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Solving 'The Assignment Problem' with Lambda
The Setup The problem is simple. Given a 'cost matrix', assign tasks to workers to minimize total cost needed to complete the tasks. Workers may not perform more than 1 task. Assignment p...
In attached file PQ Assignment2 generates the required rows only
Though, it's slower than djclements initial approach (PQ Assignment1)
Really Interesting Problem!! My approach is similar to yours - generate all the permutations and filter for minimum total.
=LET(
workers, Workers,
tasks, Tasks,
matrix, Costs,
nWorkers, ROWS(workers),
nTasks, COLUMNS(tasks),
s, SEQUENCE(, nTasks),
div, nWorkers ^ s,
permuta, ROUNDUP(
(MOD(SEQUENCE(MAX(div)) - 1, div) + 1) / (div / nWorkers),
),
permut, FILTER(
permuta,
BYROW(permuta, LAMBDA(x, COLUMNS(UNIQUE(x, 1)))) = nTasks
),
mat, INDEX(matrix, permut, s),
Ttl, BYROW(mat, LAMBDA(x, SUM(x))),
arr, FILTER(permut, Ttl = MIN(Ttl)),
REDUCE(
tasks,
SEQUENCE(ROWS(arr)),
LAMBDA(a, b,
VSTACK(
a,
LET(
k, CHOOSEROWS(arr, b),
VSTACK(INDEX(workers, k), INDEX(matrix, k, s))
)
)
)
)
)
- Excellent
- This is excellent. I like the way you generated the permutations. It's similar to a method that was discussed in the 0-1 Knapsack discussion. It's short and very elegant.
I folded your formula into 'SolveX' and it handled the larger cost matrix with ease!Patrick2788 Thank you!! Glad to hear it worked on larger matrix.
