Factory Scheduling Research Articles

Robust optimization for integrated production and energy scheduling in low-carbon factories with captive power plants under decision-dependent uncertainty

Low-carbon factories with captive power plants represent a new industrial microgrid paradigm of energy conservation and emission reduction in many countries. However, one of the most common challenges of low-carbon management is the joint regulation of factory production and power plant operations under uncertainty. To meet this challenge, a robust optimization-based integrated production and energy (IPE) scheduling approach is proposed in this paper. Firstly, a two-stage adaptive robust optimization model is established to cover all possible realizations of decision-independent uncertainties (e.g. market demands and output power of renewable sources) and decision-dependent uncertainties (e.g. carbon emission densities depending on the choice of production lines). Secondly, a novel parametric column-and-constraint generation algorithm is utilized to derive robust scheduling schemes. The non-trivial scenarios of decision-dependent uncertainties identified in the subproblem are parametrically characterized based on Karush–Kuhn–Tucker conditions, which can be included in the master problem. Finally, simulations on different cases are conducted to test the rationality and validity of the proposed approach. Compared with the separate scheduling of production and energy, IPE scheduling may increase production and energy costs to ensure the robustness of the resulting schemes. Moreover, the proposed approach can mitigate the impacts of uncertainties on IPE scheduling without significantly increasing the computational complexity.

Virtual Simulation-Based Optimization for Assembly Flow Shop Scheduling Using Migratory Bird Algorithm.

As industrial informatization progresses, virtual simulation technologies are increasingly demonstrating their potential in industrial applications. These systems utilize various sensors to capture real-time factory data, which are then transmitted to servers via communication interfaces to construct corresponding digital models. This integration facilitates tasks such as monitoring and prediction, enabling more accurate and convenient production scheduling and forecasting. This is particularly significant for flexible or mixed-flow production modes. Bionic optimization algorithms have demonstrated strong performance in factory scheduling and operations. Centered around these algorithms, researchers have explored various strategies to enhance efficiency and optimize processes within manufacturing environments.This study introduces an efficient migratory bird optimization algorithm designed to address production scheduling challenges in an assembly shop with mold quantity constraints. The research aims to minimize the maximum completion time in a batch flow mixed assembly flow shop scheduling problem, incorporating variable batch partitioning strategies. A tailored virtual simulation framework supports this objective. The algorithm employs a two-stage encoding mechanism for batch partitioning and sequencing, adapted to the unique constraints of each production stage. To enhance the search performance of the neighborhood structure, the study identifies and analyzes optimization strategies for batch partitioning and sequencing, and incorporates an adaptive neighborhood structure adjustment strategy. A competition mechanism is also designed to enhance the algorithm's optimization efficiency. Simulation experiments of varying scales demonstrate the effectiveness of the variable batch partitioning strategy, showing a 5-6% improvement over equal batch strategies. Results across different scales and parameters confirm the robustness of the algorithm.

Prediction-Based Power Consumption Monitoring of Industrial Equipment Using Interpretable Data-Driven Models

Efficient energy optimization and scheduling in industrial factories depend on accurate, reasonable, and real-time monitoring of equipment power consumption. However, the power prediction of industrial equipment requires a large number of process data, which could be inevitably contaminated by some imperfect data, due to the harsh environments. Monitoring or predicting equipment power consumption is usually not feasible using data-driven black-box models with imperfect data. This paper proposes a prediction-based approach for power consumption monitoring using an interpretable data-driven model. First, a data preprocessing method is used to remove outliers and fill in missing values. Then, a Volterra polynomial basis function (VPBF) model is built to predict equipment power consumption. This model decomposes power values into a series of basis functions consisting of input parameters. Moreover, to compensate for data dropouts during the power consumption monitoring process, a networked predictive monitoring system is also proposed. Finally, this paper presents two case studies based on actual production equipment in an industrial manufacturing factory. The results demonstrate that the proposed approach can achieve satisfactory monitoring accuracy and adaptation ability. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —This paper is motivated by the problem of power consumption monitoring of industrial equipment in harsh production environments. A conventional solution is to predict the power consumption using data-driven black-box models, with limited feasibility and interpretability. This paper proposes a new power consumption monitoring approach, utilizing an interpretable data-driven model and a networked predictive method. This approach accurately reveals the transparent relationships between the output and input parameters. The power prediction result is consequently interpretable and more reasonable. Meanwhile, this approach actively compensates for data dropouts in the network, which can help operators real-time grasp the power consumption of equipment. Furthermore, this approach can be integrated into energy optimization systems as a basis of optimization and decision-making. Practical applications in an aluminum manufacturing company located in Guangdong Province demonstrate that this approach is feasible and applicable. Future research is to expand this approach further for energy optimization and scheduling.

