Although there are numerous methodologies and research studies on machine scheduling, most of the literature assumes that there is an unlimited number of transporters to deliver jobs from one machine to another for further processing and that transportation times can be neglected. These two assumptions are not applicable if one intends to generate an accurate schedule for the shop floor. In this research, a flowshop scheduling problem with two machines, denoted as M1 and M2, and a single transporter with capacity c is considered. The main focus is on the development of a dynamic programming algorithm to generate a schedule that minimizes the makespan. The transporter takes t1 time units to travel with at least one job from machine M1 to machine M2, and t2 time units to return empty to machine M1. When the processing times for all n jobs on machine M1 are constant, denoted as pj1≡p1, and the capacity of the transporter c is at least ()12121−⎥⎥⎤⎢⎢⎡+ptt, the computational complexity of the proposed algorithm is shown to be .
Progress in Material Handling Research: 2010
Mendoza, Abraham; Ventura, Jose A.; and Huang, Kwei Long, "A Flowshop Scheduling Problem With Transportation Times and Capacity Constraints" (2010). 11th IMHRC Proceedings (Milwaukee, Wisconsin. USA – 2010). 22.