Handling flexibility in a “generalised job shop” with a fuzzy approach

In this paper, we deal with a particular scheduling problem inspired by a practical case coming from a Belgian Pharmaceutical Company. This problem has some particularities with respect to the ‘classical job shop problem’. The principal one is the existence of a delay between the end of an operation and the start of the next operation of the same job. This delay is not fixed but belongs generally to an interval range of possible values. A resolution method (the horizon method) has been proposed in the deterministic case (fixed data and strict constraints). In this method, the horizon time of each machine is discretised by unit times and at each unit time a binary value is associated; all the operations applied on the machines horizons are logic operations (OR, AND, roght or left shifting and so on). Unfortunately, this method does not take into account several aspects of the problem: the existence of a preference relation on the possible values of the delay between successive operations and of flexible due dates. In this work, we modelise such flexible parameters using the fuzzy logic. We propose a new method generalizing the horizon method. This new method tries to find (for the realisation of jobs) a compromise between the choice of good values for the delay between couples of successive operations of the same job and good values for the competion time of the jobs.