Conversational Modeling for Constraint Satisfaction

Many problems, from Sudoku to factory scheduling, can be regarded as constraint satisfaction problems. A key component of real world problem solving is a conversation between a constraint programming expert and a problem domain expert to specify the problem to be solved. This presentation argues that the time is ripe for progress in automating the constraint programmer side of this conversation and suggests promising avenues for this pursuit.

Federated deep reinforcement learning for dynamic job scheduling in cloud-edge collaborative manufacturing systems

The cloud-edge collaborative manufacturing system (CCMS) connects distributed factories to a cloud centre through cloud-edge collaborative communication, introducing both opportunities and challenges to conventional dynamic job scheduling. Enhancing each factory's scheduling performance by sharing general scheduling knowledge among heterogeneous factories under the consideration of data privacy protection remains challenging. To this end, this paper proposes to solve the dynamic job scheduling in the context of CCMS with a novel federated deep reinforcement learning (FDRL) approach. Within each factory, the scheduling objective involves minimising the makespan and energy consumption, accounting for machine warm-up procedures and real-time dynamics. To handle heterogeneous policy structures, we aggregate their hidden parameters through FDRL, with states, actions, and rewards designed to facilitate the aggregation. The two-phase algorithm, comprising iterative local training and global aggregation, trains the scheduling policies. Constraint items are introduced to the loss functions to smooth local training, and the global aggregation considers production scales and obtained objectives. The proposed approach enhances the solution quality and generalisation of each factory's scheduling policy without exposing original production data. Numerical experiments conducted on sixty scheduling instances validate the superiority of the proposed approach compared to twelve dynamic scheduling methods. Compared to independently trained DRL-based approaches, the proposed FDRL-based approach achieves up to an 8.9% reduction in makespan and a 22.3% decrease in energy consumption through knowledge sharing.

Energy-Efficient Iterative Greedy Algorithm for the Distributed Hybrid Flow Shop Scheduling With Blocking Constraints

With the global energy shortage, climate anomalies, environmental pollution becoming increasingly prominent, energy saving scheduling has attracted more and more concern than before. This paper studies the energy-efficient distributed hybrid flow-shop scheduling problem (DHFSP) with blocking constraints. Our aim is to find the job sequence with low energy consumption as much as possible in a limited time. In this paper, we formulate a mathematical model of the DHFSP with blocking constraints and propose an improved iterative greedy (IG) algorithm to optimize the energy consumption of job sequence. In the proposed algorithm, first, a problem-specific strategy is presented, namely, the global search strategy, which can assign appropriate jobs to the factory and minimize the energy consumption of each processing factory. Next, a new selection mechanism inspired by Q-learning is proposed to provide strategic guidance for factory scheduling. This selection mechanism provides historical experience for different factories. Finally, five types of local search strategies are designed for blocking constraints of machines and sequence to be scheduled. These proposed strategies can further improve the local search ability of the QIG algorithm and reduce the energy consumption caused by blocking. Simulation results and statistical analysis on 90 test problems show that the proposed algorithm is superior to several high-performance algorithms on convergence rate and quality of solution.

Precise Short-Term Small-Area Sunshine Forecasting for Optimal Seedbed Scheduling in Plant Factories

