Multiple Job Classes Research Articles

Two robust meta-heuristics for scheduling multiple job classes on a single machine with multiple criteria

We consider a single machine scheduling problem consisted of two groups of jobs with two different criteria that are minimizing total weighted completion time for the first group and minimizing maximum lateness for the second one. This problem which minimizes a mix of these criteria is in the NP-hard class of problems. Hence, inevitably we make use of meta-heuristic methods to tackle large scale problems. In this paper two meta-heuristics such as genetic algorithm and hybrid kangaroo simulated annealing are taken into consideration. Taguchi method is employed to tune the parameters of these algorithms and analyze the parameters of the studying problem simultaneously.

Optimal Scheduling and Incentive Compatible Pricing for a Service System with Quality of Service Guarantees

This paper proposes a resource allocation and pricing mechanism for a service system that serves multiple classes of jobs within an organization. Each class of service request is subject to a class-dependent quality of service (QoS) guarantee on the expected delay bound, which may be imposed by business rules in an organization or other application-specific technical constraints. We develop an extension of a resource allocation and pricing mechanism for an M/M/1 system. In contrast to the system without the QoS guarantee, where a fixed priority scheduling policy—known as the cμ rule—is optimal, we show that the system may need to adopt a more general randomized priority scheduling policy to maximize the overall system profit. We also develop a transfer pricing scheme that is both optimal and incentive compatible, allowing users to act in their self-interests while collectively achieving the system optimum. We show that the pricing scheme with the QoS guarantee depends on the scheduling policy implemented and has different characteristics from that without the QoS guarantee.

Heavy-Traffic Optimality of a Stochastic Network Under Utility-Maximizing Resource Allocation

We study a stochastic network that consists of a set of servers processing multiple classes of jobs. Each class of jobs requires a concurrent occupancy of several servers while being processed, and each server is shared among the job classes in a head-of-the-line processor-sharing mechanism. The allocation of the service capacities is a real-time control mechanism: in each network state, the resource allocation is the solution to an optimization problem that maximizes a general utility function. Whereas this resource allocation optimizes in a “greedy” fashion with respect to each state, we establish its asymptotic optimality in terms of (a) deriving the fluid and diffusion limits of the network under this allocation scheme, and (b) identifying a cost function that is minimized in the diffusion limit, along with a characterization of the so-called fixed-point state of the network.

A recursive analysis technique for multi-dimensionally infinite Markov chains

Performance analysis of multiserver systems with multiple classes of jobs often has a common source of difficulty: the state space needed to capture the system behavior grows infinitely in multiple dimensions. For example, consider two processors, each serving its own M/M/1 queue, where one of the processors (the "donor") can help the other processor (the "beneficiary") with its jobs, during times when the donor processor is idle [5, 16] or when some threshold conditions are met [14, 15]. Since the behavior of beneficiary jobs depends on the number of donor jobs in system, performance analysis of beneficiary jobs involves a two dimensionally infinite (2D-infinite) state space, where one dimension corresponds to the number of beneficiary jobs and the other dimension corresponds to the number of donor jobs. Another example is an M/M/2 queue with two priority classes, where high priority jobs have preemptive priority over low priority jobs (see for example [1, 3, 4, 8, 10, 11, 12, 17] and references therein). Since the behavior of low priority jobs depends on the number of high priority jobs in system, performance analysis of low priority jobs involves 2D-infinite state space, where each dimension corresponds to the number of each class of jobs in system. As we will see, when there are <i>m</i> priority classes, performance analysis of the lowest priority classes involves <i>m</i> dimensionally infinite state space.

