Two-stage flexible flow shop scheduling subject to fixed job sequences

This paper investigates the scheduling problem in a two-stage flexible flow shop, which consists of m stage-1 parallel dedicated machines and a stage-2 bottleneck machine, subject to the condition that n _l jobs per type l∈{1, …, m} are processed in a fixed sequence. Four regular performance metrics, including the total completion time, the maximum lateness, the total tardiness, and the number of tardy jobs, are considered. For each considered objective function, we aim to determine an optimal interleaving processing sequence of all jobs coupled with their starting times on the stage-2 bottleneck machine. The problem under study is proved to be strongly NP-hard. An O(m²Π_l=1 ^m n _l ²) dynamic programming algorithm coupled with numerical experiments is presented.     

Scheduling for fabrication and assembly in a two-machine flowshop with a fixed job sequence

This paper studies a problem of scheduling fabrication and assembly operations in a two-machine flowshop, subject to the same predetermined job sequence on each machine. In the manufacturing setting, there are n products, each of which consists of two components: a common component and a unique component which are fabricated on machine 1 and then assembled on machine 2. Common components of all products are processed in batches preceded by a constant setup time. The manufacturing process related to each single product is called a job. We address four regular performance measures: the total job completion time, the maximum job lateness, the total job tardiness, and the number of tardy jobs. Several optimality properties are presented. Based upon the concept of critical path and block schedule, a generic dynamic programming algorithm is developed to find an optimal schedule in O(n ⁷) time.     

Flexible job shop scheduling problem for parallel batch processing machine with compatible job families

Flexible Job-Shop Scheduling Problem (FJSP) with Parallel Batch processing Machine (PBM) is studied. First, a Mixed Integer Programming (MIP) formulation is proposed for the first time. In order to address an NP-hard structure of this problem, the formulation is modified to selectively schedule jobs. Although there are many jobs on a given floor, semiconductor manufacturing is most challenged by priority jobs that promise a significant amount of financial compensation in exchange for an expedited delivery. This modification could leave some non-priority jobs unscheduled. However, it vastly expedites the discovery of improving solutions by first branching on integer variables with higher priority jobs. This study then turns job-dependent processing times into job-independent ones by assuming a machine has an equal processing time on different jobs. This assumption is roughly true or acceptable for the sake of the reduced computational time in the industry. These changes significantly reduce computational time compared to the original model when tested on a set of common problem instances from the literature. Computational results show that this proposed model can generate an effective schedule for large problems. Author encourages other researchers to propose an improved MIP model.     

Two-machine flowshop scheduling problem with coupled-operations

This paper addresses a generalization of the coupled-operations scheduling problem in the context of a flow shop environment. We consider the two-machine scheduling problem with the objective of minimizing the makespan. Each job consists of a coupled-operation to be processed first on the first machine and a single operation to be then processed on the second machine. A coupled-operation contains two operations separated by an exact time delay. The single operation can start on the second machine only when the coupled-operation on the first machine is completed. We prove the NP-completeness of two restricted versions of the general problem, whereas we also exhibit several other well solvable cases.

     

Resolution of a scheduling problem in a flowshop robotic cell

We develop in this paper a generic and precise identification of a scheduling problem in a flexible manufacturing system. We consider a flowshop robotic cell that processes several jobs. We assume that there is no intermediate buffer between machines. So, jobs may be blocked when downstream machines are busy. We present an integer programming model to determine the sequence of jobs that minimizes the makespan criterion. In order to solve large size problems, we propose a genetic algorithm (GA). Finally, computational experiments are proposed in order to compare the makespan returned by the GA to a lower bound.     

Fuzzy scheduling of job orders in a two-stage flowshop with batch-processing machines

In this paper, we present a mixed-integer fuzzy programming model and a genetic algorithm (GA) based solution approach to a scheduling problem of customer orders in a mass customizing furniture industry. Independent job orders are grouped into multiple classes based on similarity in style so that the required number of setups is minimized. The family of jobs can be partitioned into batches, where each batch consists of a set of consecutively processed jobs from the same class. If a batch is assigned to one of available parallel machines, a setup is required at the beginning of the first job in that batch. A schedule defines the way how the batches are created from the independent jobs and specifies the processing order of the batches and that of the jobs within the batches. A machine can only process one job at a time, and cannot perform any processing while undergoing a setup. The proposed formulation minimizes the total weighted flowtime while fulfilling due date requirements. The imprecision associated with estimation of setup and processing times are represented by fuzzy sets.     