Photosynthesis is one of the key issues for vertical cultivation in plant factories, and efficient natural sunlight utilization requires predicting the light falling on each seedbed in a real-time manner. However, public weather services neither provide sunshine data nor meet spatial resolution requirement. Facing these short-term and small-area weather forecasting challenges, we propose a cross-scale approach to infer seedbed-sized areas of sunshine from the city-level public weather services, and then design a seedbed rotation scheduling system for optimal natural sunlight utilization. First, an end-edge-cloud coordinated computing architecture was employed to concurrently aggregate the multi-scale data from weather satellites to sunshine sensors in the plant factory. Second, the small area of sunshine deterministically depends on the meteorological data given a fixed environment, and this correlation was described by a hybrid mapping model, which combined the long short-term memory (LSTM) and gradient boosting decision tree (GBDT) algorithms to form the LSTM-GBDT hybrid prediction algorithm (LGHPA). By training the LGHPA with historical local sensory sunshine and the city-scale meteorological data, the hourly sunshine on a seedbed can be predicted from the public weather forecasting service. Finally, a dynamic seedbed scheduling scheme was constructed to provide uniform solar energy absorption according to the one-hour-ahead radiation estimation. Experiment results show that the hourly sunshine prediction error was less than 18.44% over a seasonal period and the deviation for different solar absorption by seedbeds with rotation capability is less than 7.1%. Consequently, it was demonstrated that the application of short-term, small-area sunshine forecasting improved the performance of seedbed rotation for uniformly absorbed solar radiation. The proposed method verifies the feasibility of precisely predicting small-area sunshine down to the seedbed scale by leveraging a model-based approach and a cloud-edge-end merged cybernetic computing paradigm.

One-step production and two-step assembly scheduling in identical factories

In this article, a production–assembly scheduling problem is presented in three steps. In the first step, the production operation is performed by dedicated parallel machines; in the second step, the assembly operation is performed by the same parallel machines, and in the third step, the post-assembly operation is performed by one machine, and these three steps exist in parallel factories. This problem is NP hard and cannot be solved in a reasonable time by mathematical models. Therefore, a mixed integer linear programming algorithm is presented for small-sized problems, and a new metaheuristic algorithm is presented for large-sized problems, by combining quantum-behaved particle swarm optimization (QPSO), shortest processing time (SPT) and dominance rules, which is called the hybrid QPSOSPT dominance rules (HQSD) algorithm. Accurate parameter adjustment was achieved by analysis of variance. The HQSD algorithm was shown to obtain better results than the other algorithms.

Dynamic Scheduling Optimization of Production Workshops Based on Digital Twin

Production scheduling is the key to manufacturing process decision support, which directly affects the efficiency and competitiveness of enterprises. The production process of discrete workshops is complex and changeable, and it is usually difficult to make adjustments quickly and accurately in response to disturbance events. In this paper, a workshop production scheduling method based on digital twin is proposed and applied to the manufacturing workshop of an aerospace factory. Combined with the advantages of real-time virtual real interaction fusion of digital twin technology, the dynamic scheduling problem under fault disturbance factors is studied. A high-fidelity digital twin workshop is established to realize the mapping and interaction between the real production and the virtual factory. Based on the vibration data of machine tool spindle, a fault prediction method of learning vector quantization neural network is proposed. The dynamic scheduling strategy of workshop production based on digital twin is constructed and compared with the scheduling results without digital twin under fault disturbance. The results show that the scheduling method based on digital twin can effectively deal with disturbances and improve workshop productivity. This study can be used for the application of digital twin and production scheduling in practical factories.

From Marginalia to Bookends: Industrialization, Capitalism, and Advertising in Hungary’s Modern Literary Journal, Nyugat

[1],this paper examines Nyugat [‘West’], the premier journal ofmodern Hungarian literature published from 1908 to 1941 and edited by ErnőOsvát (1876-1929), Ignotus (1869-1949), and Miksa Fenyő (1877-1972) until 1917.Although Hungarian scholarship has detailed the role played by Osvát andIgnotus, Fenyő’s contribution to this triumvirate has received less attention,a lack that may have hindered literary historians’ understanding of the morewidespread, sociological reasons underlying Nyugat’s long-lastingpresence in a highly competitive book market. Rather than rely exclusively uponthe sources (correspondence, personal journals, memoirs, reports bycontemporaries, etc.) commonly used to investigate the editorial decisionsunderpinning a journal’s trajectory, I argue that examining Fenyő’s editorial positiondemands the inclusion of marginalia, the term this study utilises to denotethe factory advertisements, banking-related notifications, military supplyannouncements, railway schedules, and eulogies that display Fenyő’s ties to theindustrial lobby organisation GyOSz [‘National Association of HungarianIndustrialists’, also referred to as ‘the Association’] within the pages of ajournal dedicated to promoting fin-de-siècle aestheticism. Although the connectionbetween GyOSz and Nyugat has been examined from the perspective ofpublishing strategies or patronage systems, it has not been detailed within thecontext of the era’s expanding market economy. Exploring what Bernard Lahire woulddescribe as Fenyő’s ‘double life’[2] therebypaves the way to theorising what beliefs and ‘rules of the game’ (illusio)may have determined the connection between Hungary’s wealthiest industrialistsand Nyugat during a period when the journal’s editors and authors soughtto attain both authorial and financial autonomy.[1][2] Bernard Lahire, ‘The Double Lifeof Writers’, New Literary History, 41.2 (2010), 443‒465.

