Multiple Job Classes Research Articles

Sequencing a tri-criteria multiple job classes and customer orders problem on a single machine by using heuristics and simulated annealing method

Sequencing a tri-criteria multiple job classes and customer orders problem on a single machine by using heuristics and simulated annealing method

Bicriteria single-machine scheduling with multiple job classes and customer orders

Customer order scheduling problems focus on completing all jobs of the same order consecutively to reduce the holding costs. Multiple job-class scheduling problems involving sequence independent family (class) setup times require completing all jobs of the same class consecutively to reduce the setup times. While these problems have been extensively studied in the literature, the scheduling problems jointly incorporating job classes and customer orders are relatively unexplored in the existing literature. Therefore, in this paper, we contribute to the existing literature by (1) addressing a single-machine scheduling problem involving multiple job classes with setup times and customer orders to minimize the bicriteria objective that is a linear combination of the makespan of all jobs and the sum of the holding costs of all orders; (2) proposing a mixed integer linear programming formulation; (3) developing a branch and bound algorithm that is equipped with a lower bound and two dominance properties to find an optimal solution needed to evaluate the effectiveness of the proposed heuristic algorithms; and (4) proposing six two-phase polynomially bounded heuristic algorithms and six variants of the water-wave optimization algorithms for producing approximate solutions The effectiveness and efficiency of the proposed algorithms are empirically evaluated through extensive computational experiments.

Sequencing single machine multiple-class customer order jobs using heuristics and improved simulated annealing algorithms

The multiple job class scheduling problem arises in contexts where a group of jobs belong to multiple classes and in which if all jobs in the same class are operated together, extra setup times would not be needed. On the other hand, the customer order scheduling problem focuses on finishing all jobs from the same order at the same time in order to reduce shipping costs. However, works on customer orders coupled with class setup times do not appear often in the literature. Hence we address here a bicriteria single machine customer order scheduling problem together with multiple job classes. The optimality criterion minimizes a linear combination of the sum of the ranges and sum of tardiness of all customer orders. In light of the high complexity of the concerned problem, we propose a lower bound formula and a property to be used in a branch-and-bound method for optimal solutions. To find approximate solutions, we then propose four heuristics together with a local search method, four cloudy theoretical simulated annealing and a cloudy theoretical simulated annealing hyperheuristic along with five low-level heuristics. The simulation results of the proposed heuristics and algorithms are analyzed.

Composite heuristics and water wave optimality algorithms for tri-criteria multiple job classes and customer order scheduling on a single machine

Among the well-known scheduling problems, the customer order scheduling problem (COSP) has always been of great importance in manufacturing. To reflect the reality of COSPs as much as possible, this study considers that jobs from different orders are classified in various classes. This paper addresses a tri-criteria single-machine scheduling model with multiple job classes and customer orders on which the measurement minimizes a linear combination of the sum of the ranges of all orders, the tardiness of all orders, and the total completion times of all jobs. Due to the NP-hard complexity of the problem, a lower bound and a property are developed and utilized in a branch-and-bound for solving an exact solution. Afterward, four heuristics with three local improved searching methods each and a water wave optimality algorithm with four variants of wavelengths are proposed. The tested outputs report the performances of the proposed methods.

Parallel Server Systems with Cancel-on-Completion Redundancy

We consider a parallel server system with so-called cancel-on-completion redundancy. There are n servers and multiple job classes j. An arriving class j job consists of dj components placed on a randomly selected subset of servers; the job service is complete as soon as kj components out of dj (with [Formula: see text]) complete their service, at which point the unfinished service of all remaining [Formula: see text] components is canceled. The system is in general non-work-conserving in the sense that the average amount of new workload added to the system by an arriving class j job is not defined a priori—it depends on the system state at the time of arrival. This poses the main challenge for the system analysis. For the system with a fixed number of servers n, our main results include: the stability properties; the property that the stationary distributions of the relative server workloads remain tight uniformly in the system load. We also consider the mean-field asymptotic regime when [Formula: see text] while each job class arrival rate per server remains constant. The main question we address here is: under which conditions the steady-state asymptotic independence (SSAI) of server workloads holds and, in particular, when the SSAI for the full range of loads (SSAI-FRL) holds. (Informally, SSAI-FRL means that SSAI holds for any system load less than one.) We obtain sufficient conditions for SSAI and SSAI-FRL. In particular, we prove that SSAI-FRL holds in the important special case when job components of each class j are independent and identically distributed with an increasing-hazard-rate distribution.

