Integrated production scheduling and maintenance policy for robustness in a single machine

This paper addresses the problem of finding robust production and maintenance schedules for a single machine with failure uncertainty. Both production and maintenance activities occupy the machine׳s capacity, while production depletes the machine׳s reliability and maintenance restores its reliability. Thus, we propose a proactive joint model which simultaneously determines the production scheduling and maintenance policy to optimize the robustness of schedules. Then, a three-Phase heuristic algorithm is devised to solve the mathematic model. Computational results indicate that the performance of solution can be significantly improved using our algorithm compared with the solutions by the traditional way. Furthermore, the balance of quality robustness and solution robustness and the impact of jobs׳ due dates are explored in detail.     

A genetic algorithm approach for the single machine scheduling problem with linear earliness and quadratic tardiness penalties

In this paper, we consider the single machine scheduling problem with linear earliness and quadratic tardiness costs, and no machine idle time. We propose a genetic approach based on a random key alphabet. Several genetic algorithms based on this approach are presented. These versions differ on the generation of the initial population, as well as on the use of local search. The proposed procedures are compared with existing heuristics, as well as with optimal solutions for the smaller instance sizes.     

Dispatching heuristics for the single machine weighted quadratic tardiness scheduling problem

In this paper, we consider the single machine scheduling problem with weighted quadratic tardiness costs. Several efficient dispatching rules are proposed. These include existing heuristics for the linear problem, as well as procedures suitably adapted to the quadratic objective function. Also, both forward and backward scheduling procedures are considered.The computational results show that the heuristics that specifically take into account the quadratic objective significantly outperform their linear counterparts. Also, the backward scheduling approach proves to be superior, and the difference in performance is even more noticeable for the harder instances.The best of the backward scheduling heuristics is both quite efficient and effective. Indeed, this procedure can quickly generate a schedule even for large instances. Also, its relative deviation from the optimum is usually rather low, and it performs adequately even for the more difficult instances.     

Metaheuristics for the single machine weighted quadratic tardiness scheduling problem

This paper considers the single machine scheduling problem with weighted quadratic tardiness costs. Three metaheuristics are presented, namely iterated local search, variable greedy and steady-state genetic algorithm procedures. These address a gap in the existing literature, which includes branch-and-bound algorithms (which can provide optimal solutions for small problems only) and dispatching rules (which are efficient and capable of providing adequate solutions for even quite large instances). A simple local search procedure which incorporates problem specific information is also proposed.The computational results show that the proposed metaheuristics clearly outperform the best of the existing procedures. Also, they provide an optimal solution for all (or nearly all, in the case of the variable greedy heuristic) the smaller size problems. The metaheuristics are quite close in what regards solution quality. Nevertheless, the iterated local search method provides the best solution, though at the expense of additional computational time. The exact opposite is true for the variable greedy procedure, while the genetic algorithm is a good all-around performer.     

Weighted tardiness for the single machine scheduling problem:An examination of precedence theorem productivity

Earlier research by Kanet [11] has provided a number of new theorems for deciding precedence between pairs of jobs for 1∣∣Σw_jT_j. The theorems supplant those of Rinnooy Kan, Lageweg, and Lenstra [16]. Presented here are the results of an analysis of the marginal benefit these new theorems provide over the earlier versions of Rinnooy Kan et al. Results show that the new theorems can provide noteworthy improvements in the ability to discover precedence relations between job pairs. For a large set of problem instances the new theorems uncovered up to 8% more precedence relations than the original theorems of Rinnooy Kan et al. The improvement in the productivity in discovering precedence relations shows to be dependent on the coefficient of variation of the distribution of job weights. Logical application of the theorems is to include them in search procedures and/or heuristic approaches to 1||Σw_jT_j. One such heuristic based on the theorems is provided here in which the solutions to a large set of sample problems are within 8–12% of the optimum.     

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.     

Strong NP-hardness of the single machine multi-operation jobs total completion time scheduling problem

We consider the single machine multi-operation jobs total completion time scheduling problem. Each job consists of several operations that belong to different families. In a schedule, each family of job operations may be processed in batches with each batch incurring a set-up time. A job completes when all of its operations have been processed. The objective is to minimize the sum of the job completion times. In the literature, the computational complexity of this problem is posed as open. We show that the problem is strongly NP-hard even when the set-up times are common and the processing time of each operation is 0 or 1.     

Heuristics for the single machine scheduling problem with quadratic earliness and tardiness penalties

In this paper, we consider the single machine scheduling problem with quadratic earliness and tardiness costs, and no machine idle time. We propose several dispatching heuristics, and analyse their performance on a wide range of instances. The heuristics include simple and widely used scheduling rules, as well as adaptations of those rules to a quadratic objective function. We also propose heuristic procedures that specifically address both the earliness and the tardiness penalties, as well as the quadratic cost function. Several improvement procedures were also analysed. These procedures are applied as an improvement step, once the heuristics have generated a schedule.     

Meta-heuristics for stable scheduling on a single machine

This paper presents a model for single-machine scheduling with stability objective and a common deadline. Job durations are uncertain, and our goal is to ensure that there is little deviation between planned and actual job starting times. We propose two meta-heuristics for solving an approximate formulation of the model that assumes that exactly one job is disrupted during schedule execution, and we also present a meta-heuristic for the global problem with independent job durations.     

Beam search algorithms for the single machine total weighted tardiness scheduling problem with sequence-dependent setups

In this paper, we consider the single machine weighted tardiness scheduling problem with sequence-dependent setups. We present heuristic algorithms based on the beam search technique. These algorithms include classic beam search procedures, as well as the filtered and recovering variants. Previous beam search implementations use fixed beam and filter widths. We consider the usual fixed width algorithms, and develop new versions that use variable beam and filter widths.     