Capacity analysis of an automated kit transportation system

In this paper, we present a capacity analysis of an automated transportation system in a flexible assembly factory. The transportation system, together with the workstations, is modeled as a network of queues with multiple job classes. Due to its complex nature, the steady‐state behavior of this network is not described by a product‐form solution. Therefore, we present an approximate method to determine the capacity of the network. We first study a number of key elements of the system separately and subsequently combine the results of this analysis in an Approximate Mean Value Analysis (AMVA) algorithm. The key elements are a buffer/transfer system (the bottleneck of the system), modeled as a preemptive‐repeat priority queue with identical deterministic service times for the different job classes, a set of elevators, modeled as vacation servers, a number of work cells, modeled as multi‐server queues, and several non‐accumulating conveyor belts, modeled as ample servers. The AMVA algorithm exploits the property that the initial multi‐class queueing network can be decomposed into a sequence of single‐class queueing networks and hence is very efficient. Comparison of numerical results of the AMVA algorithm for the throughputs for the different job classes to simulation results shows that the AMVA algorithm is also accurate. For several series of instances, the maximum relative error that we found was only 4.0%.

On Certain Greedoid Polyhedra, Partially Indexable Scheduling Problems, and Extended Restless Bandit Allocation Indices

We present a polyhedral framework for establishing general structural properties on optimal solutions of stochastic scheduling problems, where multiple job classes vie for service resources: the existence of an optimal priority policy in a given family, characterized by a greedoid (whose feasible class subsets may receive higher priority), where optimal priorities are determined by class-ranking indices, under restricted linear performance objectives (partial indexability). This framework extends that of Bertsimas and Ni?o-Mora (1996), which explained the optimality of priority-index policies under all linear objectives (general indexability). We show that, if performance measures satisfy partial conservation laws (with respect to the greedoid), which extend previous generalized conservation laws, then the problem admits a strong LP relaxation over a so-called extended greedoid polytope, which has strong structural and algorithmic properties. We present an adaptive-greedy algorithm (which extends Klimov's) taking as input the linear objective coefficients, which (1) determines whether the optimal LP solution is achievable by a policy in the given family; and (2) if so, computes a set of class-ranking indices that characterize optimal priority policies in the family. In the special case of project scheduling, we show that, under additional conditions, the optimal indices can be computed separately for each project (index decomposition). We further apply the framework to the important restless bandit model (two-action Markov decision chains), obtaining new index policies, that extend Whittle's (1988), and simple sufficient conditions for their validity. These results highlight the power of polyhedral methods (the so-called achievable region approach) in dynamic and stochastic optimization.

Aggregate scheduling and network solving of multi-stage and multi-item manufacturing systems

This paper is concerned with the modeling of aggregate scheduling problems in multi-stage and multi-item dynamic manufacturing systems with storage space limitations and production capacity constraints of workstations. The model aims to minimize the total cost which is the sum of all costs incurred in holding, processing, transporting and schedule delay over the whole study horizon. In order to solve this model efficiently, we show that it can be transferred into an equivalent static job assignment problem with multiple job classes over a space-time network which is a temporal expansion of the base workstation network. Then, an adapted network algorithm based on Frank-Wolfe's is proposed to solve the equivalent problem. The results are illustrated with their application to a numerical example. The computation times on several problem types and problem sizes are investigated. The model solution represents a system optimum scheduling pattern and, hence, could help to improve the existing scheduling works.

MEM for arbitrary closed queueing networks with RS-blocking and multiple job classes

A new product-form approximation, based on the method of entropy maximisation (MEM), is characterised for arbitrary closed queueing networks with multiple and distinct classes of jobs, Generalised Exponential (GE) service times, mixed service disciplines, complete buffer sharing and repetitive-service blocking with both fixed (RS-FD) and random destinations (RS-RD). The maximum entropy (ME) approximation implies decomposition of the network into individual multiple class GE/GE/1/N queues satisfying constraints on population and flow conservation which is, in turn, truncated and efficiently implemented by a general convolution recursive procedure for the efficient calculation of the normalising constant and typical performance metrics. A relationship between MEM and reversible closed multiple class queueing networks is identified and it is shown how the ME approximation reduces to the exact solution. Numerical validation experiments against simulation are included to demonstrate the credibility of ME results.