Multi-agent reinforcement learning for online scheduling in smart factories

• A distributed architecture for smart factories is proposed by integrating heterogeneous manufacturing units (e.g., warehouses, machines, and material handlers). • We design an artificial intelligence (AI) scheduler with novel neural networks for each unit to schedule low-volume-high-mix workorders in real time. • New composite reward functions are designed to improve AI schedulers’ decision-making abilities in shortening makespan and balancing workloads . • AI schedulers make scheduling policies on their own and collaborate to handle unexpected events such as urgent workorders and machine failures. • The proposed methodology improves scheduling effectiveness and operating robustness of manufacturing systems . Rapid advances in sensing and communication technologies connect isolated manufacturing units, which generates large amounts of data. The new trend of mass customization brings a higher level of disturbances and uncertainties to production planning. Traditional manufacturing systems analyze data and schedule orders in a centralized architecture, which is inefficient and unreliable for the overdependence on central controllers and limited communication channels. Internet of things (IoT) and cloud technologies make it possible to build a distributed manufacturing architecture such as the multi-agent system (MAS). Recently, artificial intelligence (AI) methods are used to solve scheduling problems in the manufacturing setting. However, it is difficult for scheduling algorithms to process high-dimensional data in a distributed system with heterogeneous manufacturing units. Therefore, this paper presents new cyber-physical integration in smart factories for online scheduling of low-volume-high-mix orders. First, manufacturing units are interconnected with each other through the cyber-physical system (CPS) by IoT technologies. Attributes of machining operations are stored and transmitted by radio frequency identification (RFID) tags. Second, we propose an AI scheduler with novel neural networks for each unit (e.g., warehouse, machine) to schedule dynamic operations with real-time sensor data. Each AI scheduler can collaborate with other schedulers by learning from their scheduling experiences. Third, we design new reward functions to improve the decision-making abilities of multiple AI schedulers based on reinforcement learning (RL). The proposed methodology is evaluated and validated in a smart factory by real-world case studies. Experimental results show that the new architecture for smart factories not only improves the learning and scheduling efficiency of multiple AI schedulers but also effectively deals with unexpected events such as rush orders and machine failures.

Multiobjective optimization for complex flexible job-shop scheduling problems

In this paper, we are concerned with the resolution of a multiobjective complex job-shop scheduling problem stemming from semiconductor manufacturing. To produce feasible and industrially meaningful schedules, this paper extends the recently proposed batch-oblivious approach by considering unavailability periods and minimum time lags and by simultaneously optimizing multiple criteria that are relevant in the industrial context. A novel criterion on the satisfaction of production targets decided at a higher level is also proposed. Because the solution approach must be embedded in a real-time application, decision makers must express their preferences before the optimization phase. In addition, a preference model is introduced where trade-off is only allowed between some criteria. Two a priori multiobjective extensions of Simulated Annealing are proposed, which differ in how the simultaneous use of a lexicographic order and weights is handled when evaluating the fitness. A known a posteriori approach of the literature is used as a benchmark. All the metaheuristics are embedded in a Greedy Randomized Adaptive Search Procedure. The different versions of the archived GRASP approach are compared using large industrial instances. The numerical results show that the proposed approach provides good solutions regarding the preferences. Finally, the comparison of the optimized schedules with the actual factory schedules shows the significant improvements that our approach can bring.

Multi-agent capacitated scheduling for profit-maximizing using a decomposition-based branch and cut algorithm

ABSTRACT This paper considers a distributed production network scheduling that involves heterogeneous factories with the parallel machine. Although, each factory has its own local customers as a production agent, for better load balancing of machines in the production network, the jobs can transfer among factories. In order to make the problem more realistic, in addition to considering the ability of factories in processing of jobs, the capacity constraints of factories are also included in the scheduling. The aim of this paper is to maximize the profits of jobs such that each job is assigned to precisely one factory subject to their deadlines. To solve this problem, based on the decomposition algorithm, for the first time, an efficient decomposition-based branch and cut algorithm is designed. In this regard, first, the problem is formulated as a mixed-integer linear program (MILP), then using the Benders decomposition structure and after reformulating as an assignment subproblem and single factory scheduling subproblems, a branch and cut algorithm is proposed. Finally, the obtained results of the proposed algorithm, the original MILP, and non-cooperative local scheduling, all solved by CPLEX, are compared.