A game-theoretic approach for the web services scheduling problem

We address the design of an Internet-based business process composed of several web services by using multiobjective optimization and game-theoretic methods. Adopting a suitable representation for the business process, we present a mathematical optimization problem which considers several quality-of-service objectives: cost, execution time, reliability, availability and reputation. The web service scheduling problem is formulated as a multiobjective mixed-integer linear optimization problem and solved through a goal optimization method. The optimal solution of the scheduling problem assigns suppliers to all the tasks that comprise the business process, thus establishing the revenues – utilities – of all the suppliers. We then model the interaction between the suppliers as an incomplete information (Bayesian) game: the structure of the game is common knowledge of all the suppliers, but each supplier knows only his/her own utility function. A characterization of the Bayes–Nash equilibria of the game is provided. The paper includes numerical examples.     

A hybrid approach to the single line scheduling problem with multiple products and sequence-dependent time

The present paper presents a hybrid approach for solving manufacturing scheduling problems, based on the integration between Constraint Logic Programming (CLP) and Genetic Algorithm (GA) approaches. The proposed methodology is applied to a single line with multiple products and sequence-dependent time. This system model derives from a real case of a company producing sheets for catalytic converters. A sensitivity analysis of the hybrid methodology is carried out to compare the performance of the CLP, GA and integrated CLP–GA approaches.     

Dispatching heuristics for the single machine early/tardy scheduling problem with job-independent penalties

In this paper, we consider the single machine earliness/tardiness scheduling problem with job-independent penalties, and no machine idle time. Several dispatching heuristics are proposed, and their performance is analysed on a wide range of instances. The heuristics include simple scheduling rules, as well as a procedure that takes advantage of the strengths of each of those rules. We also consider early/tardy dispatching procedures, and a heuristic method based on existing adjacent precedence conditions. An improvement procedure that can be used to improve the schedules generated by the heuristics is also proposed.

The computational tests show that the best results are given by the early/tardy dispatching rules. These heuristics are also quite fast, and are capable of quickly solving even very large instances. The use of the improvement procedure is recommended, since it improves the solution quality, with little additional computational effort.     

Minimizing the makespan in a single machine scheduling problem with a time-based learning effect

Both the building cost and the multiple-source routing cost are important considerations in construction of a network system. A spanning tree with minimum building cost among all spanning trees is called a minimum spanning tree (MST), and a spanning tree with minimum k-source routing cost among all spanning trees is called a k-source minimum routing cost spanning tree (k-MRCT). This paper proposes an algorithm to construct a spanning tree T for a metric graph G with a source vertex set S such that the building cost of T is at most 1+2/(α−1) times of that of an MST of G, and the k-source routing cost of T is at most α(1+2(k−1)(n−2)/k(n+k−2)) times of that of a k-MRCT of G with respect to S, where α>1, k=|S| and n is the number of vertices of G.     

A family of inequalities valid for the robust single machine scheduling polyhedron

We consider the problem of sequencing a set of jobs in a single machine to minimize the maximum of the total weighted completion time of the jobs over a number of scenarios, each corresponding to a set of job processing times. We give a large family of inequalities that are valid for the convex hull of the set of feasible schedules. We then present computational experience in which some of the inequalities are added to the original formulation. We demonstrate through the computational results that their addition to the formulation can substantially improve, among other things, the time required to solve difficult instances of the problem through branch-and-cut.     

Two branch-and-bound algorithms for the robust parallel machine scheduling problem

Uncertainty is an inevitable element in many practical production planning and scheduling environments. When a due date is predetermined for performing a set of jobs for a customer, production managers are often concerned with establishing a schedule with the highest possible confidence of meeting the due date. In this paper, we study the problem of scheduling a given number of jobs on a specified number of identical parallel machines when the processing time of each job is stochastic. Our goal is to find a robust schedule that maximizes the customer service level, which is the probability of the makespan not exceeding the due date. We develop two branch-and-bound algorithms for finding an optimal solution; the two algorithms differ mainly in their branching scheme. We generate a set of benchmark instances and compare the performance of the algorithms based on this dataset.     

Lot scheduling on a single machine

In a practical situation, a manufacturer receives different orders from its customers. Different orders may contain different quantities of the product. Therefore, the manufacturer has to decide how to group these orders into different lots based on the capacity of the lot processing machine (such as integrated circuit tester, heated container, etc.) and then decides the sequence of these lots. In this paper, we study a lot scheduling problem with orders which can be split. The objective is to minimize the total completion time of all orders. We show that this problem can be solved in polynomial time.     

On a parallel machine scheduling problem with precedence constraints

We characterize a nontrivial special case with a polynomial-time algorithm for a well-known parallel machine scheduling problem with precedence constraints, with a fixed number of machines, and with tasks of unit length. The special case is related to instances with given maximum path length and maximum degree of the task precedence graph. The method is based on the observation that the number of tasks is either small and bounded by a constant depending on the maximum path length and maximum degree, or alternatively, the number of tasks is large, giving a “dense” schedule.     

An improved approximation algorithm for single machine scheduling with job delivery

In single machine scheduling with release times and job delivery, jobs are processed on a single machine and then delivered by a capacitated vehicle to a single customer. Only one vehicle is employed to deliver these jobs. The vehicle can deliver at most c jobs in a shipment. The delivery completion time of a job is defined as the time in which the delivery batch containing the job is delivered to the customer and the vehicle returns to the machine. The objective is to minimize the makespan, i.e., the maximum delivery completion time of the jobs. We provide an approximation algorithm for this problem which is better than that given in the literature, improving the performance ratio from 5/3 to 3/2.