Uniform stability of some large-scale parallel server networks

In this paper we study the uniform stability properties of two classes of parallel server networks with multiple classes of jobs and multiple server pools of a tree topology. These include a class of networks with a single nonleaf server pool, such as the ‘N’ and ‘M’ models, and networks of any tree topology with class-dependent service rates. We show that with \(\sqrt{n}\) safety staffing, and no abandonment, in the Halfin–Whitt regime, the diffusion-scaled controlled queueing processes are exponentially ergodic and their invariant probability distributions are tight, uniformly over all stationary Markov controls. We use a unified approach in which the same Lyapunov function is used in the study of the prelimit and diffusion limit. A parameter called the spare capacity (safety staffing) of the network plays a central role in characterizing the stability results: the parameter being positive is necessary and sufficient that the limiting diffusion is uniformly exponentially ergodic over all stationary Markov controls. We introduce the concept of “system-wide work conserving policies," which are defined as policies that minimize the number of idle servers at all times. This is stronger than the so-called joint work conservation. We show that, provided the spare capacity parameter is positive, the diffusion-scaled processes are geometrically ergodic and the invariant distributions are tight, uniformly over all “system-wide work conserving policies." In addition, when the spare capacity is negative we show that the diffusion-scaled processes are transient under any stationary Markov control, and when it is zero, they cannot be positive recurrent.

Zero Queueing for Multi-Server Jobs

Cloud computing today is dominated by multi-server jobs. These are jobs that request multiple servers simultaneously and hold onto all of these servers for the duration of the job. Multi-server jobs add a lot of complexity to the traditional one-server-per-job model: an arrival might not "fit" into the available servers and might have to queue, blocking later arrivals and leaving servers idle. From a queueing perspective, almost nothing is understood about multi-server job queueing systems; even understanding the exact stability region is a very hard problem. In this paper, we investigate a multi-server job queueing model under scaling regimes where the number of servers in the system grows. Specifically, we consider a system with multiple classes of jobs, where jobs from different classes can request different numbers of servers and have different service time distributions, and jobs are served in first-come-first-served order. The multi-server job model opens up new scaling regimes where both the number of servers that a job needs and the system load scale with the total number of servers. Within these scaling regimes, we derive the first results on stability, queueing probability, and the transient analysis of the number of jobs in the system for each class. In particular we derive sufficient conditions for zero queueing. Our analysis introduces a novel way of extracting information from the Lyapunov drift, which can be applicable to a broader scope of problems in queueing systems.

Zero Queueing for Multi-Server Jobs

Cloud computing today is dominated by multi-server jobs. These are jobs that request multiple servers simultaneously and hold onto all of these servers for the duration of the job. Multi-server jobs add a lot of complexity to the traditional one-server-per-job model: an arrival might not "fit'' into the available servers and might have to queue, blocking later arrivals and leaving servers idle. From a queueing perspective, almost nothing is understood about multi-server job queueing systems; even understanding the exact stability region is a very hard problem. In this paper, we investigate a multi-server job queueing model under scaling regimes where the number of servers in the system grows. Specifically, we consider a system with multiple classes of jobs, where jobs from different classes can request different numbers of servers and have different service time distributions, and jobs are served in first-come-first-served order. The multi-server job model opens up new scaling regimes where both the number of servers that a job needs and the system load scale with the total number of servers. Within these scaling regimes, we derive the first results on stability, queueing probability, and the transient analysis of the number of jobs in the system for each class. In particular we derive sufficient conditions for zero queueing. Our analysis introduces a novel way of extracting information from the Lyapunov drift, which can be applicable to a broader scope of problems in queueing systems.

Large-scale parallel server system with multi-component jobs

A broad class of parallel server systems is considered, for which we prove the steady-state asymptotic independence of server workloads, as the number of servers goes to infinity, while the system load remains sub-critical. Arriving jobs consist of multiple components. There are multiple job classes, and each class may be of one of two types, which determines the rule according to which the job components add workloads to the servers. The model is broad enough to include as special cases some popular queueing models with redundancy, such as cancel-on-start and cancel-on-completion redundancy. Our analysis uses mean-field process representation and the corresponding mean-field limits. In essence, our approach relies almost exclusively on three fundamental properties of the model: (a) monotonicity, (b) work conservation and (c) the property that, on average, “new arriving workload prefers to go to servers with lower workloads.”

