General Job Shop Scheduling Problem Research Articles

A Hybrid Algorithm Based on Particle Swarm Optimization and Artificial Immune for an Assembly Job Shop Scheduling Problem

To produce the final product, parts need to be fabricated in the process stages and thereafter several parts are joined under the assembly operations based on the predefined bill of materials. But assembly relationship between the assembly parts and components has not been considered in general job shop scheduling problem model. The aim of this research is to find the schedule which minimizes completion time of Assembly Job Shop Scheduling Problem (AJSSP). Since the complexity of AJSSP is NP-hard, a hybrid particle swarm optimization (HPSO) algorithm integrated PSO with Artificial Immune is proposed and developed to solve AJSSP. The selection strategy based on antibody density makes the particles of HPSO maintain the diversity during the iterative process, thus overcoming the defect of premature convergence. Then HPSO algorithm is applied into a case study development from classical FT06. Finally, the effect of key parameters on the proposed algorithm is analyzed and discussed regarding how to select the parameters. The experiment result confirmed its practice and effectiveness.

Hybrid Fuzzy Adaptive Particle Swarm Optimization Algorithm for Fuzzy Job Shop Scheduling Problem (FJSSP)

The processing time for each job in JSSP is often imprecise in many real world applications. Therefore, JSSP with fuzzy processing time was addressed in this paper. Triangular fuzzy numbers were used to describe the fuzzy processing time. In this paper, a hybrid particle swarm optimization (HPSO) algorithm was presented for solving JSSP. The quality of the PSO algorithm final solution depends on two factors: the quality of initial solutions and adjustment of PSO parameters. In this study, to improve the quality of initial solutions, a constructive greedy randomized adaptive search procedure (GRASP) algorithm was proposed. Furthermore, in order to adjust HPSO parameters, a fuzzy interference system was applied to compute these parameters at each iteration of HPSO. Therefore, the presented algorithm in this study was called hybrid fuzzy adoptive PSO (HFAPSO). Benchmarks with fuzzy processing time were used for testing the presented algorithm. General Terms Fuzzy job shop scheduling problem, Greedy randomized adaptive search procedure, Hybrid Particle Swarm Optimization.

A tabu search and a genetic algorithm for solving a bicriteria general job shop scheduling problem

This paper deals with a general job shop scheduling problem with multiple constraints, coming from printing and boarding industry. The objective is the minimization of two criteria, the makespan and the maximum lateness, and we are interested in finding an approximation of the Pareto frontier. We propose a fast and elitist genetic algorithm based on NSGA-II for solving the problem. The initial population of this algorithm is either randomly generated or partially generated by using a tabu search algorithm, that minimizes a linear combination of the two criteria. Both the genetic and the tabu search algorithms are tested on benchmark instances from flexible job shop literature and computational results show the interest of both methods to obtain an efficient and effective resolution method.

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.

Polynomial time approximation schemes for general multiprocessor job shop scheduling

We study preemptive and non-preemptive versions of the general multiprocessor job shop scheduling problem: Given a set of n tasks each consisting of at most μ ordered operations that can be processed on different (possibly all) subsets of m machines with different processing times, compute a schedule (preemptive or non-preemptive, depending on the model) with minimum makespan where operations belonging to the same task have to be scheduled according to the specified order. We propose algorithms for both preemptive and non-preemptive variants of this problem that compute approximate solutions of any positive ϵ accuracy and run in O( n) time for any fixed values of m, μ, and ϵ. These results include (as special cases) many recent developments on polynomial time approximation schemes for scheduling jobs on unrelated machines, multiprocessor tasks, and classical open, flow and job shops.

