Minimizing the number of workers in a paced mixed-model assembly line

Abstract

We study a problem of minimizing the maximum number of identical workers over all cycles of a paced assembly line comprised of m stations and executing n parts of k types. There are lower and upper bounds on the workforce requirements and the cycle time constraints. We show that this problem is equivalent to the same problem without the cycle time constraints and with fixed workforce requirements. We prove that the problem is NP-hard in the strong sense if m = 3 and if m = 4 and the workforce requirements are station independent, and present an Integer Linear Programming model, an enumeration algorithm and a dynamic programming algorithm. Polynomial in k and polynomial in n algorithms for special cases with two part types or two stations are also given. The relation to the Bottleneck Traveling Salesman Problem and its generalizations are discussed.

Workforce reconfiguration strategies in manufacturing systems: a state of the art

“…In these studies, workers can be removed from one cell and assigned to another cell in each time period. A similar production line configuration, in which workers can move from one station to another after completing a task in the MMAL, was considered in (Battaïa et al, 2015;Dolgui et al, 2018;Delorme et al, 2019). This movement changes the number of workers assigned to the tasks at stations, which, in turn, either increases or decreases corresponding task processing times.…”

“…In contrast, due to the fact that only one product can be produced by a DMS, there are only few studies regarding workforce reconfigurability (e.g., Corominas et al, 2008;Moreira & Costa, 2009;Stadnicka et al, 2017;Gebennini et al, 2018). On the other hand, a large body of literature is dedicated to workforce assignment problems related to mixed/multi-model assembly lines (e.g., Battaïa et al, 2015;Delorme et al, 2019), since such lines are usually manual. In most cases, see Figure 2, the line's adaptability is achieved by walking workers, who, upon completion of a task, can be assigned to another task at another station.…”

A complex garment assembly line balancing using simulation‐based optimization

“…This involved mapping all the processes and tasks or operations (1-72) assigned to 69 workstations. The line was divided into 11 sections or subassembly processes including front preparation (FP) for making both right and left trouser front (TF) leg (1-5 and 9-14), back preparation (BP) for assembling both right and left trouser back (TB) leg (15 and 17-19, 25-27), side pocket preparation (SPP) for stitching both left and right side pockets (6)(7)(8), back patch preparation (BPP) for making both left and right back patch (16), hip flap preparation (HFP) for preparing both left and F I G U R E 1 Methodology approach for this study…”

“…[5][6][7] However, assembly line balancing is a very complex phenomenon which has been dubbed as a nondeterministic polynomial (NP) hard problem or complex combinatorial problem. 8,9 Despite the fact that research on assembly line balancing dates back to more than a century, it is still of interest to many researchers. This is because assembly line balancing problem (ALBP) is directly related to production efficiency.…”

“…The balancing of assembly lines is an important issue in manufacturing engineering, management, and control 5‐7 . However, assembly line balancing is a very complex phenomenon which has been dubbed as a nondeterministic polynomial (NP) hard problem or complex combinatorial problem 8,9 . Despite the fact that research on assembly line balancing dates back to more than a century, it is still of interest to many researchers.…”