Search heuristics for a parallel machine scheduling problem with ready times and due dates

We consider a problem of scheduling orders on identical parallel machines. An order can be released after a given ready time and must be completed before its due date. An order is split into multiple jobs (batches) and a job is processed on one of the parallel machines. The objective of the scheduling problem is to minimize the holding costs of orders including work-in-process as well as finished job inventories. We suggest two local search heuristics, simulated annealing and taboo search algorithms, for the problem. Performance of the suggested algorithms is tested through computational experiments on randomly generated test problems.     

Ordinal algorithms for parallel machine scheduling with nonsimultaneous machine available times

This paper considers ordinal algorithms for parallel machine scheduling with nonsimultaneous machine available times. Two objects of minimizing the latest job completion time and minimizing the latest machine completion time are studied. For the first objective, we present the optimal algorithms for m = 2, 3, 4 machine cases. For m ≥ 5, we propose an algorithm with competitive ratio 2 - 1/(m - 1) while the lower bound is 5/3. For the second objective, the optimal algorithm is also given. Furthermore, for a special case, an algorithm with significantly improved competitive ratio is given.     

A hybrid genetic algorithm for parallel machine scheduling with setup times

Journal of Intelligent Manufacturing - This paper addresses the unrelated parallel machine scheduling problem with sequence and machine dependent setup times and machine eligibility constraints....     

Online batch scheduling on parallel machines with delivery times

We study the online batch scheduling problem on parallel machines with delivery times. Online algorithms are designed on m parallel batch machines to minimize the time by which all jobs have been delivered. When all jobs have identical processing times, we provide the optimal online algorithms for both bounded and unbounded versions of this problem. For the general case of processing time on unbounded batch machines, an online algorithm with a competitive ratio of 2 is given when the number of machines m=2 or m=3, respectively. When m≥4, we present an online algorithm with a competitive ratio of 1.5+o(1).     

并行机成组调度问题的启发式算法

研究了优化目标为总拖后/提前时间最小化的并行机成组调度问题,提出了一种三阶段启发式近似求解算法。首先把并行机问题看成单机问题,以最小化总拖后时间为优化目标排列工件的加工次序;然后将工件按第一阶段所求得的次序指派到最先空闲的并行的机器上;最后采用改进的GTW算法对各机器上的工件调度插入适当的空闲时间。计算表明该算法能够在很短的时间内给出大规模调度问题的近似最优解。     

Single machine batch scheduling with release times and delivery costs

We study single machine batch scheduling with release times. Our goal is to minimize the sum of weighted flow times (or completion times) and delivery costs. Since the problem is strongly $\mathcal{NP}$ -hard even with no delivery cost and identical weights for all jobs, an approximation algorithm is presented for the problem with identical weights. This uses the polynomial time solution we give for the preemptive version of the problem. We also present an evolutionary metaheuristic algorithm for the general case. Computational results show very small gaps between the results of the metaheuristic and the lower bound.     

An improved heuristic for parallel machine weighted flowtime scheduling with family set-up times

This paper studies the identical parallel machine scheduling problem with family set-up times and an objective of minimizing total weighted completion time (weighted flowtime). The family set-up time is incurred whenever there is a switch of processing from a job in one family to a job in another family. A heuristic is proposed in this paper for the problem. Computational results show that the proposed heuristic outperforms an existing heuristic, especially for large-sized problems, in terms of both solution quality and computation times. The improvement of solution quality is as high as 4.753% for six-machine problem and 7.822% for nine-machine problem, while the proposed heuristic runs three times faster than the existing one.     

Rolling-horizon and fix-and-relax heuristics for the parallel machine lot-sizing and scheduling problem with sequence-dependent set-up costs

In this paper we develop new rolling-horizon and fix-and-relax heuristics for the identical parallel machine lot-sizing and scheduling problem with sequence-dependent set-up costs. Unlike previous papers, our procedures are based on a compact formulation relying on the hypotheses of identical machines. This feature makes our approach suitable for large-scale applications (with hundreds of machines) arising in the textile and fiberglass industries. Moreover, our procedures are shown to provide a feasible solution for any feasible instance. Comparisons with lower bounds provided by a truncated branch-and-bound show that the gap between the best heuristic solution and the lower bound never exceeds 3%.     