Statistical Assessment of IP Multimedia Subsystem in a Softwarized Environment: A Queueing Networks Approach

The Next Generation 5G Networks can greatly benefit from the synergy between virtualization paradigms, such as the Network Function Virtualization (NFV), and service provisioning platforms such as the IP Multimedia Subsystem (IMS). The NFV concept is evolving towards a lightweight solution based on containers that, by contrast to classic virtual machines, do not carry a whole operating system and result in more efficient and scalable deployments. On the other hand, IMS has become an integral part of the 5G core network, for instance, to provide advanced services like Voice over LTE (VoLTE). In this paper we combine these virtualization and service provisioning concepts, deriving a containerized IMS infrastructure, dubbed cIMS, providing its assessment through statistical characterization and experimental measurements. Specifically, we: i) model cIMS through the queueing networks methodology to characterize the utilization of virtual resources under constrained conditions; ii) draw an extended version of the Pollaczek-Khinchin formula, which is useful to deal with bulk arrivals; iii) afford an optimization problem focused at maximizing the whole cIMS performance in the presence of capacity constraints, thus providing new means for the service provider to manage service level agreements (SLAs); $iv)$ evaluate a range of cIMS scenarios, considering different queuing disciplines including also multiple job classes. An experimental testbed based on the open source platform Clearwater has been deployed to derive some realistic values of key parameters (e.g. arrival and service times).

Infinite horizon asymptotic average optimality for large-scale parallel server networks

We study infinite-horizon asymptotic average optimality for parallel server networks with multiple classes of jobs and multiple server pools in the Halfin–Whitt regime. Three control formulations are considered: (1) minimizing the queueing and idleness cost, (2) minimizing the queueing cost under constraints on idleness at each server pool, and (3) fairly allocating the idle servers among different server pools. For the third problem, we consider a class of bounded-queue, bounded-state (BQBS) stable networks, in which any moment of the state is bounded by that of the queue only (for both the limiting diffusion and diffusion-scaled state processes). We show that the optimal values for the diffusion-scaled state processes converge to the corresponding values of the ergodic control problems for the limiting diffusion. We present a family of state-dependent Markov balanced saturation policies (BSPs) that stabilize the controlled diffusion-scaled state processes. It is shown that under these policies, the diffusion-scaled state process is exponentially ergodic, provided that at least one class of jobs has a positive abandonment rate. We also establish useful moment bounds, and study the ergodic properties of the diffusion-scaled state processes, which play a crucial role in proving the asymptotic optimality.

Off-site construction optimization: Sequencing multiple job classes with time constraints

Off-site construction is a unique hybrid of manufacturing operations and on-site construction activities. Maximizing the production output has long been the main challenge for off-site manufacturers. Among other responses to this challenge, the use of multi-task shared resources has proved its effectiveness in improving tangible performance measures of production. However, multi-skilled resources often become bottlenecks (overloaded) when producing multiple classes of products and prevent the production network from meeting due dates. This paper analytically models the problem of defining the optimal product sequencing using optimization-based metaheuristics with the aim of minimizing changeover time, which is wasted switching from a product class to another. Production data of two Australian off-site manufacturers are used in the subsequent empirical analysis resulting in advancement of five research propositions. This research contributes to the scheduling theory by expanding the insight into dynamics of resource sharing and job sequencing. The developed models and propositions are of practical value for off-site manufacturers of building elements to maximize their production output.

A c-mu Rule for Two-Tiered Parallel Servers

The cμ rule is known to be optimal in many queueing systems with memoryless service and inter-arrival times. We establish a cμ rule for a parallel flexible server system with two tiers. Multiple job classes arrive and wait in separate queues. The first tier contains classes that can only be served by one server each, and the second tier contains a class that can be served by all servers. The cμ preferences give priority to the first tier. Sequencing decisions are made to minimize linear holding costs.

Multi-resource Fair Sharing for Multiclass Workflows

Multi-resource sharing for concurrent workows necessitates a fairness criteria to allocate multiple resources to work-flows with heterogeneous demands. Recently, this problem has attracted increasing attention and has been investigated by assuming that each workow has a single class of jobs and that each class contains jobs of the same demand profile. The demand profile of a class represents the required multi-resources of a job. However, for typical applications in cloud computing and distributed data processing systems, a workow usually needs to process multiple classes of jobs. Relying on the concept of slowdown, we characterize fairness for multi-resource sharing and address scheduling for multiclass workows. We optimize the mixture of different classes of jobs for a workow as optimal operation points to achieve the least slowdown, and discuss desirable properties for these operation points. These studies assume that the jobs are infinitely divisible. When jobs are non-preemptive and indivisible, any fairness criteria that only relies on the instantaneous resource allocation cannot be strictly maintained at every time point. To this end, we relax the instantaneous fairness to an average metric within a time interval. This relaxation introduces a time average to fairness and allows occasional, but not too often, violations of instantaneous fairness. In addition, it brings exibility and opportunities for further optimization on resource utilization, e.g., using bin-packing, within the constraint on fairness.

