Parallel machine scheduling subject to auxiliary resource constraints

This paper is motivated by scheduling photolithography machines in semiconductor manufacturing wherein reticle requirements are the auxiliary resource constraints. As the problem is NP hard, two different heuristic solution approaches are developed. The performance of our network-based mathematical model and heuristics are evaluated through an extensive set of problem instances. The best performing heuristic method typically produces solutions that are 1.72% above optimal. If this method is used as the seed solution for a Tabu search-based post processing algorithm, schedules that are 0.78% above the optimal solution, on average, are possible.     

Heuristic for scheduling in a two-machine bicriteria dynamic flowshop with setup and processing times separated

This paper addresses the two-machine bicriteria dynamic flowshop problem where setup time of a job is separated from its processing time and is sequenced independently. The performance considered is the simultaneous minimization of total flowtime and makespan, which is more effective in reducing the total scheduling cost compared to the single objective. A frozen-event procedure is first proposed to transform a dynamic scheduling problem into a static one. To solve the transformed static scheduling problem, an integer programming model with N ² + 5N variables and 7N constraints is formulated. Because the problem is known to be NP-complete, a heuristic algorithm with the complexity of O (N ³) is provided. A decision index is developed as the basis for the heuristic. Experimental results show that the proposed heuristic algorithm is effective and efficient. The average solution quality of the heuristic algorithm is above 99%. A 15-job case requires only 0.0235 s, on average, to obtain a near or even optimal solution.     

Applying statistical tests to empirically compare tabu search parameters for MAX 3-SATISFIABILITY: A case study

The application of stochastic heuristic, like tabu search or simulated annealing, to address hard discrete optimization problems has been an important advance for efficiently obtaining good solutions in a reasonable amount of computing time. A challenge when applying such heuristics is assessing when a particular set of parameter values yields better performance compared to other such sets of parameter values. For example, it can be difficult to determine the optimal mix of memory types to incorporate into tabu search. This in turn prompts users to undertake a trial and error phase to determine the best combination of parameter settings for the problem under study. Moreover, for a given problem instance, one set of heuristic parameter settings may yield a better solution than another set of parameters, for a given initial solution. However, the performance of this heuristic on this instance for a single heuristic execution is not sufficient to assert that the first set of parameter settings will always produce superior results than the second set of parameters, for all initial solutions.     

The permutation flow shop problem with just in time production considerations

This research presents a variation to the permutation flow shop problem where Just In Time (JIT) production requirements are taken into account. The model developed in this research employs dual objectives. In addition to the traditional objective of minimizing the production makespan, minimization of Miltenburg's material usage rate is also incorporated. In this model, multiple units of any product are permitted in the production sequence. However, the minimization of material usage rates attempts to prevent batch scheduling of products and allows unit flow of products as required in demand flow manufacturing. A solution method is proposed for determining an optimal production sequence via an efficient frontier approach and Simulated Annealing (SA). Test problems and specific performance criteria are used to assess the solutions generated by the proposed method. Experimental results presented in this paper show that the use of the efficient frontier and SA provide solutions that approach the optimal solution for the performance measures used in this research.     

A heuristic to minimize total flow time in permutation flow shop

In this paper, we address an n-job, m-machine permutation flow shop scheduling problem for the objective of minimizing the total flow time. We propose a modification of the best-known method of Framinan and Leisten [An efficient constructive heuristic for flowtime minimization in permutation flow shops. Omega 2003;31:311–7] for this problem. We show, through computational experimentation, that this modification significantly improves its performance while not affecting its time-complexity.     

A multiobjective genetic algorithm for job shop scheduling

In this paper, a Multi Objective Genetic Algorithm (MOGA) is proposed to derive the optimal machine-wise priority dispatching rules ( pdrs ) to resolve the conflict among the contending jobs in the Giffler and Thompson (GT) procedure applied for job shop problems. The performance criterion considered is the weighed sum of the multiple objectives minimization of makespan, minimization of total idle time of machines and minimization of total tardiness. The weights assigned for combining the objectives into a scalar fitness function are not constant. They are specified randomly for each evaluation. This in turn leads to the multidirectional search in the proposed MOGA, which in turn mitigates the solution being entrapped in local minima. The applicability and usefulness of the proposed methodology for the scheduling of job shops is illustrated with 28 benchmark problems available in the open literature.     

Two approaches to solving the multi-depot vehicle routing problem with time windows in a time-based logistics environment

This paper presents a two-phase heuristic method that can be used to efficiently solve the intractable multi-depot vehicle routing problem with time windows. The waiting time that was ignored by previous researchers is considered in this study. The necessity of this consideration is verified through an initial experiment. The results indicate that the waiting time has a significant impact on the total distribution time and the number of vehicles used when solving test problems with narrow time windows. In addition, to fairly evaluate the performance of the proposed heuristic method, a meta-heuristic method, which extends the unified tabu search of Cordeau et al., is proposed. The results of a second experiment reveal that the proposed heuristic method can obtain a better solution in the case of narrow time windows and a low capacity ratio, while the proposed meta-heuristic method outperforms the proposed heuristic method, provided that wide time windows and a high capacity ratio are assumed. Finally, a well-known logistics company in Taiwan is used to demonstrate the method, and a comparison is made, which shows that the proposed heuristic method is superior to the current method adopted by the case company.     

