A Mathematical Model for Job Shop Scheduling with Resource Availability Constraints

摘要

A common assumption carried by most of the machine scheduling literature is that machines are supposed to be always available to process jobs. However it is not true when a machine breaks down or a preventive maintenance activity is scheduled. It is thus interesting to study the possibility for an operation to be interrupted due to machine unavailability. In this paper we take into account all possible cases for an operation to be interrupted or not by an unavailability period and we present a general mathematical model. In our knowledge there is no study which includes all these cases. In this paper we also introduce flexibility on starting dates of unavailability periods which means that an unavailability period can start in a time window defined by an earliest and a latest starting dates. This flexibility is relevant when scheduling a preventive maintenance. Numerical experiment on generated benchmarks were performed with ILOG CPLEX 10.