Ching-Fang Liaw

A hybrid genetic algorithm for the open shop scheduling problem

Abstract This paper examines the development and application of a hybrid genetic algorithm (HGA) to the open shop scheduling problem. The hybrid algorithm incorporates a local improvement procedure based on tabu search (TS) into a basic genetic algorithm (GA). The incorporation of the local improvement procedure enables the algorithm to perform genetic search over the subspace of local optima. The algorithm is tested on randomly generated problems, and benchmark problems from the literature. Computational results show that the HGA is able to find an optimum solution for all but a tiny fraction of the test problems. Some of the benchmark problems in the literature are solved to optimality for the first time. Moreover, the results are compared to those obtained with list scheduling heuristic, insertion heuristic (IH), simulated annealing and pure TS algorithms. The HGA significantly outperforms the other methods in terms of solution quality.

A branch-and-bound algorithm for the single machine earliness and tardiness scheduling problem

Abstract This paper addresses the problem of scheduling a given set of independent jobs on a single machine to minimize the sum of weighted earliness and weighted tardiness without considering machine idle time. Efficient lower and upper bounds are developed. The lower bound is obtained based on a Lagrangian relaxation that decomposes the problem into two subproblems, and an efficient lower bounding procedure for each of the subproblems. The upper bound is obtained using a two-phase heuristic procedure that combines a priority dispatching rule with a local improvement procedure. A branch-and-bound algorithm incorporating these bounds and some dominance rules is proposed. Computational experiments on problems with up to 50 jobs show that both the lower and upper bounds are very tight and the branch-and-bound algorithm performs very well. Scope and purpose Single-machine scheduling models involving both earliness and tardiness costs have received significant attention in recent years. These models are consistent with the just-in-time (JIT) production philosophy in the sense that they force jobs to be completed as close to their due dates as possible. This paper examines a single-machine scheduling model where the objective is to minimize the sum of weighted earliness and weighted tardiness subject to the constraint that no machine idle time is allowed. The assumption of no machine idle time represents a type of production setting where the machine idle cost is larger than the job earliness cost, or the machine capacity is limited compared to demand. The problem is known to be NP-hard. A branch-and-bound algorithm based on powerful lower and upper bounding procedures together with some dominance rules is presented. Computational experience is also reported.

Scheduling unrelated parallel machines to minimize total weighted tardiness

This paper addresses the batch scheduling problem of unrelated parallel machines attempting to minimize the total weighted tardiness. Identical or similar jobs are typically processed in batches to decrease setup and/or processing times. Local dispatching rules such as the earliest weighted due date, the shortest weighted processing time, and the earliest weighted due date with a process utilization spread are tailored to the batch scheduling requirements. Based on the features of batch scheduling, a two-level batch scheduling framework is suggested. Existing heuristics, which show excellent performance in terms of total weighted tardiness for the single machine scheduling, such as the modified earliest due date rule and the modified cost over time rule, are extended for the problem. The simulated annealing algorithm as a meta-heuristic is also presented to obtain near optimal solutions. The proposed heuristics are compared through computational experiments with data from the dicing process of a compound semiconductor manufacturing facility

A tabu search algorithm for the open shop scheduling problem

An approximation algorithm of finding a minimum makespan in a nonpreemptive open shop is presented. The algorithm is based on the tabu search technique with a neighborhood structure defined using blocks of operations on a critical path. An efficient procedure is also developed for evaluating a neighborhood. The algorithm is tested on 450 randomly generated problems and a set of 60 benchmarks. Computational results show that the algorithm finds extremely high-quality solutions for all of the test problems in a reasonable amount of computation time, and hence demonstrate the potential of the algorithm to efficiently schedule open shops. Scope and purpose Shop scheduling problems like flow shop problems, job shop problems and open shop problems, which are widely used for modeling industrial production processes, have been receiving increasing attention from researchers. Most of the published results in this area have been focused on flow shop or job shop scheduling problems. This paper addresses the problem of scheduling open shops. An efficient local search algorithm based on the tabu search technique is proposed for solving the open shop scheduling problem with the objective of minimizing makespan. Computational results show that the algorithm performs extremely well on both benchmarks and randomly generated problems.