A THRESHOLD-ACCEPTING METAHEURISTIC METHOD FOR SCHEDULING THE OPERATIONS OF DEHYDRATION PLANTS

ABSTRACT Dehydration plants are broadly characterized by a multi-product nature chiefly attributed to the utilization of different raw materials to be processed sequentially so that demand constraints are met. Processing of raw materials is implemented through a series of preprocessing operations that together with drying constitute the production procedure of a pre-specified programme. The core of the manufacturing system that a typical dehydration plant involves, is scheduling of operations so that demand is fulfilled within a pre-determined time horizon imposed by production planning. The typical scheduling operation that dehydration plants involve can be formulated as a general job shop scheduling problem. The aim of this study is to describe a new metaheuristic method for solving the job shop scheduling problem of dehydration plants, termed as the Backtracking Adaptive Threshold Accepting (BATA) method. Our effort focuses on developing an innovative method, which produces reliable and high quality solutions, requiring reasonable computing effort. The main innovation of this method, towards a typical threshold accepting algorithm, is that during the optimization process the value of the threshold is not only lowered, but also raised or backtracked according to how effective a local search is. BATA is described in detail while a characteristic job shop scheduling case study for dehydration plant operations is presented.

A modern local search method for operations scheduling of dehydration plants

Drying operations constitute an important field of food engineering, which is still governed by empiricism. The utilisation of different raw materials to be processed sequentially so that demand constraints are met, broadly characterise dehydration plants as multi-product. Processing of raw materials is implemented through a series of pre-processing operations that together with drying constitute the production procedure of a pre-specified campaign. The basic component of the manufacturing system that a typical dehydration plant involves, is scheduling of operations so that demand is fulfilled within a pre-described time horizon imposed by production planning. The typical scheduling operation that dehydration plants involve, can be formulated as a general job shop scheduling problem. The aim of this study is to describe a new metaheuristic method for solving the job shop scheduling problem of dehydration plants, termed as backtracking adaptive threshold accepting (BATA) method. Our effort focuses on developing an innovative method, which produces reliable and good solutions, requiring reasonable computing effort. The main innovation of the method, towards a typical threshold accepting algorithm, is that the value of the threshold is not only lowered, but also raised or backtracked according to how effective a local search is. BATA is described in detail while its performance and characteristic job shop scheduling case studies for dehydration plant operations are presented.

A list-based threshold accepting method for job shop scheduling problems

Process plants typically produce a family of related products that require similar processing techniques. The most important problem encountered in such manufacturing systems is scheduling of operations so that demand is fulfilled within a pre-described time horizon imposed by production planning. The typical scheduling operation that process plants involve can be formulated as a general job shop scheduling problem. The aim of this study is to describe a new metaheuristic method for solving the job shop scheduling problem of process plants, termed as list-based threshold accepting (LBTA) method. The main advantage of this method over the majority of other metaheuristics is that it produces quite satisfactory solutions in reasonable amount of time by tuning only one parameter of the method. This property makes the LBTA a reliable and a practical tool for every decision support system designed for solving real life scheduling problems. The LBTA is described in detail, tested over classical benchmark problems found in literature and a while characteristic job shop scheduling case study for dehydration plant operations is presented.

Using Genetic Algorithms and Heuristics for Job Shop Scheduling with Sequence-Dependent Setup Times

The importance of job shop scheduling as a practical problem has attracted the attention of many researchers. However, most research has focused on special cases such as single machine, parallel machine, and flowshop environments due to the “hardness” of general job shop problems. In this paper, a hybrid algorithm based on an integration of a genetic algorithm and heuristic rules is proposed for a general job shop scheduling problem with sequence-dependent setups (Jm|sjk|Cmax ). An embedded simulator is employed to implement the heuristic rules, which greatly enhances the flexibility of the algorithm. Knowledge relevant to the problem is inherent in the heuristic rules making the genetic algorithm more efficient, while the optimization procedure provided by the genetic algorithm makes the heuristic rules more effective. Extensive numerical experiments have been conducted and the results have shown that the hybrid approach is superior when compared to recently published existing methods for the same problem.

A heuristic solution concept for a generalized machine sequencing problem with an application to radiator manufacturing

The job shop scheduling problem has received considerable attention from production and operations researchers since the early 1950s. However, scheduling practice in manufacturing systems up to now has tended to ignore the wealth of methods, techniques and results of scheduling theory. Relatively few articles have reported on successful applications of this theory. This paper considers a real problem in practice, namely a generalized job shop scheduling problem for a supplier for the automotive industry, which can be seen as typical for this line of business.The problem is described by a mixed integer programming model. Because an exact solution concept is not suited for the practical problem (the dimension of the real problem is too large) an approximative search-based algorithm is developed. Simulation results that show the qualitity level of the approximative scheme are reported.