Spatial–temporal out-of-order execution for advanced planning and scheduling in cyber-physical factories

Cyber-Physical System (CPS) is one of the most promising directions of Industry 4.0 smart manufacturing. Abundant manufacturing data and information are available for decision-makers in real-time thanks to the application of various frontier technologies in CPS. However, the inherent complexity and uncertainty of manufacturing optimization still plague scholars and practitioners and impede further progress of smart manufacturing. The production planning and scheduling is such a complex and stochastic problem that has received considerable research attention. Whereas how to leverage the strengths of CPS for breaking the bottleneck of complexity and uncertainty, is still a question that needs further exploration. This paper proposes a novel “divide and conquer” approach, Spatial–Temporal Out-Of-Order execution (ST-OOO), for achieving real-time planning and scheduling in cyber-physical factories. ST-OOO divides the space and time scopes of a factory into finite areas and intervals to reduce complexity and localize uncertainties so that the original complex optimization problem is decomposed into a set of subproblems with different spatial and temporal characteristics. These small-size subproblems can be assembled using data and information visibility and traceability, and then solved in a rolling spatiotemporal manner to generate a global solution. A case study shows that ST-OOO has a well-balanced and more stable performance compared to traditional strategies. Sensitivity analysis is carried out to study the impacts of spatial and temporal scales on the results.

A Dynamic Just‐in‐Time Component Delivery Framework for Off‐Site Construction

Off‐site construction entails various advantages compared with the traditional construction method; however, the fragmentation of the prefabrication and assembly results in a complex supply chain. Both general contractors and factories often encounter production deviation, making the original component delivery plan nonoptimal. Traditionally, both parties tend to rely on internal resources or third‐party resources to manage schedule changes, paying little attention to the optimisation of the component delivery process. The static compensation mechanisms reported in existing literature require factories to manage demand fluctuations but fail to encourage general contractors to control schedule deviations. Therefore, a dynamic compensation mechanism is proposed to achieve just‐in‐time component delivery, with which a factory shares possible changes for each component’s delivery date to its clients on an inverse Kanban system. First, unfavourable changes for the factory schedule are allocated with surcharges, and the general contractor should compensate the factory if it accepts the date changes; secondly, schedule changes that are beneficial for the factory are assigned as incentives, and the general contractor receives the factory’s incentive upon agreeing to the changes. Based on these two scenarios, genetic algorithm‐based optimisation models are developed to achieve optimal delivery planning solutions. General contractors can obtain an optimal component delivery date to reduce the additional cost when they have changed the assembly schedule. General contractors can also optimise their component delivery schedule to trade their duration flexibility for incentives offered by factories. The models can help both parties to reduce component delivery waste when either side has the motivation to change the original component delivery schedules.

An improved genetic algorithm for the flexible job shop scheduling problem with multiple time constraints

Abstract The flexible job shop scheduling problem is a very important problem in factory scheduling. Most of existing researches only consider the processing time of each operation, however, jobs often require transporting to another machine for the next operation while machines often require setup to process the next job. In addition, the times associated with these steps increase the complexity of this problem. In this paper, the flexible job scheduling problem is solved that incorporates not only processing time but setup time and transportation time as well. After presenting the problem, an improved genetic algorithm is proposed to solve the problem, with the aim of minimizing the makespan time, minimizing total setup time, and minimizing total transportation time. In the improved genetic algorithm, initial solutions are generated through three different methods to improve the quality and diversity of the initial population. Then, a crossover method with artificial pairing is adopted to preserve good solutions and improve poor solutions effectively. In addition, an adaptive weight mechanism is applied to alter mutation probability and search ranges dynamically for individuals in the population. By a series of experiments with standard datasets, we demonstrate the validity of our approach and its strong performance.

