp) returns a solution, or failure
     return BACKTRACK({ }, csp)

function BACKTRACK(assignment, csp) returns a solution, or failure
     if assignment is complete then return assignment
     var = SELECT-UNASSIGNED-VARIABLE(csp)
     for each value in ORDER-DOMAIN-VALUES(var, assignment, csp) do
        if value is consistent with assignment then
           add {var = value} to assignment
           result = BACKTRACK(assignment, csp)
           if result != failure then
              return result
           remove {var = value} 
     return failure

The variable is a time slot. The possible values assigned to a variable are the workers. The combination of a variable and its actual assignment is a node in the tree. Thus the search space is all the possible combinations of time slots and workers. The constraints prune nodes from the search space.

A constraint can be a workers availability. So if time slot A is assigned Worker X, but X is not able to work in time slot A, then this node will be ruled inconsistent.

I solved the problem of a particular time slot being assigned multiple workers by considering each time slot / worker combination to be it's OWN time slot. So if the childrens' nursery has 2 workers to fill, I consider it as two individual time slots to fill, each getting assigned its own worker. That way each variable is assigned just one value. It makes for MUCH simpler algorithms.

Thanks for all the help whittling this down to a solvable problem.