Applying simulated annealing to the open shop scheduling problem

This paper addresses the problem of scheduling a nonpreemptive open shop with the objective of minimizing makespan. A neighborhood search algorithm based on the simulated annealing technique is proposed. The algorithm is tested on randomly generated problems, benchmark problems in the literature, and new hard problems generated in this paper. Computational results show that the algorithm performs well on all of the test problems. In many cases, an optimum solution is found, and in others the distance from the optimum or lower bound is quite small. Moreover, some of the benchmark problems in the literature are solved to optimality for the first time.

An efficient tabu search approach for the two-machine preemptive open shop scheduling problem

This article considers the problem of scheduling two-machine preemptive open shops to minimize total tardiness. The problem is known to be NP-hard. An optimal timing algorithm is presented to determine the completion time of each job in a given job completion sequence. Then a tabu search (TS) approach is adopted together with the optimal timing algorithm to generate job completion sequences and final schedules. An efficient heuristic is developed to obtain an initial solution for the TS approach. Diversification and intensification strategies are suggested. Finally, computational experiments are conducted to demonstrate the performance of the proposed approach. The results show that the proposed TS approach finds extremely high-quality solutions within a reasonable amount of time.

An efficient simple metaheuristic for minimizing the makespan in two-machine no-wait job shops

This paper examines the problem of scheduling two-machine no-wait job shops to minimize makespan. The problem is known to be strongly NP-hard. A two-phase heuristic is developed to solve the problem. Phase 1 of the heuristic transforms the problem into a no-wait flow shop problem and solves it using the well known Gilmore and Gomory algorithm. Phase 2 of the heuristic improves the solution obtained in phase 1 using a simple tabu search algorithm. Computational results show that the proposed heuristic performs extremely well in terms of both solution quality and computation time. It finds an optimal solution to about 90% of the problem instances and the average deviation from the lower bond for the other problem instances is infinitesimal.

Scheduling two-machine no-wait open shops to minimize makespan

This paper examines the problem of scheduling two-machine no-wait open shops to minimize makespan. The problem is known to be strongly NP-hard. An exact algorithm, based on a branch-and-bound scheme, is developed to optimally solve medium-size problems. A number of dominance rules are proposed to improve the search efficiency of the branch-and-bound algorithm. An efficient two-phase heuristic algorithm is presented for solving large-size problems. Computational results show that the branch-and-bound algorithm can solve problems with up to 100 jobs within a reasonable amount of time. For large-size problems, the solution obtained by the heuristic algorithm has an average percentage deviation of 0.24% from a lower bound value.

The total completion time open shop scheduling problem with a given sequence of jobs on one machine

This paper addresses the open shop scheduling problem to minimize the total completion time, provided that one of the machines has to process the jobs in a given sequence. The problem is NP-hard in the strong sense even for the two-machine case. A lower bound is derived based on the optimal solution of a relaxed problem in which the operations on every machine may overlap except for the machine with a given sequence of jobs. This relaxed problem is NP-hard in the ordinary sense, however it can be quickly solved via a decomposition into subset-sum problems. Both heuristic and branch-and-bound algorithm are proposed. Experimental results show that the heuristic is efficient for solving large-scaled problems, and the branch-and-bound algorithm performs well on small-scaled problems.

Scheduling preemptive open shops to minimize total tardiness

This article considers the problem of scheduling preemptive open shops to minimize total tardiness. The problem is known to be NP-hard. An efficient constructive heuristic is developed for solving large-sized problems. A branch-and-bound algorithm that incorporates a lower bound scheme based on the solution of an assignment problem as well as various dominance rules are presented for solving medium-sized problems. Computational results for the 2-machine case are reported. The branch-and-bound algorithm can handle problems of up to 30 jobs in size within a reasonable amount of time. The solution obtained by the heuristic has an average deviation of less than 2% from the optimal value, while the initial lower bound has an average deviation of less than 11% from the optimal value. Moreover, the heuristic finds approved optimal solutions for over 65% of the problems actually solved.