Eugeniusz Nowicki

A fast tabu search algorithm for the permutation flow-shop problem

Abstract A fast and easily implementable approximation algorithm for the problem of finding a minimum makespan in the permutation flow shop is presented. The algorithm is based on a tabu search technique with a specific neighborhood definition which employs a block of jobs notion. Computational experiments (up to 500 jobs and 20 machines) show its excellent numerical properties.

An Advanced Tabu Search Algorithm for the Job Shop Problem

The job shop scheduling problem with the makespan criterion is a certain NP-hard case from OR theory having excellent practical applications. This problem, having been examined for years, is also regarded as an indicator of the quality of advanced scheduling algorithms. In this paper we provide a new approximate algorithm that is based on the big valley phenomenon, and uses some elements of so-called path relinking technique as well as new theoretical properties of neighbourhoods. The proposed algorithm owns, unprecedented up to now, accuracy, obtainable in a quick time on a PC, which has been confirmed after wide computer tests.

A survey of results for sequencing problems with controllable processing times

Abstract The paper deals with the sequencing problems in which job processing times, along with a processing order, are decision variables having their own associated linearly varying costs. The existing results in this area are surveyed and some new results are provided. In the paper, an attention is focussed on the computational complexity aspects, polynomial algorithms and the worst-case analysis of approximation algorithms.

The flow shop with parallel machines: A tabu search approach

A fast and easily implementable approximation algorithm for the problem of finding a minimum makespan in a flow shop with parallel machines is presented. The algorithm is based on a tabu search technique with a specific neighborhood definition which employs notions of a critical path in a graph and a block of jobs. This is the first improvement algorithm for the considered problem. A special advanced method of implementation improves the local search significantly and increases the speed of the algorithm. Computational experiments (up to 3000 operations and 60 machines) show its excellent numerical properties. The proposed approach can be used for modeling and solving a broad class of flexible flow line scheduling problems.

A block approach for single-machine scheduling with release dates and due dates

Abstract The problem of scheduling jobs on a single machine subject to given release dates and due dates is considered. A new algorithm of the branch-and-bound type for solving this problem is proposed. The approach used in the paper is fully based on the eliminative properties of a block of jobs and in contradiction to the existing algorithms, it does not require any heuristic method to generate a current solution in a search tree. However, a heuristic may be used in order to obtain a good initial solution. Extensive computational experiments show a high efficiency of the algorithm.

The permutation flow shop with buffers: A tabu search approach

The paper deals with the criteria of makespan minimisation for the permutation flow shop problem with buffers of limited capacity located between successive machines. As the problem is NP-hard, an approximation algorithm is proposed which has been designed using a non-trivial generalisation of the block elimination properties known for the classic flow shop problem. This algorithm is able to achieve excellent results for problems up to 200 jobs and 20 machines as it exploits the structural properties defined in the problem and combines these with a local search technique controlled by a tabu search strategy.

Some aspects of scatter search in the flow-shop problem

Abstract The flow-shop scheduling problem with the makespan criterion is a certain strongly NP-hard case from the domain of OR. This problem, having simple formulation contrasting with its troublesome, complex and time-consuming solution methods, is ideal for testing the quality of advanced combinatorial optimization algorithms. Although many excellent approximate algorithms for the flow-shop problem have been provided, up till now, in the literature, some theoretical and experimental problems associated with an algorithm’s activity still remain unexamined. In this paper, we provide a new view on the solution space and the search process. Relying upon it, we are proposing the new approximate algorithm, which applies some properties of neighborhoods, refers to the big valley phenomenon, uses some elements of the scatter search as well as the path relinking technique. This algorithm shows up to now unprecedented accuracy, obtainable within a short time on a PC, which has been confirmed in a wide variety of computer tests. Good properties of the algorithm remain scalable if the size of instances increases.

A two-machine flow shop scheduling problem with controllable job processing times

Abstract The paper deals with a two-machine flow shop scheduling problem in which both the sequence of jobs and their processing times are decision variables. It is assumed that the cost of performing a job is a linear function of its processing time, and the schedule cost to be minimized is the total processing cost plus maximum completion time cost. In is shown that the decision form of this problem is NP-complete, even when the processing times on one machine only are controllable and all the processing cost units are identical. Two heuristic methods for solving the problem are proposed and their worst-case analysis is presented.

A bicriterion approach to preemptive scheduling of parallel machines with controllable job processing times

Abstract The papers deals with a bicriterion approach to preemptive scheduling of m parallel machines for jobs having processing costs which are linear functions of variable processing times. One of the objective functions is a completion time and the other, a processing cost. In the case of identical machines, an O(n2) greedy algorithm is given which generates all breakpoints of a piecewise linear efficient frontier; it is shown that in the problem with n jobs there are at most 2n + 1 breakpoints, which is a tight bound. For uniform machines, an algorithm is provided which solves a problem of least processing cost under limited completion time in O(nmaxm, log n) time. Basing on this algorithm, a procedure for finding an e-approximation of the efficient frontier is proposed.

Worst-case analysis of an approximation algorithm for flow-shop scheduling

A worst-case analysis of an algorithm proposed by Campbell et al. for the m-machine permutation flow-shop problem is presented. The tight worst-case performance ratio [m/2] is found.