Preface: Queueing Networks with Blocking

Queueing Network Models (QNMs) with Finite Capacity provide powerful and realistic tools for the performance evaluation and prediction of discrete flow systems such as computer systems, communication networks and flexible manufacturing systems. Over recent years, there has been a great deal of progress towards the analysis and application of QNMs with finite capacity, and high quality research work has appeared in diverse scientific journals of learning and conference proceedings in the fields of Operations Research, Computer Science, Telecommunication Networks, Management and Industrial Engineering. However, there are still many important and interesting finite capacity queues and QNMs to be resolved, such as those involving multiple-job classes, bounds and theoretical properties, exact analysis, numerical solutions and approximate methods, as well as application studies to computer and distributed systems, high-speed networks and production systems.This volume of Annals of Operations Research on Queueing Networks with Finite Capacity presents 17 extended research papers, both from industry and academia, reflecting current original contributions in the theory and applications of finite capacity queues and networks worldwide. Earlier short versions of these papers were amongst those presented at QNets '95, The Third International Workshop on Queueing Networks with Finite Capacity, 6th-7th July, 1995, Ilkley, West Yorkshire, UK. The papers are classified into four parts covering exact analysis, approximate methods, error bounds and performance modelling studies.

Single machine hierarchical scheduling with customer orders and multiple job classes

In this paper, we consider single machine bi-criteria scheduling problems where jobs are from multiple job classes and there are customer orders such that each customer order consists of at least one job from each of the job classes. A set-up time is needed whenever the machine is changed over from a job in one class to a job in another class. One objective is to minimize the makespan which is equivalent to minimizing the total set-up time. The other objective is to minimize total carrying costs of the customer orders. The carrying cost of a customer order is measured by the length of the time interval between the completion times of the first job and the last job in the customer order. We propose constructive polynomial time algorithms for the two hierarchical scheduling problems with these two objectives, i.e. the two scheduling problems in which one objective is to be optimized while holding the other objective fixed at its optimal value.

Real-world extensions to scheduling algorithms based on lagrangian relaxation

Recently, efficient scheduling algorithms based on Lagrangian relaxation have been proposed for scheduling parallel machine systems and job shops. In this article, we develop real-world extensions to these scheduling methods. In the first part of the paper, we consider the problem of scheduling single operation jobs on parallel identical machines and extend the methodology to handle multiple classes of jobs, taking into account setup times and setup costs. The proposed methodology uses Lagrangian relaxation and simulated annealing in a hybrid framework. In the second part of the paper, we consider a Lagrangian relaxation based method for scheduling job shops and extend it to obtain a scheduling methodology for a real-world flexible manufacturing system with centralized material handling.

Modeling Truck–Shovel Systems as Closed Queueing Network with Multiple Job Classes

In this paper an analytical method is proposed to model the truck–shovel system as a closed queueing network with multiple job classes. This approach would provide the capability of estimating system performance measures (mine throughput, mean number of trucks, mean waiting time etc.) for planning purposes when the truck fleet is not necessarily composed of identical trucks. A computational study is presented to show how choosing different types of trucks affect the production level in a truck–shovel system. Mean Value Analysis (MVA) approach is used to compute all performance measures of the truck–shovel system.

Modeling truck-shovel systems as closed queueing network with multiple job classes

Abstract In this paper an analytical method is proposed to model the truck-shovel system as a closed queueing network with multiple job classes. This approach would provide the capability of estimating system performance measures (mine throughput, mean number of trucks, mean waiting time etc.) for planning purposes when the truck fleet is not necessarily composed of identical trucks. A computational study is presented to show how choosing different types of trucks affect the production level in a truck-shovel system. Mean Value Analysis (MVA) approach is used to compute all performance measures of the truck-shovel system.

Multigranularity locking in multiple job classes transaction processing system

The conditions of when to apply fine and coarse granularity to different kinds of transaction are well understood. However, it is not very clear how multiple job classes using different lock granularities affect each other. This study aims at exploring the impact of multigranularity locking on the performance of multiple job classes transaction processing system which is common in multiuser database system. There are two key findings in the study. Firstly, lock granularity adopted by identical job classes should not differ from each other by a factor of more than 20; otherwise, serious data contention may result. Secondly, short job class transactions are generally benefited when its level of granularity is similar to that of the long job class since this will reduce the additional lock overhead and data contention which are induced by multigranularity locking.

