Optimal workforce assignment to operations of a paced assembly line

- A paced line is designed to assemble different types of products in large series.
- Workers can move among stations to adapt workstation capacities to workloads.
- The problem is to minimize the total number of workers employed at the line.
- Computational complexity for various special cases of the problem is established.
- Heuristics and integer linear programs are developed, numerical tests are reported.

We study a paced assembly line intended for manufacturing different products. Workers with identical skills perform non-preemptable operations whose assignment to stations is known. Operations assigned to the same station are executed sequentially, and they should follow the given precedence relations. Operations assigned to different stations can be performed in parallel. The operation's processing time depends on the number of workers performing this operation. The problem consists in assigning workers to operations such that the maximal number of workers employed simultaneously in the assembly line is minimized, the line cycle time is not exceeded and the box constraints specifying the possible number of workers for each operation are not violated. We show that the general problem is NP-hard in the strong sense, develop conventional and randomized heuristics, propose a reduction to a series of feasibility problems, present a MILP model for the feasibility problem, show relation of the feasibility problem to multi-mode project scheduling and multiprocessor scheduling, establish computational complexity of several special cases based on this relation and provide computer experiments with real and simulated data.