Unrelated parallel machine scheduling with setup times and a total weighted tardiness objective

This paper presents several search heuristics and their performance in batch scheduling of parallel, unrelated machines. Identical or similar jobs are typically processed in batches in order to decrease setup times and/or processing times. The problem accounts for allotting batched work parts into unrelated parallel machines, where each batch consists of a fixed number of jobs. Some batches may contain different jobs but all jobs within each batch should have an identical processing time and a common due date. Processing time of each job of a batch is determined according to the machine group as well as the batch group to which the job belongs. Major or minor setup times are required between two subsequent batches depending on batch sequence but are independent of machines. The objective of our study is to minimize the total weighted tardiness for the unrelated parallel machine scheduling. Four search heuristics are proposed to address the problem, namely (1) the earliest weighted due date, (2) the shortest weighted processing time, (3) the two-level batch scheduling heuristic, and (4) the simulated annealing method. These proposed local search heuristics are tested through computational experiments with data from dicing operations of a compound semiconductor manufacturing facility.     

Size-reduction heuristics for the unrelated parallel machines scheduling problem

In this paper we study the unrelated parallel machines problem where n independent jobs must be assigned to one out of m parallel machines and the processing time of each job differs from machine to machine. We deal with the objective of the minimisation of the maximum completion time of the jobs, usually referred to as makespan or C_max. This is a type of assignment problem that has been frequently studied in the scientific literature due to its many potential applications. We propose a set of metaheuristics based on a size-reduction of the original assignment problem that produce solutions of very good quality in a short amount of time. The underlying idea is to consider only a few of the best possible machine assignments for the jobs and not all of them. The results are simple, yet powerful methods. We test the proposed algorithms with a large benchmark of instances and compare them with current state-of-the-art methods. In most cases, the proposed size-reduction algorithms produce results that are statistically proven to be better by a significant margin.     

Single-machine scheduling with past-sequence-dependent delivery times and release times

This paper studies the problem of single-machine scheduling with past-sequence-dependent delivery times, which was introduced in Koulamas and Kyparisis (2010) [5]. We focus on the scenario with release times such that any job is available for processing on or after its specific release time. Both preemptive and non-preemptive models are considered, aiming at minimizing the total completion time. An optimal algorithm is presented for the preemptive model where any job may be preempted during processing on the machine and then resumed from where it was interrupted later on. For the non-preemptive model, we show that it is NP-hard and mainly develop an approximation algorithm.     

Single and parallel machine capacitated lotsizing and scheduling: New iterative MIP-based neighborhood search heuristics

We propose a general-purpose heuristic approach combining metaheuristics and mixed integer programming to find high quality solutions to the challenging single- and parallel-machine capacitated lotsizing and scheduling problem with sequence-dependent setup times and costs. Commercial solvers fail to solve even medium-sized instances of this NP-hard problem; therefore, heuristics are required to find competitive solutions. We develop construction, improvement and search heuristics all based on MIP formulations. We then compare the performance of these heuristics with those of two metaheuristics and other MIP-based heuristics that have been proposed in the literature, and to a state-of-the-art commercial solver. A comprehensive set of computational experiments shows the effectiveness and efficiency of the main approach, a stochastic MIP-based local search heuristic, in solving medium to large size problems. Our solution procedures are quite flexible and may easily be adapted to cope with model extensions or to address different optimization problems that arise in practice.     

Single machine scheduling with batch-dependent setup times

We address a single-machine batch scheduling problem. The setup times (incurred whenever starting a new batch) are assumed to be a function of the number of batches processed previously, i.e., batch-dependent. The objective is minimum total flow-time. We focus on the case of identical processing time jobs. Given the number of jobs and the setup times, we have to determine the optimal number of batches and their (integer) size. An efficient (O(n)) solution procedure is introduced.     

An exact algorithm for parallel machine scheduling with conflicts

We consider an extension of classic parallel machine scheduling where a set of jobs is scheduled on identical parallel machines and an undirected conflict graph is part of the input. Each node in the graph represents a job, and an edge implies that its two jobs are conflicting, meaning that they cannot be scheduled on the same machine. The goal is to find an assignment of the jobs to the machines such that the maximum completion time (makespan) is minimized. We present an exact algorithm based on branch and price that combines methods from bin packing, scheduling, and graph coloring, with appropriate modifications. The algorithm has a good computational performance even for parallel machine scheduling without conflicting jobs.     

