Time-constrained project scheduling with adjacent resources

We develop a decomposition method for project scheduling problems with adjacent resources. Adjacent resources are resources for which the units assigned to a job are required to be in some sense adjacent. Possible examples of adjacent resources are dry docks, shop floor spaces, and assembly areas. We focus on the Time-Constrained Project Scheduling Problem (TCPSP), [4], with one 1-dimensional adjacent resource. However, the presented concepts and methods can be easily extended to more general models, e.g. multiple 1-dimensional adjacent resources or 2-dimensional adjacent resources. The Time-Constrained Project Scheduling Problem (TCPSP) with an adjacent resource is defined as follows. We are given a set of jobs, a set of renewable resources and one 1-dimensional adjacent resource. Each job is characterized by a release date, processing time, deadline and its resource requirements, and has to be scheduled without preemption. The processing of jobs is further restricted by precedence relations. The adjacent resource is a special type of resource that is characterized by two properties. First, the resource units of adjacent resource are somehow topologically ordered (in this case ordered on a line) and the resource units assigned to a job have to be neighbored/adjacent and reassignment is not allowed. Second, motivated by the occurrence of adjacent resources in real life problems, we consider the more general case that the adjacent resource is not required only by a single job but by groups of jobs (called job