A bi-criteria two-machine flowshop scheduling problem with a learning effect

This paper addresses a bi-criteria two-machine flowshop scheduling problem when the learning effect is present. The objective is to find a sequence that minimizes a weighted sum of the total completion time and the maximum tardiness. In this article, a branch-and-bound method, incorporating several dominance properties and a lower bound, is presented to search for the exact solution for small job-size problems. In addition, two heuristic algorithms are proposed to overcome the inefficiency of the branch-and-bound algorithm for large job-size problems. Finally, computational results for this problem are provided to evaluate the performance of the proposed algorithms.     

A note on batch scheduling on a two-machine flowshop with machine-dependent processing times

4OR - We study a batch scheduling problem on a two-machine flowshop. Unlike most relevant research papers focusing on batching with identical job processing times, we assume machine-dependent...     

Surgical case scheduling as a generalized job shop scheduling problem

Surgical case scheduling allocates hospital resources to individual surgical cases and decides on the time to perform the surgeries. This task plays a decisive role in utilizing hospital resources efficiently while ensuring quality of care for patients. This paper proposes a new surgical case scheduling approach which uses a novel extension of the Job Shop scheduling problem called multi-mode blocking job shop (MMBJS). It formulates the MMBJS as a mixed integer linear programming (MILP) problem and discusses the use of the MMBJS model for scheduling elective and add-on cases. The model is illustrated by a detailed example, and preliminary computational experiments with the CPLEX solver on practical-sized instances are reported.     

Unbounded parallel batch scheduling with job delivery to minimize makespan

We consider unbounded parallel batch scheduling with job delivery to minimize makespan. When the jobs have identical size, we provide a polynomial-time algorithm. When the jobs have non-identical sizes, we provide a heuristic with a worst-case performance ratio 7/4.     

Cooperative metaheuristics for the permutation flowshop scheduling problem

In this work, we propose cooperative metaheuristic methods for the permutation flowshop scheduling problem considering two objectives separately: total tardiness and makespan. We use the island model where each island runs an instance of the algorithm and communications start when the islands have reached certain level of evolution, that is, communication is not allowed from the beginning of the execution. Subsequent ones occur when new better solutions are found. We carry out an exhaustive comparison of the cooperative methods against the sequential counterparts running in completely comparable scenarios. Results have been carefully analysed by means of statistical procedures and we can conclude that the cooperative methods yield much better results than the sequential algorithms and state-of-the-art methods running in the same number of processors but without communications. The proposed cooperative schemes are easy to apply to other algorithms and problems.     

Realistic two-stage flowshop batch scheduling problems with transportation capacity and times

This paper investigates single-batch and batch-single flow shop scheduling problem taking transportation among machines into account. Both transportation capacity and transportation times are explicitly considered. While the single processing machine processes one job at a time, the batch processing machine processes a batch of jobs simultaneously. The batch processing time is the longest processing times of jobs assigned to that batch.Each problem is formulated as a mixed integer programming model to find optimal makespan. Lower bounds and heuristic algorithms are proposed and computational experiments are carried out to verify their effectiveness.     

Minimizing energy consumption and makespan in a two-machine flowshop scheduling problem

Energy consumption has become a key concern for manufacturing sector because of negative environmental impact of operations. We develop constructive heuristics and multi-objective genetic algorithms (MOGA) for a two-machine sequence-dependent permutation flowshop problem to address the trade-off between energy consumption as a measure of sustainability and makespan as a measure of service level. We leverage the variable speed of operations to develop energy-efficient schedules that minimize total energy consumption and makespan. As minimization of energy consumption and minimization of makespan are conflicting objectives, the solutions to this problem constitute a Pareto frontier. We compare the performance of constructive heuristics and MOGAs with CPLEX and random search in a wide range of problem instances. The results show that MOGAs hybridized with constructive heuristics outperform regular MOGA and heuristics alone in terms of quality and cardinality of Pareto frontier. We provide production planners with new and scalable solution techniques that will enable them to make informed decisions considering energy consumption together with service objectives in shop floor scheduling.     

