On the exact solution of the no-wait flow shop problem with due date constraints - Samarghandi, Hamed; Behroozi, Mehdi (Computers & operations research, 2017)
•Five different mathematical programming models and two constraint programming models are developed for the no-wait flow shop problem with due date constraints.•Unique characteristics of the problem are discussed and a number of propositions are proved; an exact algorithm that takes advantage of such characteristics is designed.•Solving and implementation complications are discussed in detail.•Thorough computational experiments are performed to compare the performance of the developed models and algorithms. This paper deals with the no-wait flow shop scheduling problem with due date constraints. In the no-wait flow shop problem, waiting time is not allowed between successive operations of jobs. Moreover, the jobs should be completed before their respective due dates; due date constraints are dealt with as hard constraints. The considered performance criterion is makespan. The problem is strongly NP-hard. This paper develops a number of distinct mathematical models for the problem based on different decision variables. Namely, a mixed integer programming model, two quadratic mixed integer programming models, and two constraint programming models are developed. Moreover, a novel graph representation is developed for the problem. This new modeling technique facilitates the investigation of some of the important characteristics of the problem; this results in a number of propositions to rule out a large number of infeasible solutions from the set of all possible permutations. Afterward, the new graph representation and the resulting propositions are incorporated into a new exact algorithm to solve the problem to optimality. To investigate the performance of the mathematical models and to compare them with the developed exact algorithm, a number of test problems are solved and the results are reported. Computational results demonstrate that the developed algorithm is significantly faster than the mathematical models.