Machine Scheduling Research Articles

Enhancing the best-first-search F with incremental search and restarts for large-scale single machine scheduling with release dates and deadlines

Enhancing the best-first-search F with incremental search and restarts for large-scale single machine scheduling with release dates and deadlines

Distributionally robust single machine scheduling with release and due dates over Wasserstein balls

Single machine scheduling aims at determining the job sequence with the best desired performance, and provides the basic building block for more advanced scheduling problems. In the present study, a single machine scheduling model with uncertain processing time is considered by incorporating the job release time and due date. The job processing time follows unknown probability distribution, and can be estimated via the historical data. To model the uncertainty, the processing time distribution is defined over a Wasserstein ball ambiguity set, which covers all feasible probability distributions within the confidence radius of the empirical distribution, known as the center of the ball. Then a data-driven distributionally robust scheduling model is constructed with individual chance constraints. In particular, two equivalent reformulations are derived with respect to the ℓ1-norm and ℓ2-norm metrics of the Wasserstein ball, namely, a mixed-integer linear programming and a mixed-integer second order cone programming model, respectively. To accelerate the solving of large-scale instances, a tailored constraint generation algorithm is introduced. In the numerical analysis, the proposed distributionally robust scheduling approach is compared with the state-of-the-art methods in terms of out-of-sample performance.

A new branch-and-cut approach for integrated planning in additive manufacturing

In recent years, there has been considerable interest in the transformative potential of additive manufacturing (AM) since it allows for producing highly customizable and complex components while reducing lead times and costs. The rise of AM for traditional and new business models enforces the need for efficient planning procedures for AM facilities. In this area, the assignment and sequencing of components to be built by an AM machine, also called a 3D printer, is a complex challenge combining two combinatorial problems: The first decision involves the grouping of parts into production batches, akin to the well-known bin packing problem. Subsequently, the second problem pertains to the scheduling of these batches onto the available machines, which corresponds to a parallel machine scheduling problem. For minimizing makespan, this paper proposes a new branch-and-cut algorithm for integrated planning for unrelated parallel machines. The algorithm is based on combinatorial Benders decomposition: The scheduling problem is considered in the master problem, while the feasibility of an obtained solution with respect to the packing problem is checked in the sub-problem. Current state-of-the-art techniques are extended to solve the orthogonal packing with rotation and used to speed up the solution of the sub-problem. Extensive computational tests on existing and new benchmark instances show the algorithm’s superior performance, improving the makespan by 18.7% on average, with improvements reaching up to 97.6% for large problems compared to an existing integrated mixed-integer programming model.

Parallel Machine Scheduling Problems with Learning and Deterioration Effects

Parallel Machine Scheduling Problems with Learning and Deterioration Effects

Scheduling of e-commerce packaging machines: blocking machines and their impact on the performance–waste tradeoff

AbstractTo streamline their fulfillment processes, many e-commerce retailers today use automated packaging machines for their outbound parcels. An important performance–waste tradeoff is associated with these machines: To reduce packaging waste when handling different sized goods, packaging machines should be able to handle different carton sizes. However, more carton sizes lead to a more involved scheduling process, so that the throughput performance deteriorates (and vice versa). To investigate this tradeoff, this paper develops scheduling procedures for a specific type of packaging machine, called blocking machines. These packaging machines provide multiple back-to-back packaging devices, each continuously processing a dedicated carton size, but blocking each other whenever incoming goods are not properly ordered according to carton sizes on the infeed conveyor. To reduce the resulting throughput loss, we derive various scheduling problems for optimizing the inflow of goods, provide a thorough analysis of the computational complexity, and derive an exact dynamic programming approach that is polynomial in the number of orders to be packed. This allows us to solve even large real-world instances to proven optimality with which we can analyze the performance–waste tradeoff of blocking machines.

Novel mathematical formulations for parallel-batching processing machine scheduling problems

We study mathematical formulations for batch-processing machine scheduling problems (BPMPs), which are the challenging issues in the machine scheduling literature where machines are capable of processing a batch of jobs simultaneously if jobs with non-identical sizes can be packed in a capacitated machine. In this paper, we tackle single- and parallel-machine BPMPs, and other interesting problem variants that aim at minimizing the makespan. We develop novel formulations along with valid inequalities and an algorithm framework that makes use of dual information and bounding techniques to achieve efficiency when instances are intractable. Extensive computational experiments on benchmark instances show that our approaches achieve state-of-the-art results and prove the optimality of intractable instances in the literature.