Exact solutions for networks of queues with blocking-after-service

The paper has two major parts. The first part deals with two-station networks with blocking-after-service (BAS) mechanism and different station types. In this part only single class of jobs is allowed. The contribution here is to show that exact solutions exist for two-station queueing networks with BAS mechanism having different station types. The exact equilibrium state probability distributions are derived. Insensitivity is investigated and formulas for performance measures are obtained. It is demonstrated that the throughput, mean number of jobs and mean number of Cblocked jobs depend on the scheduling discipline. A queueing network model with more than two stations is analyzed in the second part. Multiple-job classes with job class change, and different station types are allowed in the model. Exact solutions for equilibrium state probabilities and performance measures are obtained under the condition that only a certain total number of jobs is allowed in the network.

Exact analysis of queueing networks with multiple job classes and blocking-after-service

Two models of closed queueing networks with blocking-after-service and multiple job classes are analyzed. The first model is a network withN stations and each station has either type II or type III. The second model is a star-like queueing network, also called a central server model, in which the stations may have either type I or type IV, with the condition that the neighbors of these stations must be of type II or type III such that blocking will be caused only by this set of station types. Exact product form solutions are obtained for the equilibrium state probabilities in both models. Formulae for performance measures such as throughput and the mean number of jobs are also derived.

Minimizing the Range of Order Completion Times with Multiple Job Classes

A number of important contributions have been made toward the problem of minimizing the difference in ‘customer’ treatment on a single machine. However, so far, all the research has been to solve the problem of minimizing the ‘job’ difference. That is, it is assumed implicitly that each customer places only one job, and hence minimizing the difference in customer treatment is equivalent to minimizing the difference in job treatment. In many practical situations, a customer may place an order which consists of several jobs. The jobs usually can be grouped into different classes. Thus, the range, i.e. the difference between the maximum and the minimum, of order completion times becomes an appropriate performance measure for treating customers equally. In this paper, a dynamic programming (DP) algorithm is developed to provide the optimal solution. Due to the exponential time complexity of the DP algorithm, two heuristic methods are also proposed to solve large-sized problems. Computational results for the heuristics are provided.

Minimizing the Range of Order Completion Times with Multiple Job Classes

Minimizing the Range of Order Completion Times with Multiple Job Classes

Minimizing the Range of Order Completion Times with Multiple Job Classes

A number of important contributions have been made toward the problem of minimizing the difference in ‘customer’ treatment on a single machine. However, so far, all the research has been to solve the problem of minimizing the ‘job’ difference. That is, it is assumed implicitly that each customer places only one job, and hence minimizing the difference in customer treatment is equivalent to minimizing the difference in job treatment. In many practical situations, a customer may place an order which consists of several jobs. The jobs usually can be grouped into different classes. Thus, the range, i.e. the difference between the maximum and the minimum, of order completion times becomes an appropriate performance measure for treating customers equally. In this paper, a dynamic programming (DP) algorithm is developed to provide the optimal solution. Due to the exponential time complexity of the DP algorithm, two heuristic methods are also proposed to solve large-sized problems. Computational results for the heuristics are provided.

Approximate solution of a dynamic job shop model with several job classes

A closed job shop system with a FIFO managed dispatch area is considered, under the assumption that the machine shop subsystem is constrained by an upper limit on the number of circulating jobs. An approach for the approximate solution of the nonproduct form queueing network model of the system is well established only for the case of a single class of jobs flowing through the system. In this paper we extend the previous approach to cover the case of multiple job classes. We combine hierarchical decomposition with the class aggregation technique, in order to obtain a practical approximate solution method. Class aggregation also enables to incorporate in our method the consolidated ‘exponentialization approach’. Hence the method also covers the case of machine centers having different and nonexponential service times per job class. The approximations developed are validated by simulation experiments.