A three-phased local search approach for the clique partitioning problem

This paper presents a three-phased local search heuristic CPP-P\(^{3}\) for solving the Clique Partitioning Problem (CPP). CPP-P\(^{3}\) iterates a descent search, an exploration search and a directed perturbation. We also define the Top Move of a vertex, in order to build a restricted and focused neighborhood. The exploration search is ensured by a tabu procedure, while the directed perturbation uses a GRASP-like method. To assess the performance of the proposed approach, we carry out extensive experiments on benchmark instances of the literature as well as newly generated instances. We demonstrate the effectiveness of our approach with respect to the current best performing algorithms both in terms of solution quality and computation efficiency. We present improved best solutions for a number of benchmark instances. Additional analyses are shown to highlight the critical role of the Top Move-based neighborhood for the performance of our algorithm and the relation between instance hardness and algorithm behavior.     

Two new robust genetic algorithms for the flowshop scheduling problem

The flowshop scheduling problem (FSP) has been widely studied in the literature and many techniques for its solution have been proposed. Some authors have concluded that genetic algorithms are not suitable for this hard, combinatorial problem unless hybridization is used. This work proposes new genetic algorithms for solving the permutation FSP that prove to be competitive when compared to many other well known algorithms. The optimization criterion considered is the minimization of the total completion time or makespan (_Cmax$C_{\max }$). We show a robust genetic algorithm and a fast hybrid implementation. These algorithms use new genetic operators, advanced techniques like hybridization with local search and an efficient population initialization as well as a new generational scheme. A complete evaluation of the different parameters and operators of the algorithms by means of a Design of Experiments approach is also given. The algorithm's effectiveness is compared against 11 other methods, including genetic algorithms, tabu search, simulated annealing and other advanced and recent techniques. For the evaluations we use Taillard's well known standard benchmark. The results show that the proposed algorithms are very effective and at the same time are easy to implement.     

On approximation of the fixed charge transportation problem

In this paper we present a new approximation for computing lower bound for the fixed charge transportation problem (FCTP). The lower bounds thus generated delivered 87% optimal solutions for 56 randomly generated small, up to 6×10 in size, problems in an experimental design. For somewhat larger, 10×10 and 10×15 size problems, the lower bounds delivered an average error of 5%, approximately, using a fraction of CPU times as compared to CPLEX to solve these problems. The proposed lower bound may be used as a superior initial solution with any other existing branch-and-bound method or tabu search heuristic procedure to enhance convergence to the optimal solution for large size problems which cannot be solved by CPLEX due to time constraints.     

A comparison between genetic algorithms and the RAND method for solving the joint replenishment problem

The purpose of this paper is to compare the performance of genetic algorithms (GAs) and the best available heuristic, known as the RAND, for solving the joint replenishment problem (JRP). An important feature of the JRP which makes it suitable for GAs is that it can be formulated as a problem having one continuous decision variable and a number of integer decision variables equal to the number of products being produced or ordered. Experiments on randomly generated problems indicate that GAs can provide better solutions to the JRP than the RAND for some problems, and at worst can almost match the performance of the RAND from a practical point of view for the rest of the problems. GAs never converged to solution with a total cost of more than 0.08% of the total cost of the RAND for 1600 randomly generated problems. In addition, GAs have the advantages of: (i) being easy to implement (e.g. less than 200 lines of code); (ii) having a code which is easy to understand and modify; and (iii) dealing easily with constrained JRPs which are neglected by most of the available methods including the RAND, in spite of their importance in practice.     

A heuristic algorithm for minimizing maintenance workforce level

We develop a heuristic algorithm for minimizing the workforce level required to accommodate all the maintenance jobs requested within a specific time interval. Each maintenance job has its own release and due dates as well as the required man-days, and must be scheduled in a noninterrupted time interval, i.e. without preemption. However, the duration of each job is not fixed, but to be determined within a specific range. We show that this problem can be seen as a variant of the two-dimensional bin-packing problem with some additional constraints. We develop a non-linear mixed integer programming model for the proposed problem, and employ some well-known bin-packing algorithms to develop an efficient heuristic algorithm. In order to evaluate the performance of the proposed heuristic, we present a computationally efficient scheme for getting a good lower bound for the actual minimum. The computational experiment shows that the proposed heuristic algorithm performs quite satisfactorily in practice.     

An investigation into the vehicle routing problem with time windows and link capacity constraints

In this work, we investigate a new, yet practical, variant of the vehicle routing problem called the vehicle routing problem with time windows and link capacity constraints (VRPTWLC). The problem considers new constraints imposed on road links with regard to vehicle passing tonnage, which is motivated by a business project with a Hong Kong transportation company that transports hazardous materials (hazmats) across the city and between Hong Kong and mainland China. In order to solve this computationally challenging problem, we develop a tabu search heuristic with an adaptive penalty mechanism (TSAP) to help manage the company's vehicle fleet. A new data set and its generation scheme are also presented to help validate our solutions. Extensive computational experiments are conducted, showing the effectiveness of the proposed solution approach.     

