Multiprocessor task scheduling in multistage hybrid flowshops: A hybrid artificial bee colony algorithm with bi-directional planning

In this paper, the problem of scheduling multistage hybrid flowshops with multiprocessor tasks is contemplated. This is a strongly NP-hard problem for which a hybrid artificial bee colony (HABC) algorithm with bi-directional planning is developed to minimize makespan. To validate the effectiveness of the proposed algorithm, computational experiments were tested on two well-known benchmark problem sets. The computational evaluations manifestly support the high performance of the proposed HABC against the best-so-far algorithms applied in the literature for the same benchmark problem sets.     

Lagrangian relaxation with cut generation for hybrid flowshop scheduling problems to minimize the total weighted tardiness

In this paper, we address a new Lagrangian relaxation (LR) method for solving the hybrid flowshop scheduling problem to minimize the total weighted tardiness. For the conventional LR, the problem relaxing machine capacity constraints can be decomposed into individual job-level subproblems which can be solved by dynamic programming. The Lagrangian dual problem is solved by the subgradient method. In this paper, a Lagrangian relaxation with cut generation is proposed to improve the Lagrangian bounds for the conventional LR. The lower bound is strengthened by imposing additional constraints for the relaxed problem. The state space reductions for dynamic programming for subproblems are also incorporated. Computational results demonstrate that the proposed method outperforms the conventional LR method without significantly increasing the total computing time.     

A new Lagrangian relaxation algorithm for hybrid flowshop scheduling to minimize total weighted completion time

We investigate the problem of scheduling n jobs in s-stage hybrid flowshops with parallel identical machines at each stage. The objective is to find a schedule that minimizes the sum of weighted completion times of the jobs. This problem has been proven to be NP-hard. In this paper, an integer programming formulation is constructed for the problem. A new Lagrangian relaxation algorithm is presented in which precedence constraints are relaxed to the objective function by introducing Lagrangian multipliers, unlike the commonly used method of relaxing capacity constraints. In this way the relaxed problem can be decomposed into machine type subproblems, each of which corresponds to a specific stage. A dynamic programming algorithm is designed for solving parallel identical machine subproblems where jobs may have negative weights. The multipliers are then iteratively updated along a subgradient direction. The new algorithm is computationally compared with the commonly used Lagrangian relaxation algorithms which, after capacity constraints are relaxed, decompose the relaxed problem into job level subproblems and solve the subproblems by using the regular and speed-up dynamic programming algorithms, respectively. Numerical results show that the new Lagrangian relaxation method produces better schedules in much shorter computation time, especially for large-scale problems.     

A tabu search heuristic for the hybrid flowshop scheduling with finite intermediate buffers

This paper investigates the hybrid flowshop scheduling with finite intermediate buffers, whose objective is to minimize the sum of weighted completion time of all jobs. Since this problem is very complex and has been proven strongly NP-hard, a tabu search heuristic is proposed. In this heuristic there are two main features. One is that a scatter search mechanism is incorporated to improve the diversity of the search procedure. And the other is that a permutation of N jobs representing their processing order in the first stage instead of a complex complete schedule is used to denote a solution. Computational experiments on randomly generated instances with different structures show that the proposed tabu search heuristic can provide good solutions compared to both the lower bounds and the algorithm proposed for this problem in a lately published literature.     

Single machine scheduling with controllable processing times to minimize total tardiness and earliness

In most deterministic scheduling problems job processing times are considered as invariable and known in advance. Single machine scheduling problem with controllable processing times with no inserted idle time is presented in this study. Job processing times are controllable to some extent that they can be reduced or increased, up to a certain limit, at a cost proportional to the reduction or increase. In this study, our objective is determining a set of compression/expansion of processing times in addition to a sequence of jobs simultaneously, so that total tardiness and earliness are minimized. A mathematical model is proposed firstly and afterward a net benefit compression–net benefit expansion (NBC–NBE) heuristic is presented so as to acquire a set of amounts of compression and expansion of jobs processing times in a given sequence. Three heuristic techniques in small problems and in medium-to-large instances two meta-heuristic approaches, as effective local search methods, as well as these heuristics are employed to solve test examples. The single machine total tardiness problem (SMTTP) is already NP-hard, so the considered problem is NP-hard obviously. The computational experiments demonstrate that our proposed heuristic is efficient approach for such just-in-time (JIT) problem, especially equipped with competent heuristics.     