A new constructive heuristic for the flowshop scheduling problem

This paper presents a simple constructive heuristic (HFC) for the flowshop makespan problem which is capable of producing non-permutation schedules when it deems it appropriate. HFC determines the order of any two jobs in the final schedule based on their order in all two-machine problems embedded in the problem. Computational experiments indicate that HFC performs as well as NEH which is the currently best available constructive heuristic on problems where a permutation schedule is expected to be optimal. However, HFC outperforms NEH on problems where a non-permutation schedule may be optimal.     

A branch-and-bound algorithm with fuzzy inference for a permutation flowshop scheduling problem

This paper considers an m-machine permutation flowshop scheduling problem of minimizing the makespan. This classical scheduling problem is still important in modern manufacturing systems, and is well known to be intractable (i.e., NP-hard). In fact branch-and-bound algorithms developed so far for this problem have not come to solve large scale problem instances with over a hundred jobs. In order to improve the performance of branch-and-bound algorithms this paper proposes a new dominance relation by which the search load could be reduced, and notices that it is based on a sufficient precondition. This suggests that the dominance relation holds with high possibility even if the precondition approximately holds, thus being more realistic. The branch-and-bound algorithm proposed here takes advantage of this possibility for obtaining an optimal solution as early as possible in the branch-and-bound search. For this purpose this paper utilizes membership functions in the context of the fuzzy inference. Extensive numerical experiments that were executed through Monte Carlo simulations and benchmark tests show that the developed branch-and-bound algorithm can solve 3-machine problem instances with up to 1000 jobs with probability of over 99%, and 4-machine ones with up to 900 jobs with over 97%.     

Solving a chemical batch scheduling problem by local search

In this paper the following chemical batch scheduling problem is considered: a set of orders has to be processed on a set of facilities. For each order a given amount of a product must be produced by means of chemical reactions before a given deadline. The production consists of a sequence of processes whereby each process has to be performed by one facility out of a given subset of facilities allowed for this process. The processing times depend on the choice of the facility and the processing is done in batch mode with given minimum and maximum sizes. The problem is to assign the processes to the facilities, splitting them into batches, and scheduling these batches in order to produce the demands within the given deadlines. For the scheduling part of the problem we present an approach based on the following steps. First, a procedure to calculate the minimum number of batches needed to satisfy the demands is presented. Based on this, the given problem is modeled in two different ways: as a general shop scheduling problem with set-up times or as scheduling problem with positive time-lags. Finally, a two-phase tabu search method is presented which is based on the two different formulations of the problem. The method is tested on some real world data. This revised version was published online in June 2006 with corrections to the Cover Date.     

A filter-and-fan approach to the job shop scheduling problem

The job shop scheduling problem (JSSP) is a notoriously difficult problem in combinatorial optimization. Extensive investigation has been devoted to developing efficient algorithms to find optimal or near-optimal solutions. This paper proposes a new heuristic algorithm for the JSSP that effectively combines the classical shifting bottleneck procedure (SBP) with a dynamic and adaptive neighborhood search procedure. Our new search method, based on a filter-and-fan (F&F) procedure, uses the SBP as a subroutine to generate a starting solution and to enhance the best schedules produced. The F&F approach is a local search procedure that generates compound moves by a strategically abbreviated form of tree search. Computational results carried out on a standard set of 43 benchmark problems show that our F&F algorithm performs more robustly and effectively than a number of leading metaheuristic algorithms and rivals the best of these algorithms.     

A single machine batch scheduling problem with bounded batch size

We address a single-machine batch scheduling problem to minimize total flow time. Processing times are assumed to be identical for all jobs. Setup times are assumed to be identical for all batches. As in many practical situations, batch sizes may be bounded. In the first setting studied in this paper, all batch sizes cannot exceed a common upper bound. In the second setting, all batch sizes share a common lower bound. An optimal solution consists of the number of batches and their (integer) size. We introduce an efficient solution for both problems.