Recursive heuristic scheduling method for multi-crop plant factory with solar panel roof

Plant factory can provide stable crop cultivation environment, shorten cultivation duration, and deliver better produce quality by controlling temperature, humidity, lighting, nutrient supply, and other cultivating factors. Due to the high cost of operation, how to select crops and plan the cultivation schedule to enhance profitability is an important issue. In this research, the plant factory scheduling problem was formulated as a mixed integer linear programming (MILP) problem. The objective function is to seek the maximum revenue by considering several practical operating conditions such as (1) crop market value per unit and time, (2) crop adjacency issue, (3) cleaning and maintenance, and (4) sunlight blocking by solar panel on the roof. Although the scheduling problem can be solved by the optimization solver, it presents challenges of rack-level modification when applying the optimization method on the field. Therefore, this study further developed a heuristic algorithm, named Heuristic Plant Factory Scheduler (HPFS), which applies a recursive technique to schedule crops rack by rack. This approach provides ease of implementation and modification. The experimental results show that HPFS is able to accelerate the computational performance with acceptable scheduling quality when the problem space is large.

An improved differential evolution algorithm for solving a distributed assembly flexible job shop scheduling problem

The single-factory manufacturing is gradually transiting to the multi-factory collaborative production with the globalization. The decentralization of resources and the heterogeneity of the production modes make it difficult to solve this kind of problem. Therefore, the distributed assembly flexible job shop scheduling problem (DAFJSP) is studied. DAFJSP can be decomposed into several flexible job shop scheduling problems and several single machine factory scheduling problems. To begin with, a mixed integer linear programming model for the DAFJSP is formulated to minimize the earliness/tardiness and the total cost simultaneously. Then, an improved differential evolution simulated annealing algorithm (IDESAA) is proposed. The balanced scheduling algorithm is designed to trade off the two objectives. Two crossover and mutation operators are designed. Due to its strong robustness, simulated annealing is integrated to local search the best Pareto solutions. The greedy idea combined with the Non-Dominated Sorted selection is employed to select the offspring. Finally, comprehensive experiments are conducted and the results show that the proposed algorithm can solve DAFJSP effectively and efficiently.

ORGANIC APPLE JUICE CLARIFICATION: PHYSICOCHEMICAL AND SENSORY EVALUATION

In the Brazilian market of non-alcoholic beverages, apple juice is found clarified orturbid. In addition to its consumption as juice itself and nectar, it can also be used in soft drinks formulation.The aim of this work was to clarify organic apple juice of Eva variety using enzymatic complex (pectinases), gelatin and bentonite (phase 1) and to compare physicochemical and sensorial clarified and unclarified Eva apple juices (phase 2). The experimental design was completely randomized. In phase 1, the tests were performed on bench scale, adopting a factorial schedule and in phase 2, the tests were performed on a pilot plant scale. Parameters such assoluble solids, titratable acidity, ratio, pH, reducing sugars, total reducing sugars, non-reducing sugars, phenolic compounds, turbidity and color were evaluated for the physicochemical characterization of juices. The sensory analysis of juices wereperformed by affective test (hedonic scale). In phase 1, the best juice clarification results were obtained using the enzymatic complex, gelatin at concentrations of 8, 10 and 12 g.100 L-1 and bentonite at 50 g.100 L-1, with final juice filtration in paper of 28 μm pore. In phase 2, the clarification process interferedon physicochemical characteristics of the juice for all analyzed parameters, except for total reducing sugars and non-reducing sugars. Despite differences in physicochemical composition, the panel of tasters showed equal acceptability between clarified and unclarified juices

Evaluation and Scheduling of the Car Manufacturing Factory’s Employers’ Work Shifts

This study is made an application related to the regulation of working hours of workers in car factory. This factory has thick to work 24 hour shifts need to work with the system as needed. In this study, which is open 24 hours a day and 7 days in a car factory, it has made application serving with 3 shifts. The attention of employees serving in this industry and are crucial to productivity. Mistakes will be made, which can lead to irreparable consequences. The working hours of workers at the factory scheduling process is usually carried out by personnel chief in the factory. In this study, in consultation with the chief engineer in charge of drafting the schedule and made relevant studies were identified by examining the constraints to be considered. Then it established a mathematical model that can be used in a general sense with integer linear programming techniques. Established model applies to data in a unit of a car factory and has been found to be optimal solutions with the help of LINGO software. Unlike other shift scheduling problems in the literature, this study aimed to run for a minimum of additional workers outside the factory. There is also a model that defined the mathematical model and skillful workers to shift some concessions to be assigned any number of workers in particular experience has been established.