Józef Grabowski

A very fast Tabu search algorithm for the permutation flow shop problem with makespan criterion

This paper deals with a classic flow-shop scheduling problem with makespan criterion. Some new properties of the problem associated with the blocks have been presented and discussed, These properties allow us to propose a new very fast local search procedure based on a tabu search approach. Computational experiments (up to 500 jobs and 20 machines) are given and compared with the results yielded by the best algorithms discussed in the literature. These results show that the algorithm proposed solves the flow-shop instances with high accuracy in a very short time. The presented properties and ideas can be applied in any local search procedures.

Sequencing of jobs in some production system

Abstract We consider a real-life problem of scheduling clients orders in the production of concrete blocks in a factory of building industry. This problem can be modelled as a hybrid flow shop scheduling problem with mixed no-wait/no-store constraints and mixed bottleneck/non-bottleneck machines. The objective function is to minimize maximum completion time. To solve the problem, we propose an approximation algorithm based on the tabu search approach.

Some local search algorithms for no-wait flow-shop problem with makespan criterion

This paper develops and compares different local search algorithms for the no-wait flow-shop problem with makespan criterion (Cmax). We present several variants of descending search and tabu search algorithms. In the algorithms the multimoves are used that consist in performing several moves simultaneously in a single iteration of algorithm and allow us to accelerate the convergence to good solutions. Besides, in the tabu search algorithms a dynamic tabu list is proposed that assists additionally to avoid trapped at a local optimum. The proposed algorithms are empirically evaluated and found to be relatively more effective in finding better quality solutions than existing algorithms. The presented ideas can be applied in any local search procedures.

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.

New block properties for the permutation flow shop problem with application in tabu search

This paper deals with the classic flow-shop scheduling problem with the make-span criterion. Some new properties of the problem associated with the so-called blocks have been presented and discussed. The properties allow us to skip some non-perspective solutions during the search of the solution space. Applied to local search algorithms, they result in a significant reduction of neighbourhood size and quickly direct the search trajectory to promising regions of the solution space. The implementation of the proposed properties in a tabu search algorithm is also presented. Computational experiments (up to 500 jobs and 20 machines) are given and compared with the results yielded by the best known algorithms.

Block approach-tabu search algorithm for single machine total weighted tardiness problem

Problem of scheduling on a single machine to minimize total weighted tardiness of jobs can be described as follows: there are n jobs to be processed, each job has an integer processing time, a weight and a due date. The objective is to minimize the total weighted tardiness of jobs. The problem belongs to the class of NP-hard problems. Some new properties of the problem associated with the blocks have been presented and discussed. These properties allow us to propose a new fast local search procedure based on a tabu search approach with a specific neighborhood which employs blocks of jobs and a compound moves technique. A compound move consists in performing several moves simultaneously in a single iteration of algorithm and allows us to accelerate the convergence to good solutions. In the algorithm, we use an idea which decreases the complexity for the search of neighborhood from O(n^3) to O(n^2). Additionally, the neighborhood is reduced by using some elimination criteria. The method presented in this paper is deterministic one and has not any random element, as distinct from other effective but non-deterministic methods proposed for this problem, such as tabu search of Crauwels, H. A. J., Potts, C. N., & Van Wassenhove, L. N. (1998). Local search heuristics for the single machine total weighted tardiness Scheduling Problem. INFORMS Journal on Computing, 10(3), 341-350, iterated dynasearch of Congram, R. K., Potts C. N., & Van de Velde, S. L. (2002). An iterated dynasearch algorithm for the single-machine total weighted tardiness scheduling problem. INFORMS Journal on Computing, 14(1), 52-67 and enhanced dynasearch of Grosso, A., Della Croce, F., & Tadei, R. (2004). An enhanced dynasearch neighborhood for single-machine total weighted tardiness scheduling problem. Operations Research Letters, 32, 68-72. Computational experiments on the benchmark instances from OR-Library (http://people.brunel.ac.uk/mastjjb/jeb/info.html) are presented and compared with the results yielded by the best algorithms discussed in the literature. These results show that the algorithm proposed allows us to obtain the best known results for the benchmarks in a short time. The presented properties and ideas can be applied in any local search procedures.

Job-shop scheduling with resource-time models of operations

Abstract The job-shop problems with allocation of continuously-divisible nonrenewable resource is considered. The mathematical models of operations are linear, decreasing functions with respect to an amount of resource. The objective is sequencing operations and allocation of constrained resource such that the project duration is minimized. Thus, the problem considered is a generalization of the classical job-shop problem. Some properties of the optimal solution are presented. The algorithm of solving this problem is based on the disjunctive graphs theory and branch-and-bound technique. The theory of the algorithm is based on the critical path concept using the segment system approach. The special feature of the algorithm is that it gives a complete solution which is associated with each node of the enumeration tree. Possible generalizations of the results presented are indicated.

A New Algorithm of Solving the Flow — Shop Problem

The general flow — shop problem indicated by n|m|F|Cmax, can be formulated as follows. Each of n jobs J,…,Jn has to be processed on m machines M1,…,Mm in that order. Job Jj, j=1,…,n, thus consists of a sequence of m operations oj1..,,…,0. jm0jk corresponds to the processing of Jj on Mk during a processing time Pjk We want to find a processing order on each machine Mk such that the time required to complete all jobs is minimized. If the processing order is assumed to be the same on each machine, the resulting problem is called the permutation flow — shop problem, and indicated by n|m|F|Cmax.

Scheduling in Production of Concrete Wares

We consider a real-life problem of scheduling clients orders in the production of concrete wares in a factory of building industry. This problem can be modeled as hybrid flow shop scheduling problem with mixed no wait/no store constraints and the makespan criterion. To solve the problem, we propose an approximation algorithm based on the tabu search approach.