A generalized combination of parallel machine scheduling and path

A generalized combination of parallel machine scheduling and path

Scheduling Splitable Jobs on Identical Parallel Machines to Minimize Makespan using Mixed Integer Linear

The scheduling of parallel machines with and without a job-splitting property, deterministic demand,and sequence-independent setup time with the goal of minimizing makespan is examined in this work.For simultaneous processing by multiple machines, single-stage splitable jobs are broken into random(job) sections. When a job starts to be processed on a machine, an operator has to setup the machinefor an hour. By creating two Mixed Integer Linear Programming models, this work proposes amathematical programming strategy (MILP). A MILP model takes the job-splitting property intoaccount. Another model, however, does not include the job-splitting property. This study investigatesthe performance of the proposed models using Gurobi solver. These programs' numerical calculationsare based on actual problems in the Indonesian city of Bandung's plastics industry. On four identicalparallel injection molding machines, 318 jobs must be finished in 22 periods. The real schedulingmethod is contrasted with these two MILP models. The maximum workload imbalance, the maximumrelative percentage of imbalance, and the makespan of these three scheduling systems are used toevaluate their effectiveness. Without the job-splitting property, MILP can handle the real issue ofscheduling identical parallel machines on injection molding machines to reduce makespan, resultingin a 36% average decrease. The MILP model's job-splitting property can reduce makespan by anadditional 2.40%. The order of relative ranking is MILP with job-splitting property, MILP withoutjob-splitting property, and actual scheduling based on the makespan minimization, workloadimbalance, and relative percentage of imbalance.

Identical Parallel Machine Scheduling to Minimize Makespan Using Suggested Algorithm Method at XYZ Company

XYZ company produce the various shape of motor spare parts product. The company has threeidentical parallel spot welding machines that use a random method of production scheduling, basedon machine capacity without any sequence of jobs, and only use daily production targets given tooperators. Based on the data, the actual scheduling of the machines has a very large completion timedifference between each machine, or the machine loading is uneven. As a result, the makespanbecomes longer with a value of 440000 seconds (26 days). This research aims to minimize the existingmakespan by giving proposed scheduling, using the suggested algorithm method, which has a smallnumber of iterations and has an optimal result. The method begins with the longest processing timesequence rule which is used as the upper bound for the first iteration, then continued to calculate thelower bound and machine workload. The calculation stops at the 15th iteration because the completiontime value exceeds the lower and upper bound so that the optimal scheduling taken is scheduled inthe 14th iteration with a makespan value of 914412 seconds (16 days). The proposed scheduling canminimize the makespan from the actual schedule by 38%.

Research on charging scheduling optimization of pure electric buses considering peak-valley time-of-use electricity prices and battery loss costs

In recent years, with the accelerated progress of pure electric buses in my country, the charging scheduling and operation plan of pure electric buses urgently needs to be rationalized and scientific. This study takes the charging scheduling operation in the daily operation of pure electric buses as the starting point, and effectively describes the battery loss cost function by analyzing the optimal fluctuation range of the state of charge of the power battery of pure electric buses. Combined with the analysis of the characteristics of peak and valley time-of-use electricity prices during the charging period, the problem is refined into a pure electric bus charging scheduling decision with controllable operation completion, and the parallel machine scheduling theory is used to characterize and solve the mathematical optimization model, with the aim of minimizing the operating cost of bus companies. At the same time, an immune optimization algorithm based on random key encoding and a greedy algorithm based on the idea of avoiding peaks and filling valleys are developed to solve large-scale problems. In addition, the effectiveness of the algorithm and the applicability of the method are verified through the real bus network in Shanghai.

Lower and upper bounds for scheduling a real-life assembly problem with precedences and resource constraints

In this work, we consider a real-life scheduling problem involving the production of off-road vehicles using a three-level assembly process, subject to precedence, machines, and resource constraints. This problem shares multiple characteristics with other scheduling problems such as the Parallel Machine Scheduling and Flexible Flow Shop Problems. However, it also comprises less investigated aspects such as a specific job precedence structure resulting in a directed rooted in-tree and a global resource constraint limiting the number of simultaneously active machines. We present a straightforward adaptation of a time-indexed mathematical formulation to the problem and introduce a new lower-bounding procedure. To solve the problem, we propose constructive heuristics based on classical priority rules and adaptations of job sequencing heuristics. We also propose CORE, a specialized approach tailored to leverage the problem structure. All the algorithms are extensively evaluated on two benchmark sets, various shop floor configurations, and eight real-life scenarios. Our results reveal the general effectiveness of job sequencing approaches and demonstrate the overall superiority of CORE.

