Dynamic set-up rules for hybrid flow shop scheduling with parallel batching machines

An S-stage hybrid (or flexible) flow shop, with sequence-independent uniform set-up times, parallel batching machines with compatible parallel batch families (like in casting or heat treatments in furnaces, chemical or galvanic baths, painting in autoclave, etc.) has been analysed with the purpose of reducing the number of tardy jobs (and the makespan); in Graham’s notation: FPB(m_1, m_2, … , m_S)|p-batch, STsi,b|SUM(Ui). Jobs are sorted dynamically (at each new delivery); batches are closed within sliding (or rolling) time windows and processed in parallel by multiple identical machines. Computation experiments have shown the better performance on benchmarks of the two proposed heuristics based on new formulations of the critical ratio (CRsetup) considering the ratio of allowance set-up and processing time in the scheduling horizon, which improves the weighted modified operation due date rule

Practical solutions for a dock assignment problem with trailer transportation.

We study a distribution warehouse in which trailers need to be assigned to docks for loading or unloading. A parking lot is used as a buffer zone and transportation between the parking lot and the docks is performed by auxiliary resources called terminal tractors. Each incoming trailer has a known arrival time and each outgoing trailer a desired departure time. The primary objective is to produce a docking schedule such that the weighted sum of the number of late outgoing trailers and the tardiness of these trailers is minimized; the secondary objective is to minimize the weighted completion time of all trailers, both incoming and outgoing. The purpose of this paper is to produce high-quality solutions to large instances that are comparable to a real-life case. We implement several heuristic algorithms: truncated branch and bound, beam search and tabu search. Lagrangian relaxation is embedded in the algorithms for constructing an initial solution and for computing lower bounds. The different solution frameworks are compared via extensive computational experiments.Dock assignment; Multicriteria scheduling; Branch and bound; Beam search; Lagrangian relaxation; Tabu search;

Approximation Schemes for Machine Scheduling

In the classical problem of makespan minimization on identical parallel machines, or machine scheduling for short, a set of jobs has to be assigned to a set of machines. The jobs have a processing time and the goal is to minimize the latest finishing time of the jobs. Machine scheduling is well known to be NP-hard and thus there is no polynomial time algorithm for this problem that is guaranteed to find an optimal solution unless P=NP. There is, however, a polynomial time approximation scheme (PTAS) for machine scheduling, that is, a family of approximation algorithms with ratios arbitrarily close to one. Whether a problem admits an approximation scheme or not is a fundamental question in approximation theory. In the present work, we consider this question for several variants of machine scheduling. We study the problem where the machines are partitioned into a constant number of types and the processing time of the jobs is also dependent on the machine type. We present so called efficient PTAS (EPTAS) results for this problem and variants thereof. We show that certain cases of machine scheduling with assignment restrictions do not admit a PTAS unless P=NP. Moreover, we introduce a graph framework based on the restrictions of the jobs and use it in the design of approximation schemes for other variants. We introduce an enhanced integer programming formulation for assignment problems, show that it can be efficiently solved, and use it in the EPTAS design for variants of machine scheduling with setup times. For one of the problems, we show that there is also a PTAS in the case with uniform machines, where machines have speeds influencing the processing times of the jobs. We consider cases in which each job requires a certain amount of a shared renewable resource and the processing time is depended on the amount of resource it receives or not. We present so called asymptotic fully polynomial time approximation schemes (AFPTAS) for the problems

AN ALGORITHM TO SOLVE THE ASSOCIATIVE PARALLEL MACHINE SCHEDULING PROBLEM

Effective production scheduling is essential for improved performance. Scheduling strategies for various shop configurations and performance criteria have been widely studied. Scheduling in parallel machines (PM) is one among the many scheduling problems that has received considerable attention in the literature. An even more complex scheduling problem arises when there are several PM families and jobs are capable of being processed in more than one such family. This research addresses such a situation, which is defined as an Associative Parallel Machine scheduling (APMS) problem. This research presents the SAPT-II algorithm that solves a highly constrained APMS problem with the objective to minimize average flow time. A case example from a make-to-order industrial product manufacturer is used to illustrate the complexity of the problem and evaluate the effectiveness of the scheduling algorithm

Modelling activity times by hybrid synthetic method

Uncertain (manual) activity times impact a number of manufacturing system modules: plant and layout design, capacity analysis, operator assignment, process planning, scheduling and simulation. Direct observation cannot be used for non-existent production lines. A hybrid direct observation/synthetic method derived from Method Time Measurement available in industry is proposed. To determine accurate activity times required by heuristics and metaheuristics optimisation, manufacturing system modules are modelled by MILP and operator efficiency parameters are used for time standardisation. Among human factors considered are skill and ergonomics. Application to the sterilisation of reusable medical devices is extensively described. Experimental data taken from observation on the field and a worst-case date have shown the model direct applicability for professionals also to non-manufacturing cases

Measurement Based Reconfigurations in Optical Ring Metro Networks

Single-hop wavelength division multiplexing (WDM) optical ring networks operating in packet mode are one of themost promising architectures for the design of innovative metropolitan network (metro) architectures. They permit a cost-effective design, with a good combination of optical and electronic technologies, while supporting features like restoration and reconfiguration that are essential in any metro scenario. In this article, we address the tunability requirements that lead to an effective resource usage and permit reconfiguration in optical WDM metros.We introduce reconfiguration algorithms that, on the basis of traffic measurements, adapt the network configuration to traffic demands to optimize performance. Using a specific network architecture as a reference case, the paper aims at the broader goal of showing which are the advantages fostered by innovative network designs exploiting the features of optical technologies

