Multi-resource shop scheduling with resource flexibility

The shop scheduling problem tackled in this paper integrates many features that can be found in practical settings. Every operation may need several resources to be performed, and furthermore, a resource may be selected in a given set of candidates resources. Finally, we also consider that an operation may have more than one predecessor and/or more than one successor on the routing. The problem is then to both assign operations to resources and sequence operations on the resources, in order to minimize the maximum completion time. A disjunctive graph representation of this problem is presented and a connected neighborhood structure is proposed. The latter can be used to derive a local search algorithm such as tabu search. Finally, some numerical experiments are presented and discussed.     

Two-machine shop scheduling: Compromise between flexibility and makespan value

In this paper, we consider the problem of providing flexibility to solutions of two-machine shop scheduling problems. We use the concept of group-scheduling to characterize a whole set of schedules so as to provide more choice to the decision-maker at any decision point. A group-schedule is a sequence of groups of permutable operations defined on each machine where each group is such that any permutation of the operations inside the group leads to a feasible schedule. Flexibility of a solution and its makespan are often conflicting, thus we search for a compromise between a low number of groups and a small value of makespan. We resolve the complexity status of the relevant problems for the two-machine flow shop, job shop and open shop. A number of approximation algorithms are developed and their worst-case performance is analyzed. For the flow shop, an effective heuristic algorithm is proposed and the results of computational experiments are reported.     

Outsourcing and scheduling for two-machine ordered flow shop scheduling problems

This paper considers a two-machine ordered flow shop problem, where each job is processed through the in-house system or outsourced to a subcontractor. For in-house jobs, a schedule is constructed and its performance is measured by the makespan. Jobs processed by subcontractors require paying an outsourcing cost. The objective is to minimize the sum of the makespan and the total outsourcing cost. Since this problem is NP-hard, we present an approximation algorithm. Furthermore, we consider three special cases in which job j has a processing time requirement p_j, and machine i a characteristic q_i. The first case assumes the time job j occupies machine i is equal to the processing requirement divided by a characteristic value of machine i, that is, p_j/q_i. The second (third) case assumes that the time job j occupies machine i is equal to the maximum (minimum) of its processing requirement and a characteristic value of the machine, that is, max{p_j, q_i} (min{p_j, q_i}). We show that the first and the second cases are NP-hard and the third case is polynomially solvable.     

Routing open shop and flow shop scheduling problems

We consider a generalization of the classical open shop and flow shop scheduling problems where the jobs are located at the vertices of an undirected graph and the machines, initially located at the same vertex, have to travel along the graph to process the jobs. The objective is to minimize the makespan. In the tour-version the makespan means the time by which each machine has processed all jobs and returned to the initial location. While in the path-version the makespan represents the maximum completion time of the jobs. We present improved approximation algorithms for various cases of the open shop problem on a general graph, and the tour-version of the two-machine flow shop problem on a tree. Also, we prove that both versions of the latter problem are NP-hard, which answers an open question posed in the literature.     

Approximative procedures for no-wait job shop scheduling

In this article we consider the no-wait job shop problem with makespan objective. Based on a decomposition of the problem into a sequencing and a timetabling problem, we propose two local search algorithms. Extensive computational tests in which the algorithms compare favorably to the best existing strategies are reported. Although not specifically designed for that purpose, our algorithms also outperform one of the best no-wait flow shop algorithms in literature.     

Surrogate duality relaxation for job shop scheduling

Surrogate duality bounds for the job shop scheduling problem are obtained by replacing certain constraints by their weighted sum and strengthening the aggregate constraint by iterating over all possible weights. The constraints successively considered for this purpose are the capacity constraints on the machines and the precedence constraints determining the machine order for each job. The resulting relaxations are investigated from a theoretical and a computational point of view.     

Inapproximability results for no-wait job shop scheduling

We investigate the approximability of the no-wait job shop scheduling problem under the makespan criterion. We show that this problem is -hard (i) for the case of two machines with at most five operations per job, and (ii) for the case of three machines with at most three operations per job. Hence, these problems do not possess a polynomial time approximation scheme, unless .     

Approximability of flow shop scheduling

Shop scheduling problems are notorious for their intractability, both in theory and practice. In this paper, we construct a polynomial approximation scheme for the flow shop scheduling problem with an arbitrary fixed number of machines. For the three common shop models (open, flow, and job), this result is the only known approximation scheme. Since none of the three models can be approximated arbitrarily closely in the general case (unless P = NP), the result demonstrates the approximability gap between the models in which the number of machines is fixed, and those in which it is part of the input of the instance. The result can be extended to flow shops with job release dates and delivery times and to flow shops with a fixed number of stages, where the number of machines at any stage is fixed. © 1998 The Mathematical Programming Society, Inc. Published by Elsevier Science B.V.A preliminary version of this paper appeared in theProceedings of the 36th Annual IEEE Symposium on the Foundations of Computer Science, 1995.Research supported by NSF grant DMI-9496153.     

High-multiplicity cyclic job shop scheduling

We consider the High-Multiplicity Cyclic Job Shop Scheduling Problem. There are two objectives of interest: the cycle time and the flow time. We give several approximation algorithms after showing that a very restricted case is APX-hard.     