The two-stage assembly scheduling problem to minimize total completion time with setup times

We address the two-stage assembly scheduling problem where there are m machines at the first stage and an assembly machine at the second stage. The objective is to schedule the available n jobs so that total completion time of all n jobs is minimized. Setup times are treated as separate from processing times. This problem is NP-hard, and therefore we present a dominance relation and propose three heuristics. The heuristics are evaluated based on randomly generated data. One of the proposed heuristics is known to be the best heuristic for the case of zero setup times while another heuristic is known to perform well for such problems. A new version of the latter heuristic, which utilizes the dominance relation, is proposed and shown to perform much better than the other two heuristics.     

A hybrid genetic algorithm for the single machine scheduling problem with sequence-dependent setup times

This paper presents a hybrid approach based on the integration between a genetic algorithm (GA) and concepts from constraint programming, multi-objective evolutionary algorithms and ant colony optimization for solving a scheduling problem. The main contributions are the integration of these concepts in a GA crossover operator. The proposed methodology is applied to a single machine scheduling problem with sequence-dependent setup times for the objective of minimizing the total tardiness. A sensitivity analysis of the hybrid approach is carried out to compare the performance of the GA and the hybrid genetic algorithm (HGA) approaches on different benchmarks from the literature. The numerical experiments demonstrate the HGA efficiency and effectiveness which generates solutions that approach those of the known reference sets and improves several lower bounds.     

Hybrid genetic algorithms with dispatching rules for unrelated parallel machine scheduling with setup time and production availability

This article considers the unrelated parallel machine scheduling problem with sequence- and machine-dependent setup times and machine-dependent processing times. Furthermore, the machine has a production availability constraint to each job. The objective of this problem is to determine the allocation policy of jobs and the scheduling policy of machines to minimize the total completion time. To solve the problem, a mathematical model for the optimal solution is derived, and hybrid genetic algorithms with three dispatching rules are proposed for large-sized problems. To assess the performance of the algorithms, computational experiments are conducted and evaluated using several randomly generated examples.     

Rule-based scheduling in wafer fabrication with due date-based objectives

Wafer fabrication is a capital-intensive and highly complex manufacturing process. In the wafer fabrication facility (fab), wafers are grouped as a lot to go through repeated sequences of operations to build circuitry. Lot scheduling is an important task for manufacturers to improve production efficiency and meet customers’ requirements of on-time delivery. In this research we propose a dispatching rule for lot scheduling in wafer fabs, focusing on three due date-based objectives: on-time delivery rate, mean tardiness, and maximum tardiness. Although many dispatching rules have been proposed in the literature, they usually perform well in some objectives and bad in others. Our rule implements good principles in existing rules by means of (1) an urgency function for a single lot, (2) a priority index function considering total urgency of multiple waiting lots, (3) a due date extension procedure for dealing with tardy lots, and (4) a lot filtering procedure for selecting urgent lots. Simulation experiments are conducted using nine data sets of fabs. Six scenarios formed by two levels of load and three levels of due date tightness are tested for each fab. Performance verification of the proposed rule is achieved by comparing with nine benchmark rules. The experimental results show that the proposed rule outperforms the benchmark rules in terms of all concerned objective functions.     

Job shop scheduling with setup times, deadlines and precedence constraints

In the last 15 years several procedures have been developed that can find solutions of acceptable quality in reasonable computing time to Job Shop Scheduling problems in environments that do not involve sequence-dependent setup times of the machines. The presence of the latter, however, changes the picture dramatically. In this paper we adapt one of the best known heuristics, the Shifting Bottleneck Procedure, to the case when sequence dependent setup times play an important role. This is done by treating the single machine scheduling problems that arise in the process as Traveling Salesman Problems with time windows, and solving the latter by an efficient dynamic programming algorithm. The model treated here also incorporates precedence constraints, release times and deadlines. Computational experience on a vast array of instances, mainly from the semiconductor industry, shows our procedure to advance substantially the state of the art. Paper presented in New York at MISTA 2005. E. Balas supported by the National Science Foundation through grant DMI-9802773 and by the Office of Naval Research through contract #N00014-97-1-0133.     