Minimizing total completion time and makespan for a multi-scenario bi-criteria parallel machine scheduling problem

Multi-criteria scheduling problems under uncertainty remain a relatively unexplored topic in theoretical computer science despite substantial practical interests. This work studies a bi-objective identical parallel machine scheduling problem under uncertainty, in which the first objective is to minimize the total completion time, and the second is to minimize the makespan. Especially a job’s processing time is assumed to be represented by a polynomial function with respect to scenario u∈U, where U⊂R+ is an interval containing an infinite number of scenarios.In this work, we are looking for a compact and complete description of the set of possibly optimal solutions, along with their objective function values, over the set of scenarios or an approximation with a performance guarantee. First, to better understand the characteristics of the studied problem, we consider two single-objective problems: parallel machine scheduling problem under uncertainty with the total completion time and makespan criterion, respectively. For the problem with the total completion time criterion, we demonstrate that the set of possibly optimal schedules can be found in polynomial time. In contrast, for the problem with the makespan criterion, we provide a (1+ϵ)-approximation algorithm. For the bi-objective problem, we provide a 2-approximation algorithm for any number of parallel machines and a (1+ϵ)-approximation algorithm where a fixed number of parallel machines is considered.

Adaptive large-neighbourhood search for optimisation in answer-set programming

Answer-set programming (ASP) is a prominent approach to declarative problem solving that is increasingly used to tackle challenging optimisation problems. We present an approach to leverage ASP optimisation by using large-neighbourhood search (LNS), which is a meta-heuristic where parts of a solution are iteratively destroyed and reconstructed in an attempt to improve an overall objective. In our LNS framework, neighbourhoods can be specified either declaratively as part of the ASP encoding or automatically generated by code. Furthermore, our framework is self-adaptive, i.e., it also incorporates portfolios for the LNS operators along with selection strategies to adjust search parameters on the fly. The implementation of our framework, the system ALASPO, currently supports the ASP solver clingo, as well as its extensions clingo-dl and clingcon that allow for difference and full integer constraints, respectively. It utilises multi-shot solving to efficiently realise the LNS loop and in this way avoids program regrounding. We describe our LNS framework for ASP as well as its implementation, discuss methodological aspects, and demonstrate the effectiveness of the adaptive LNS approach for ASP on different optimisation benchmarks, some of which are notoriously difficult, as well as real-world applications for shift planning, configuration of railway-safety systems, parallel machine scheduling, and test laboratory scheduling.

Hybrid Electro search beetle optimization based task scheduling and game theory SOA based resource allocation in multi cloud computing

AbstractThe most complicated process in multi‐cloud computing is resource allocation, as it needs to cope with a number of configurations and constraints of cloud providers and customers. At the time of resource allocation, the centralized cloud broker monitors the virtual machines (VM) status, scheduling process, and fitness. However, VM scheduling is found tedious and has received huge attention in business, academia, and research. This enhances the demand for both task scheduling and resource allocation in a multi‐cloud environment. To bridge the gap between the consumer requirement and server infrastructure, a joint optimization‐based resource allocation and task scheduling concept is analyzed in the proposed framework. The first phase introduces the task scheduling mechanism, which uses Hybrid Electro Search and Beetle Swarm Optimization to determine the optimal task for specific VMs. The optimal selection procedure is done by analyzing a multi‐cloud environment's makespan, energy, cost, and throughput parameters. In the second step, an Adaptive Game Theory‐based Seagull optimization approach performs several rounds of reassignment iteratively to minimize the variation in the expected completion time, consequently decreasing high energy consumption and load balancing. The experimental analysis for the proposed model is implemented using Python. The proposed methodology is shown to achieve cheaper costs, shorter waiting times, improved resource allocation, and efficient load balancing. Finally, a comparative analysis is performed with some hybrid optimization models, which illustrate the efficiency of the proposed hybrid optimization model.

A new composite heuristic to minimize the total tardiness for the single machine scheduling problem with variable and flexible maintenance

Inspired by a real-world maintenance/job scheduling issue coming from the semiconductor industry, the present paper proposes a new heuristic algorithm structure for the single machine scheduling T-problem with flexible and variable maintenance, job release dates and sequence dependence setup times. Considering the typical short-term production planning needs, a single maintenance problem has to be scheduled within a certain time interval, along with a set of jobs so as to minimize the total tardiness. A twofold contribution emerges from the present paper. First, four mixed-integer linear programming models are developed for the problem at hand and compared in terms of time to convergence and computational complexity. Second, a novel heuristic algorithm, which has been configured into three distinct variants, has been compared with 17 alternative heuristics from the relevant literature based on a comprehensive experimental campaign. The numerical results allow the selection of the most suitable MILP model and confirm the effectiveness of the proposed heuristic approach.