Two simulated annealing-based heuristics for the job shop scheduling problem

In this paper, we present two simulated annealing-based algorithms for the classical, general job shop scheduling problem where the objective is to minimize the makespan. We consider sets of jobs consisting of tasks and sets of machines, which can handle at most one task at a time. To represent the problem, we employ the model of disjunctive graphs. Simulated annealing has been applied to this problem earlier, e.g., by Van Laarhoven et al., where the neighborhood function is based on reversing a single arc of a longest path of the underlying graph. In our approach, we analyze a neighborhood function which involves a non-uniform generation probability. To obtain the neighbors of a schedule, we reverse more than a single arc of longest paths and perform a control on the increase of the makespan. The selection of the arcs depends on the number of longest paths to which a particular arc belongs. Furthermore, we have designed two cooling schedules which employ a detailed analysis of the objective function. Depending on the specified neighborhood relation, the expected run-times can be either O( n 2+ ε ) or O( n 3+ ε / m) for the first cooling schedule and O( n 5/2+ ε · m 1/2) or O( n 7/2+ ε / m 1/2) for the second cooling schedule, where n is the number of tasks, m the number of machines and ε represents O( ln ln n/ ln n) . Our computational experiments on small to large benchmark problems have shown that within short series of consecutive trials relatively stable results equal or close to optimal solutions are repeatedly obtained, including the well-known benchmark problems FT10 and LA38. We could improve five upper bounds for the YN1, YN4, SWV12, SWV13, and SWV15 benchmark problems, e.g., for SWV13 the gap between the lower and the former upper bound has been shortened by about 57%. In our approach we rely only on basic information about the given problem instance.

Modelling with Objects and Constraints: Production Planning in Horticulture

Over the last decades interest in constraint networks has been rapidly increasing. In particular many papers have been published which focus on efficiency of constraint satisfaction algorithms. Often the performance of these algorithms is tested on problems such as the n-queens problem or the generalized job shop scheduling problem. In this article the activity of efficient modelling for practical applications in terms of objects and constraints is discussed. Such a discussion requires descriptions of models which are sufficiently explicit in order to be open for critic. The core of this article is such an explicit model in the context of horticultural production planning.

The One-Machine Problem with Delayed Precedence Constraints and its Use in Job Shop Scheduling

We study the one machine scheduling problem with release and delivery times and the minimum makespan objective, in the presence of constraints that for certain pairs of jobs require a delay between the completion of the first job and the start of the second (delayed precedence constraints). This problem arises naturally in the context of the Shifting Bottleneck Procedure for the general job shop scheduling problem, as a relaxation of the latter, tighter than the standard one-machine relaxation. The paper first highlights the difference between the two relaxations through some relevant complexity results. Then it introduces a modified Longest Tail Heuristic whose analysis identifies those situations that permit efficient branching. As a result, an optimization algorithm is developed whose performance is comparable to that of the best algorithms for the standard one-machine problem. Embedding this algorithm into a modified version of the Shifting Bottleneck Procedure that uses the tighter one-machine relaxation discussed here results in a considerable overall improvement in performance on all classes of job shop scheduling problems.

An effective heuristic method for generalized job shop scheduling with due dates

This paper is concerned with the generalized job shop scheduling problem with due dates wherein the objective is to minimize total job tardiness. An efficient heuristic algorithm called the revised exchange heuristic algorithm (REHA) is presented for solving this problem. It has been shown that the algorithm can be completed in polynomial time. Results, generated over a range of shop sizes with different due date tightness levels, indicate that the proposed technique is capable of yielding notable reductions in total tardiness (over initial schedules) for practical size problems. This suggests that this approach is an efficient scheduling option for this class of complex optimization problems.