Optimization Models and Approximate Algorithms for the Aerial Refueling Scheduling and Rescheduling Problems

The Aerial Refueling Scheduling Problem (ARSP) can be defined as determining the refueling completion times for fighter aircrafts (jobs) on multiple tankers (machines) to minimize the total weighted tardiness. ARSP can be modeled as a parallel machine scheduling with release times and due date-to-deadline window. ARSP assumes that the jobs have different release times, due dates, and due date-to-deadline windows between the refueling due date and a deadline to return without refueling. The Aerial Refueling Rescheduling Problem (ARRP), on the other hand, can be defined as updating the existing AR schedule after being disrupted by job related events including the arrival of new aircrafts, departure of an existing aircrafts, and changes in aircraft priorities. ARRP is formulated as a multiobjective optimization problem by minimizing the total weighted tardiness (schedule quality) and schedule instability. Both ARSP and ARRP are formulated as mixed integer programming models. The objective function in ARSP is a piecewise tardiness cost that takes into account due date-to-deadline windows and job priorities. Since ARSP is NP-hard, four approximate algorithms are proposed to obtain solutions in reasonable computational times, namely (1) apparent piecewise tardiness cost with release time rule (APTCR), (2) simulated annealing starting from random solution (SArandom ), (3) SA improving the initial solution constructed by APTCR (SAAPTCR), and (4) Metaheuristic for Randomized Priority Search (MetaRaPS). Additionally, five regeneration and partial repair algorithms (MetaRE, BestINSERT, SEPRE, LSHIFT, and SHUFFLE) were developed for ARRP to update instantly the current schedule at the disruption time. The proposed heuristic algorithms are tested in terms of solution quality and CPU time through computational experiments with randomly generated data to represent AR operations and disruptions. Effectiveness of the scheduling and rescheduling algorithms are compared to optimal solutions for problems with up to 12 jobs and to each other for larger problems with up to 60 jobs. The results show that, APTCR is more likely to outperform SArandom especially when the problem size increases, although it has significantly worse performance than SA in terms of deviation from optimal solution for small size problems. Moreover CPU time performance of APTCR is significantly better than SA in both cases. MetaRaPS is more likely to outperform SAAPTCR in terms of average error from optimal solutions for both small and large size problems. Results for small size problems show that MetaRaPS algorithm is more robust compared to SAAPTCR. However, CPU time performance of SA is significantly better than MetaRaPS in both cases. ARRP experiments were conducted with various values of objective weighting factor for extended analysis. In the job arrival case, MetaRE and BestINSERT have significantly performed better than SEPRE in terms of average relative error for small size problems. In the case of job priority disruption, there is no significant difference between MetaRE, BestINSERT, and SHUFFLE algorithms. MetaRE has significantly performed better than LSHIFT to repair job departure disruptions and significantly superior to the BestINSERT algorithm in terms of both relative error and computational time for large size problems

A strong preemptive relaxation for weighted tardiness and earliness/tardiness problems on unrelated parallel machines

Research on due date oriented objectives in the parallel machine environment is at best scarce compared to objectives such as minimizing the makespan or the completion time related performance measures. Moreover, almost all existing work in this area is focused on the identical parallel machine environment. In this study, we leverage on our previous work on the single machine total weighted tardiness (TWT) and total weighted earliness/tardiness (TWET) problems and develop a new preemptive relaxation for the TWT and TWET problems on a bank of unrelated parallel machines. The key contribution of this paper is devising a computationally effective Benders decomposition algorithm for solving the preemptive relaxation formulated as a mixed integer linear program. The optimal solution of the preemptive relaxation provides a tight lower bound. Moreover, it offers a near-optimal partition of the jobs to the machines, and then we exploit recent advances in solving the non-preemptive single machine TWT and TWET problems for constructing non-preemptive solutions of high quality to the original problem. We demonstrate the effectiveness of our approach with instances up to 5 machines and 200 jobs

A strong preemptive relaxation for weighted tardiness and earliness/tardiness problems on unrelated parallel machines

Research on due date-oriented objectives in the parallel machine environment is at best scarce compared to objectives such as minimizing the makespan or the completion time-related performance measures. Moreover, almost all existing work in this area is focused on the identical parallel machine environment. In this study, we leverage on our previous work on the single machine total weighted tardiness (TWT) and total weighted earliness/tardiness (TWET) problems and develop a new preemptive relaxation for both problems on a bank of unrelated parallel machines. The key contribution of this paper is devising a computationally effective Benders decomposition algorithm to solve the preemptive relaxation formulated as a mixed-integer linear program. The optimal solution of the preemptive relaxation provides a tight lower bound. Moreover, it offers a near-optimal partition of the jobs to the machines. We then exploit recent advances in solving the nonpreemptive single-machine TWT and TWET problems for constructing nonpreemptive solutions of high quality to the original problem. We demonstrate the effectiveness of our approach with instances of up to five machines and 200 jobs