Machine scheduling with job delivery coordination

This paper considers together machine scheduling and finished product delivery. In particular, it addresses the situation in which jobs require different amounts of storage space during delivery. Three scenarios of the problem are discussed. For the problem in which jobs are processed on a single machine and delivered by a single vehicle to one customer area, we provide a proof of NP-hardness and a heuristic with worst-case analysis. The worst-case performance ratio for our heuristic is proven to be 5/3, and the bound is tight. For the problem in which jobs are processed by either one of two parallel machines and delivered by a single vehicle to one customer area, our heuristic could cause at most 100% error under the worst-case with the bound being tight. For the problem that considers jobs to be processed by a single machine and delivered by a single vehicle to two customer areas, we provide another heuristic that is 100% error bound.