Sevast'yanov's Algorithm for the Flow-Shop Scheduling Problem

We consider the ow-shop scheduling problem. The objective is to schedule the jobs on the machines so that we minimize the time by which all jobs are completed. We studied and implemented diierent versions of the algorithm of Sevast'yanov based on linear programming to solve this problem. Using CPLEX, we did computational tests with random instances having up to 1000 jobs and 100 machines. If the size of the ow-shop scheduling problem is small or if the running time is not a critical factor, the Nawaz, Enscore and Ham approximation algorithm still performs better. But if the running time is an important factor, Sevast'yanov's algorithm can be a very good alternative especially in presence of very large scale instances with a relatively small number of machines. 1 The ow-shop scheduling problem In the ow-shop scheduling problem we are given a set of m machines fM 1 be processed by at most at one machine at a time. Let C ij be the completion time of operation O ij. The objective is to produce a schedule that minimizes the maximum completion time C max = max i;j C ij. We will also use the following notation: p max = max i;j p ij , i = P n j=1 p ij and max = max i i. In what follows, we just consider permutation schedules, i.e. the sequence in which the jobs are to be processed is the same for each machine. While this restriction is quite standard in the literature, it is important to note that an optimal schedule is not necessarily a permutation one. The study of the ow-shop scheduling problem started with the publication of the paper by Johnson 10] where he proposed a polynomial-time optimization algorithm for the two-machine ow-shop scheduling problem. In spite of the large number of papers in