Solution: mincut

M+2 layers:

0th and (M+1)th layer for source and sink, M other layers for each role in firm, each containing N nodes.

We aim to minimize the negative of productivity.

Edges:

among all pairs of nodes i,j within same layer, edge of capacity D[i][j] from j to i.

Edge from source to all nodes of layer 1, with capacity MAX-P[i][1].
Edge from all nodes of layer 1 to source, with capacity INF.
Edge from all nodes in layer M to sink  , with capacity INF.

Edge from all nodes in layer (j-1) to corresponding nodes in layer j with capacity P[i][j] for 2<=j<=M
Edge from all nodes in layer j to corresponding nodes in layer (j-1) with capacity INF for 2<=j<=M

where MAX = maximum possible value of P[i][j]

ans = maxflow - N*MAX