Job Shop Scheduling under a Non-Renewable Resource Constraint

In this paper we consider the job shop scheduling problem under a discrete non-renewable resource constraint. We assume that jobs have arbitrary processing times and resource requirements and there is a unit supply of the resource at each time period. We develop an approximation algorithm for this problem and empirically test its effectiveness in finding the minimum makespan schedules. Most of the research done in the area of scheduling deals with the allocation of a single scarce resource over time to perform a collection of tasks. In this study, the scheduling environment is extended to include an additional non-renewable resource. The term non-renewable implies that the resource is actually being consumed by the jobs competing for it. Financial constraints are typical examples of such constraints and for this reason non-renewable resource constraints are often called financial constraints1. Materials shared by different products can also be regarded as a non-renewable resource in manufacturing environments. Considering these constraints explicitly is likely to yield more realistic schedules. A limited amount of research has been done in the area of non-renewable resource constrained scheduling. There are some polynomially bounded solution algorithms for precedence constrained scheduling problems2 and for pre-emptive scheduling of independent jobs on parallel machines1. In the case of arbitrary resource requirements and availabilities, Slowinski' states that Carlier has shown that even the non-preemptive single machine scheduling problem is NP-complete if job processing times are different from unity. In Toker et al.3, it is shown that when the amount of resource available at each time period is constant, the single machine non-renewable resource constrained problem is equivalent to a resource- free, two-machine flowshop problem. Hence it is solvable in polynomial time. They also extended their results to the m-machine case and showed how to transform different types of resource constrained problems into equivalent, unconstrained problems. The scheduling environment we consider is a job shop. A single non-renewable resource becomes available over time in equal quantities (say unity) and there is a set of jobs to be processed. Each operation requires an arbitrary amount of the non-renewable resource which must be available at the start of that operation and which is consumed during its processing. We used makespan as the performance measure. Optimization algorithms for the general job shop scheduling problem are restricted to implicit enumeration techniques, such as branch-and-bound based procedures4-7. On the other hand, approximation algorithms usually use a dispatching rule to give priorities to operations to be scheduled8. The non-renewable resource constrained job shop scheduling problem is NP-complete as, when all resource requirements are zero, it reduces to the unconstrained job shop problem which is NP-complete9. This complexity result serves as a formal justification to use approximation algorithms for the constrained problem. We first describe the approximation algorithm developed and then introduce two lower bounds for the n-job, m-machine resource-constrained job shop scheduling problem. Next, we discuss the computational results. Finally, we present our conclusions.

Optimization based job shop scheduling

A generalized job shop scheduling problem is defined in detail. The proposed factory description is sufficiently realistic to model the routing and sequencing decisions made in a real manufacturing plant. An optimization problem is posed, permitting the use of very general cost functions. A variation of the method of simulated annealing is proposed as a tool for the solution of the optimization problem. A novel technique for embedding the space of feasible schedules into a permutation group is used to define a neighborhood structure for the simulated annealing process. This technique has algorithmic advantages over working directly in the space of schedules. These ideas were used in the design and implementative of a scheduling software system. A brief description of the software system, called ABES for Annealing Based Experiment in Scheduling, and comments on its effectiveness are presented. >

AN EXCHANGE HEURISTIC FOR GENERALIZED JOB SHOP SCHEDULING

Abstract An efficient heuristic for the generalized job shop scheduling problem, with or without multiple parallel machines, is herein presented. This heuristic, in a somewhat more general form, was explained in some detail in our earlier work in project scheduling; and we now suggest that, through this approach, problems in the areas of job shop scheduling and project scheduling may be viewed as elements of the same class. Given an initial feasible solution, the algorithm seeks to improve on this schedule through reduction of makespan by effectively identifying rearrangement opportunities. The quality of the final schedule appears to be, in general, directly correlated to the quality of the starting solution. However, it is recommended that the process be initiated with a reasonably good randomly-generated schedule, rather than a better one produced through rule-based scheduling (such as the Longest Processing Time rule), owing to the fact that such better schedules actually tend to offer less opportunit...

On scheduling multi-processor systems with algebraic objectives

One of the well-studied models of combinatorial optimization is the scheduling problem dealing with a finite set of tasks, which have to be executed on a fixed number of machines so that a given objective is minimized. Each task requires a set of characteristic data like operating time, due date, penalty cost and technological requirements. An algebraic approach to the objective leads to a general problem which includes all classical cases of sum and bottleneck objectives known in literature. By solving an algebraic transportation problem a lower bound for the objective value can be determined. To obtain an optimal solution we employ a branch and bound procedure. Furthermore we consider the general job shop scheduling problem with algebraic objective function.