Exact and heuristic algorithms for the aerial refueling parallel machine scheduling problem with due date-to-deadline window and ready times

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 ready times and due date-to-deadline window to minimize total weighted tardiness. ARSP assumes that the jobs have different ready times and a due date-to-deadline window between refueling due date and a deadline to return without refueling. In this paper, we first formulate the ARSP as a mixed integer programming model. The objective function is a piece-wise tardiness cost that takes into account due date-to-deadline windows and job priorities. Since ARSP is NP-hard, two heuristics are proposed to obtain solutions in reasonable computation times, namely (1) modified ATC rule (MATC), (2) a simulated annealing method (SA). The proposed heuristic algorithms are tested in terms of solution quality and CPU time through computational experiments with data randomly generated to represent aerial refueling operations of an in-theater air operation. Solutions provided by both algorithms were 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, MATC is more likely to outperform SA 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 MATC is significantly better than SA in both cases.     

A hybrid multi-objective genetic algorithm for planning order release date in two-level assembly system with random lead times

Supply planning of two-level assembly system is considered in this paper in which lead times are stochastic at both levels. Finding optimal order release dates of components is our aim which optimizes problem’s performance metrics. There is a determined due date that if demands are not prepared for delivery in that day, backlogging cost would happen. The other noticeable cost that should be taken in to consideration is holding cost, which may occur if components arrive before their time of assembling. In contrast to most of studies in this field that consider sum of these cost, this paper attempts to make a tradeoff between these objectives’ affects using multi-objective approach. This approach hybridizes an evolutionary optimizer, genetic algorithm, with an electromagnetism-like mechanism (EM). The algorithm’s effectiveness is compared against an adapted non-dominated sorting genetic algorithm II (NSGA-II) which has been presented for this problem.     

Adaptive lead time quotation in a pull production system with lead time responsive demand

In this paper, a single-stage single-class kanban controlled manufacturing system is considered, where the problem is quoting accurate lead times for orders that are generated by an MRP system. Order release mechanism as in classical MRP is sensitive to the changes in the lead time according to the concept of lead time syndrome. The objective is to establish a cost effective lead time quoting procedure. The problem is modeled as a two-dimensional Markov chain, and it is solved explicitly by using matrix geometric techniques. Comparative analysis is done between static and dynamic lead time quoting procedures, and significant cost benefits of the dynamic procedure are shown under various scenarios. Guidelines for setting design parameters such as the number of kanbans and the frequency of updating the lead time are provided through numerical tests.     

Dynamic localization with hybrid trilateration for mobile robots in intelligent space

In this paper, we propose a new localization algorithm based on a hybrid trilateration algorithm for obtaining an accurate position of a robot in intelligent space. The proposed algorithm is also able to estimate a position of the moving robot by using the extended Kalman filter, taking into consideration time synchronization and velocity of the robot. For realizing the localization system, we employ several smart sensors as beacons on the ceiling in intelligent space and as a listener attached to the robot. Finally, simulation results show the feasibility and effectiveness of the proposed localization algorithm compared with existing trilateration algorithms.     

A scheduling problem in blocking hybrid flow shop robotic cells with multiple robots

This paper addresses the robotic scheduling problem in blocking hybrid flow shop cells that consider multiple part types, unrelated parallel machines, multiple robots and machine eligibility constraints. Initially, a mixed integer linear programming (MILP) model is proposed to minimize the makespan for this problem. Due to the complexity of the model, a simulated annealing (SA) based solution approach is developed for its solution. To increase the efficiency of the SA algorithm, a new neighborhood structure based on block properties is applied. The performance of the proposed SA is assessed over a set of randomly generated instances. The computational results demonstrate that the SA algorithm is effective with the employed neighborhood structure. Additionally, this study shows that the appropriate number of robots depends on the sequence of processing operations to be performed at each stage.