Makespan minimization for scheduling unrelated parallel machines with setup times

This study considers the problem of scheduling jobs on unrelated parallel machines with machine-dependent and job sequence-dependent setup times. In this study, a restricted simulated annealing (RSA) algorithm which incorporates a restricted search strategy is presented to minimize the makespan. The proposed RSA algorithm can effective reduce the search effort required to find the best neighborhood solution by eliminating ineffective job moves. The effectiveness and efficiency of the proposed RSA algorithm is compared with the basic simulated annealing and existing meta-heuristics on a benchmark problem dataset used in earlier studies. Computational results indicate that the proposed RSA algorithm compares well with the state-of-the-art meta-heuristic for small-sized problems, and significantly outperforms basic simulated annealing algorithm and existing algorithms for large-sized problems.     

Genetic algorithm for rotary machine scheduling with dependent processing times

This paper focuses on scheduling a rotary injection molding machine with dependent processing times. The injection machine has n pairs of positions to process n pairs of shoes. It is rotated after every cycle time. Cycle time is the maximum injection time of the jobs currently loaded in the machine. Thus, for all practical purposes, the processing time of a job depends on the combination of the jobs currently assigned to the machine. The uncertainty of processing time makes this problem more complicated than traditional parallel machine scheduling problems. Additionally, since switching jobs leads to mold changes, set-up time is also included in the analysis. We develop a Sequential Genetic Algorithm (SGA) to identify the best schedule with regard to makespan. In this approach, multiple GA evolvers are connected by using a feeding strategy, where each GA evolver identifies the best schedule with minimum makespan for the corresponding product family. A multi-segment (product lines) chromosome representation is applied to represent the product line sequence as well as the job sequence within a product family. Furthermore, an adaptive feeding strategy is also proposed to improve results and reduce computation times. Besides SGA, we also improve the performance of a traditional heuristic procedure by proposing a minimum ΔIT heuristic approach. The experimentation is performed by using four experimental data sets with different demand patterns and nine data sets from a shoe manufacturing plant. The results indicate that our SGA provides better schedule with respect to makespan value, while heuristic procedures take insignificant time to obtain results. Another observation is that adaptive feeding strategy helps to find good results in a shorter time.     

Simulated-annealing heuristics for the single-machine scheduling problem with learning and unequal job release times

In scheduling of batch processing machines in the diffusion and oxidation areas of a wafer fabrication facility, it can be found that the processing times of these batching operations can be extremely long (10 h) when compared to other operations (1-2 h) in a wafer fab. Moreover, the jobs to be processed may have different priorities/weights, due dates and ready times. In the presence of unequal ready times, it would be better to wait for future job arrivals in order to increase the fullness of the batch. On the other hand, repeated processing of similar tasks improves workers’ skills. Motivated by these observations, we consider a single-machine problem with the sum of processing times based learning effect and release times. The objective is to find a schedule to minimize the total completion times. We first develop a branch-and-bound algorithm for the optimal solution. Then we propose a simulated-annealing heuristic algorithm for a near-optimal solution. Finally, we conduct a computational experiment to evaluate the performances of the proposed algorithms. The results show that the branch-and-bound algorithm can solve instances up to 24 jobs, and the average error percentage of the simulated-annealing algorithm is less than 0.1482%.     

Dispatching heuristics for the single machine weighted quadratic tardiness scheduling problem

In this paper, we consider the single machine scheduling problem with weighted quadratic tardiness costs. Several efficient dispatching rules are proposed. These include existing heuristics for the linear problem, as well as procedures suitably adapted to the quadratic objective function. Also, both forward and backward scheduling procedures are considered.The computational results show that the heuristics that specifically take into account the quadratic objective significantly outperform their linear counterparts. Also, the backward scheduling approach proves to be superior, and the difference in performance is even more noticeable for the harder instances.The best of the backward scheduling heuristics is both quite efficient and effective. Indeed, this procedure can quickly generate a schedule even for large instances. Also, its relative deviation from the optimum is usually rather low, and it performs adequately even for the more difficult instances.     

Search tree based approaches for parallel machine scheduling

This article compares two branching schemes for the parallel machine scheduling problem with release dates and tails. Both branching schemes can be used for either complete or incomplete search tree based algorithms. In particular, our study aims to prove the robustness of each of them for several search methods. We experimentally compare the efficiency of the two branching schemes when they are used in a branch-and-bound (BnB) method, in a limited discrepancy search, in a branch-and-greed (BnG) method or in a beam search (BS).