Cluster analysis and neural network-based metamodeling of priority rules for dynamic sequencing

Most sequencing problems deal with deterministic environments where all information is known in advance. However, in real-world problems multiple sources of uncertainty need to be taken into consideration. To model such a situation, in this article, a dynamic sequencing problem with random arrivals, processing times and due-dates is considered. The examined system is a manufacturing line with multiple job classes and sequence-dependent setups. The performance of the system is measured under the metrics of mean WIP, mean cycle time, mean earliness, mean tardiness, mean absolute lateness, and mean percentage of tardy jobs. Twelve job dispatching rules for solving this problem are considered and evaluated via simulation experiments. A statistically rigorous analysis of the solution approaches is carried out with the use of unsupervised and supervised learning methods. The cluster analysis of the experimental results identified classes of priority rules based on their observed performance. The characteristics of each priority rule class are documented and areas in objective space not covered by existing rules are identified. The functional relationship between sequencing priority rules and performance metrics of the production system was approximated by artificial neural networks. Apart from gaining insight into the mechanics of the sequencing approaches the results of this article can be used (1) as a component for prediction systems of dispatching rule output, (2) as a guideline for building new dispatching heuristic with entirely different characteristics than existing ones, (3) to significantly decrease the length of what-if simulation studies.

A cµ Rule for Parallel Servers with Two-Tiered cµ Preferences

The cµ rule is known to be optimal in many queueing systems with memoryless service and inter-arrival times. We establish a c rule for a parallel flexible server system with two tiers. Multiple job classes arrive and wait in separate queues. The first tier contains classes that can only be served by one server each, and the second tier contains a class that can be served by all servers. The c preferences give priority to the first tier. Sequencing decisions are made to minimize linear holding costs.

Optimal admission control in series production systems with blocking

This article studies the dynamic control of arrivals of multiple job classes in N-stage production systems with finite buffers and blocking after service. A model with multiple processing stages in series is formulated as a Markov decision process and a state definition from the queueing analysis literature is used to simplify the state-space description. This allows several fundamental admission control results from M/M/N and M/M/N/N queueing models as well as tandem models without blocking to be extended to tandem systems with blocking. Specifically, it is shown that the net benefit of admitting a job declines monotonically with the system congestion; thus the decision to admit any job class is based on threshold values of the number of jobs present in the system. Furthermore, conditions under which a job class is always or never admitted, regardless of the state, are derived. The interaction of blocking and admission control is explored by analyzing the effect of blocking on the optimal admission policy and profit. The article concludes with analyses of why extensions including loss and abandonment cannot sustain the monotonicity properties and two surrogate admission rules that may be used in practice but do not account for the blocking effect.

Priority Assignment in Emergency Response

In the aftermath of mass-casualty events, key resources (such as ambulances and operating rooms) can be overwhelmed by the sudden jump in patient demand. To ration these resources, patients are assigned different priority levels, a process that is called triage. According to triage protocols in place, each patient's priority level is determined based on that patient's injuries only. However, recent work from the emergency medicine literature suggests that when determining priorities, resource limitations and the scale of the event should also be taken into account in order to do the greatest good for the greatest number. This article investigates how this can be done and what the potential benefits would be. We formulate the problem as a priority assignment problem in a clearing system with multiple classes of impatient jobs. Jobs are classified based on their lifetime (i.e., their tolerance for wait), service time, and reward distributions. Our objective is to maximize the expected total reward, e.g., the expected total number of survivors. Using sample-path methods and stochastic dynamic programming, we identify conditions under which the state information is not needed for prioritization decisions. In the absence of these conditions, we partially characterize the optimal policy, which is possibly state dependent, and we propose a number of heuristic policies. By means of a numerical study, we demonstrate that simple state-dependent policies that prioritize less urgent jobs when the total number of jobs is large perform well, especially when jobs are time-critical.

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Design of intermodal logistics networks with hub delays

In an intermodal hub network, cost benefits can be achieved through the use of intermodal shipments and the economies of scale due to consolidation of flows at the hubs. However, due to limited resources at the logistics hubs, shipment delays may affect the service performance. In this research hub operations are modeled as a GI/G/1 queuing network and the shipments as multiple job classes with deterministic routings. By integrating the hub operation queuing model and the hub location-allocation model, the effect of limited hub resources on the design of intermodal logistics networks under service time requirements is investigated. The managerial insights gained from a study of 25-city road-rail intermodal logistics network show that the level of available hub resources significantly affects the logistics network structure in terms of number and location of hubs, total network costs, choice of single-hub and inter-hub shipments and service performance.