Integrating Order Splitting and Acceptance with Batch Delivery in Parallel Machine Scheduling

Multiple production lines can work together to efficiently manufacture certain products. Thus, when capacity is insufficient, it is necessary to decide whether to develop new production lines to ensure the timely completion of all orders. For example, running a new production line for a small number of orders is not cost-effective. Therefore, decision-making involves choosing between paying tardiness costs for a few orders, abandoning some orders, or developing new production lines to maximize efficiency. Additionally, the timely transportation of completed orders is crucial and depends on vehicle usage efficiency. From a transportation perspective, fully loading vehicles is the most efficient, but this may impact the timeliness of orders, leading to potential tardiness costs. By comprehensively considering these aspects, a multi-machine production model is constructed that incorporates transportation batch sequences and uses heuristic algorithms to solve the problem. Finally, designed case examples validate the effectiveness of the model and algorithm.

Dynamic scheduling of hybrid flow shop problem with uncertain process time and flexible maintenance using NeuroEvolution of Augmenting Topologies

AbstractA hybrid flow shop is pivotal in modern manufacturing systems, where various emergencies and disturbances occur within the smart manufacturing context. Efficiently solving the dynamic hybrid flow shop scheduling problem (HFSP), characterised by dynamic release times, uncertain job processing times, and flexible machine maintenance has become a significant research focus. A NeuroEvolution of Augmenting Topologies (NEAT) algorithm is proposed to minimise the maximum completion time. To improve the NEAT algorithm's efficiency and effectiveness, several features were integrated: a multi‐agent system with autonomous interaction and centralised training to develop the parallel machine scheduling policy, a maintenance‐related scheduling action for optimal maintenance decision learning, and a proactive scheduling action to avoid waiting for jobs at decision moments, thereby exploring a broader solution space. The performance of the trained NEAT model was experimentally compared with the Deep Q‐Network (DQN) and five classical priority dispatching rules (PDRs) across various problem scales. The results show that the NEAT algorithm achieves better solutions and responds more quickly to dynamic changes than DQN and PDRs. Furthermore, generalisation test results demonstrate NEAT's rapid problem‐solving ability on test instances different from the training set.

Machine Learning based Algorithm Selection and Genetic Algorithms for serial-batch scheduling

Whenever combinatorial optimization problems cannot be solved by exact solution methods in reasonable time, tailor-made algorithms (heuristics, meta-heuristics) are developed. Often, these heuristics exploit structural properties and perform well on selected subsets of the problem space. For example, this is how the two best-known construction heuristics solve the scheduling problem investigated in this study (i.e., the scheduling of parallel serial-batch processing machines with incompatible job families, restricted batch capacities, arbitrary batch capacity demands, and sequence-dependent setup times). However, when the properties change, the performance of one algorithm might decrease, and another algorithm might have been the better choice. To resolve this issue, we propose using Machine Learning to exploit the strengths of different algorithms and to select the probably best-performing algorithm for each problem instance individually. To that, we investigate a variety of methods from the “learning-to-rank” literature and propose several adaptations. Furthermore, because there is no algorithm for the considered scheduling problem that is capable to explore the entire solution space, we developed two Genetic Algorithms for the improvement of initial solutions computed by the selected algorithms. Here, we put special emphasis on ensuring that the solution representation (encoding) reflects the entire solution space and that the operators (e.g., for recombination and mutation) are appropriate to explore and exploit this space completely. Our computational experiments show an average increase of 39.19% in solution quality.

Integrated Working-Age Maintenance to the Unrelated Parallel Machine Scheduling with Sequence-Dependent Setup Times

Integrated Working-Age Maintenance to the Unrelated Parallel Machine Scheduling with Sequence-Dependent Setup Times

Energy-aware production lot-sizing and parallel machine scheduling with the product-specific machining tools and power requirements

This study addresses a multi-product lot-sizing and scheduling problem with sequence-dependent setup times, considering that the machining operations cause energy consumption. The production facility comprises identical parallel machines under which the production of each product requires a certain set of tools. The energy requirement of production depends on the product-specific machining tools. The problem deals with determining the minimum cost lot-sizing and scheduling plan considering the energy capacity of the production facility. We formulate the problem as a mixed integer linear programming model by introducing energy consumption-related costs and constraints. We perform a case study on CNC milling and turning workshops. Further, we propose an heuristic approach combining a decomposition-based Simulated Annealing heuristic and Fix&Optimise algorithms to handle larger-sized problem instances. The computational performance of the proposed heuristic approach is evaluated against the proposed mixed integer linear programming model on a numerical study. Our numerical experiments reveal that the proposed heuristic approach is capable of providing cost-efficient solutions without compromising time efficiency.