An iterated greedy algorithm for the flowshop scheduling problem with blocking

This paper proposes an iterated greedy algorithm for solving the blocking flowshop scheduling problem for makespan minimization. Moreover, it presents an improved NEH-based heuristic, which is used as the initial solution procedure for the iterated greedy algorithm. The effectiveness of both procedures was tested on some of Taillard’s benchmark instances that are considered to be blocking flowshop instances. The experimental evaluation showed the efficiency of the proposed algorithm, in spite of its simple structure, in comparison with a state-of-the-art algorithm. In addition, new best solutions for Taillard’s instances are reported for this problem, which can be used as a basis of comparison in future studies.     

Efficient composite heuristics for total flowtime minimization in permutation flow shops

In this paper, permutation flow shops with total flowtime minimization are considered. General flowtime computing (GFC) is presented to accelerate flowtime computation. A newly generated schedule is divided into an unchanged subsequence and a changed part. GFC computes total flowtime of a schedule by inheriting temporal parameters from its parent in the unchanged part and computes only those of the changed part. Iterative methods and LR (developed by Liu J, Reeves, CR. Constructive and composite heuristic solutions to theP∥Σ_Ci$P\parallel \Sigma C_i$ scheduling problem, European Journal of Operational Research 2001; 132:439–52) are evaluated and compared as solution improvement phase and index development phase. Three composite heuristics are proposed in this paper by integrating forward pair-wise exchange-restart (FPE-R) and FPE with an effective iterative method. Computational results show that the proposed three outperform the best existing three composite heuristics in effectiveness and two of them are much faster than the existing ones.     

A harmony search-based memetic optimization model for integrated production and transportation scheduling in MTO manufacturing

This paper investigates an integrated production and transportation scheduling problem in an MTO supply chain. A harmony search-based memetic optimization model is developed to handle this problem, in which certain heuristic procedures are proposed to convert the investigated problem into an order assignment problem. A novel improvisation process is also proposed to improve the optimum-seeking performance. The effectiveness of the proposed model is validated by numerical experiments. The experimental results show that (1) the proposed model can solve the investigated problem effectively and that (2) the proposed memetic optimization process exhibits better optimum-seeking performance than genetic algorithm-based and traditional memetic optimization processes.     

Flow shop scheduling by transportation model

This paper describes the classical problem of scheduling n jobs on m machines in a flow shop. A schedule evaluation algorithm is presented, which for job-pairs, generates a schedule evaluation matrix. The matrix is the input data to a transportation problem, the solution of which gives near-optimal jobsequence and makespan. The performance of the algorithm is discussed.     

Modeling cost-delivery trade-offs for distribution logistics by a generalized PVRP model

This article provides a mathematical model to support management in making decisions about cost-delivery trade-offs in the case of cost-delivery flexibilities in distribution logistics. The optimization problem can be modeled as a bi-objective periodic vehicle routing problem, which is known as NP-hard. In the periodic vehicle routing problem considered in this study, no delivery patterns are pre-defined, instead the patterns are the result of the optimization process of the model. In addition, delivery time flexibilities are incorporated in the model. A heuristic solution method for realistic problem sizes is based on the tabu search procedure, and a real case study illustrates the applicability of the solution concept.     

A Novel Eigenvector Technique for Large Scale Combinatorial Problems in VLSI Layout

Modern integrated circuit design involves laying out circuits which consist of millions of switching elements or transistors. Due to the sheer complexity, optimizing the connectivity between transistors is a very difficult problem. How a circuit is interconnected is the single most important factor in performance criteria such as signal delay, power dissipation, circuit size and cost. These factors dictate that interconnections—wires, be made as short as possible. The wire–minimization problem is formulated as a sequence of discrete optimization subproblems. These problems are known to be NP-hard, hence they can only be solved approximately using meta-heuristics or linear programming techniques. Nevertheless, these methods are computationally expensive and the quality of solution depends to a great extent on an appropriate choice of starting configuration. A matrix reordering technique for solving very hard discrete optimization problems in Very Large Scale Integrated (VLSI) design which overcomes some of these shortcomings is proposed. In particular, the computational cost is reasonable—of the order of n ^1.4 running time.     

Hospital resident scheduling problem

This paper addresses the resident scheduling problem (RSP) at hospitals concerned with prescribing work-nights for residents while considering departmental staffing and skill requirements as well as residents' preferences. Three scenarios that represent most situations and account for various departmental requirements and needs are described. Although similar scheduling problems are considered in the literature, no analysis exists that adequately deals with the speciffic nature of this problem. The problem is modeled as a mixed-integer program and heuristic solution procedures are developed for the different identified scheduling scenarios. These procedures exploit the inherent network structure of the problem which is an important feature that enhances problem solvability. For the sake of comparison, the problem is also solved exactly via the CPLEX-MIP (version 6.0) package. The contribution of this work is important since many hospitals are still utilizing manual techniques in preparing their own schedules, expending considerable effort and time and yet contending with limited scheduling flexibility.