No-Wait Job Shop Scheduling, a Constraint Propagation Approach

Abstract

Multi-machine scheduling problems have earned themselves a reputation of intractability. In this thesis we try to solve a special kind of these problems, the so-called no-wait job shop problems. In an instance of this problem-class we are given a number of operations that are to be executed on a given set of machines. Thereby each operation is pre-assigned a machine, an operation-specific processing time, an operation-specific release date and deadline. Between some of the operations we are given constraints like: One operation has to start some fixed number of time-units after another operation has finished processing. We try to solve such instances using a method called `constraint propagation'. The term `constraint propagation' thereby refers to the method of acquiring and propagating knowledge from one aspect of a problem instance to another one. This process is carried out until nothing can be propagated anymore. In this case we assume a possible characteristic of a solution in one branch and propagate this characteristic to the rest of the instance, while we assume the opposite characteristic in another branch. In this thesis we derive new methods to acquire and propagate knowledge for no-wait job shop instances, so-called `propagators'. These new methods are stronger than the ones found in literature, and are designed to use special features of the no-wait job shop instances. Furthermore, we give some special-designed methods to detect that a given no-wait job shop problem instance does not admit a feasible schedule at all. However, our experiments indicate that some of the methods to detected infeasibility become useless once we used a certain combination of the special designed propagators proposed in this thesis. Moreover, we investigate the connection between constraint propagation and an ILP formulation of the no-wait job shop problem. We show that there is a characterization of some of the strongest possible inequalities of this ILP in terms of propagators and some easy-to-check helper properties. These characterizations allow us to give an algorithm that finds valid inequalities that are violated by a given point of the LP relaxation of the ILP, and an algorithm that strengthens given valid inequalities.