Minimizing the makespan on a single machine subject to modular setups

Single machine scheduling with sequence-dependent setup times is one of the classical problems of production planning with widespread applications in many industries. Solving this problem under the min-makespan objective is well known to be strongly NP-hard. We consider a special case of the problem arising from products having a modular design. This means that product characteristics, (mass-)customizable by customers, are realized by separate components that can freely be combined. If consecutive products differ by a component, then a setup is necessary. This results in a specially structured setup matrix that depends on the similarities of product characteristics. We differentiate alternative problem cases where, for instance, the setup operations for multiple components either have to be executed sequentially or are allowed to be conducted in parallel. We analyze the computational complexity of various problem settings. Our findings reveal some special cases that are solvable in polynomial time, whereas most problem settings are shown to remain strongly NP-hard.