Survey on fuzzy shop scheduling

The real life scheduling problems often have several uncertainties. The solutions of these problems can provide deeper insights to the decision maker than those of deterministic problems. Fuzzy set theory as most important tool to model uncertainty represents an attractive tool to aid research in the production management. Since to the best of our knowledge, there is not a comprehensive review on the fuzzy scheduling literature, the goal of this paper is to provide an extensive review for the fuzzy machine scheduling which it covers more than 140 papers. For this purpose, first, this paper classifies and reviews the literature according to shop environments, including single machine, parallel machines, flowshop, job shop and open shop. Then the reviewed literature is quantified and measured. At the end the paper concludes by presenting some problems receiving less attention than the others and proposing some research opportunities in the field.     

A genetic algorithm for flow shop scheduling problems

Many scheduling problems are NP-hard problems. For such NP-hard combinatorial optimization problems, heuristics play a major role in searching for near-optimal solutions. In this paper we develop a genetic algorithm-based heuristic for the flow shop scheduling problem with makespan as the criterion. The performance of the algorithm is compared with the established NEH algorithm. Computational experience indicates that genetic algorithms can be good techniques for flowshop scheduling problems.     

Analysis of flow shop scheduling anomalies

Anomalies in flow shop scheduling are rare; only two anomalies have been reported. We present five new anomalies for the permutation flow shop models with the minimum makespan objective and seven more anomalies for the minimum total flow time objective. These anomalies (including the existing ones) are divided into three types corresponding to an increased processing time of a single operation, the addition of a job and the addition of a machine. We derive two properties which, when satisfied, eliminate the possibility of certain anomalies. We conclude that restrictions such as no-delay schedules, no job waiting or no machine idle time (after it starts processing) often result in anomalies. We also show that anomalies can also occur in non-permutation flow shops (four new anomalies presented).     

Flow shop scheduling with heterogeneous workers

We propose an extension to the flow shop scheduling problem named Heterogeneous Flow Shop Scheduling Problem (Het-FSSP), where two simultaneous issues have to be resolved: finding the best worker assignment to the workstations, and solving the corresponding scheduling problem. This problem is motivated by Sheltered Work centers for Disabled, whose main objective is the labor integration of persons with disabilities, an important aim not only for these centers but for any company desiring to overcome the traditional standardized vision of the workforce. In such a scenario the goal is to maintain high productivity levels by minimizing the maximum completion time, while respecting the diverse capabilities and paces of the heterogeneous workers, which increases the complexity of finding an optimal schedule. We present a mathematical model that extends a flow shop model to admit a heterogeneous worker assignment, and propose a heuristic based on scatter search and path relinking to solve the problem. Computational results show that this approach finds good solutions within a short time, providing the production managers with practical approaches for this combined assignment and scheduling problem.     

The hybrid flow shop scheduling problem

The scheduling of flow shops with multiple parallel machines per stage, usually referred to as the hybrid flow shop (HFS), is a complex combinatorial problem encountered in many real world applications. Given its importance and complexity, the HFS problem has been intensively studied. This paper presents a literature review on exact, heuristic and metaheuristic methods that have been proposed for its solution. The paper briefly discusses and reviews several variants of the HFS problem, each in turn considering different assumptions, constraints and objective functions. Research opportunities in HFS are also discussed.     

Optimal policies in stochastic shop scheduling

In this paper a survey is presented of some of the recent results in stochastic open shop, flow shop and job shop scheduling. The distributions of the processing times of the jobs are known in advance, but the actual processing times are not known in advance. The jobs may have due dates. Optimal preemptive and nonpreemptive policies are determined for the minimization of various objective functions, such as the expected makespan, the expected flow time and the expected number of late jobs. The effect of various degrees of dependence between the processing times of any given job on the various machines is investigated. Under given conditions bounds are obtained for the expected makespan in the different models.Partially supported by the National Science Foundation (NSF), under grant ECS-8115344 with the Georgia Institute of Technology.     

Job shop scheduling with beam search

Beam Search is a heuristic method for solving optimization problems. It is an adaptation of the branch and bound method in which only some nodes are evaluated in the search tree. At any level, only the promising nodes are kept for further branching and remaining nodes are pruned off permanently. In this paper, we develop a beam search based scheduling algorithm for the job shop problem. Both the makespan and mean tardiness are used as the performance measures. The proposed algorithm is also compared with other well known search methods and dispatching rules for a wide variety of problems. The results indicate that the beam search technique is a very competitive and promising tool which deserves further research in the scheduling literature.     

Fuzzy job shop scheduling with lot-sizing

This paper deals with a problem of determining lot-sizes of jobs in a real-world job shop-scheduling in the presence of uncertainty. The main issue discussed in this paper is lot-sizing of jobs. A fuzzy rule-based system is developed which determines the size of lots using the following premise variables: size of the job, the static slack of the job, workload on the shop floor, and the priority of the job. Both premise and conclusion variables are modelled as linguistic variables represented by using fuzzy sets (apart from the priority of the job which is a crisp value). The determined lots’ sizes are input to a fuzzy multi-objective genetic algorithm for job shop scheduling. Imprecise jobs’ processing times and due dates are modelled by using fuzzy sets. The objectives that are used to measure the quality of the generated schedules are average weighted tardiness of jobs, the number of tardy jobs, the total setup time, the total idle time of machines and the total flow time of jobs. The developed algorithm is analysed on real-world data obtained from a printing company.