Production Scheduling Model Research Articles

Production scheduling optimization for parallel machines subject to physical distancing due to COVID-19 pandemic

This paper, for the first time, presents a production scheduling model for a production line considering physical distancing between the machines' workforces. The production environment is an unrelated parallel-machine, in which for producing each part, different machines with different production rates and the required number of workers are available. We propose a three-objective mixed-integer linear programming mathematical model that aims to maximize the manufacturer's total benefit, parts' safety stock (SS) index, and the workforce's physical distance over a finite horizon (one year) by determining the optimal scheduling of the parts on the machines. Since a large production scheduling problem belongs to the Np-Hard category of problems, a non-dominated sorting genetic algorithm, and a non-dominated ranked GA algorithm are developed to solve the presented model in two stages using the empirical data from a Canadian plastic injection mold company. In the first stage, the LP-metrics approach is utilized for validating the meta-heuristics on a reduced-size problem. In the second stage, the validated meta-heuristics are utilized to optimize the company's yearly production schedule. The results indicate both metaheuristics are performing well in determining the optimal solution. Moreover, implementing physical distancing in the company reduces the company's monthly net benefit by around 9.56% compared to the normal operational conditions (without considering physical distancing).

Anticipating technical car sequencing rules in the master production scheduling of mixed-model assembly lines

In this paper, we propose a new linear programming-based approach that enables the consideration of technical car sequencing rules in the master production scheduling of mixed-model assembly lines at a much higher level of detail than previous approaches. To this end, we investigate certain interdependencies of car sequencing rules, which have largely been neglected, both in practice and in the research literature. We illustrate the existence and impact of these interdependencies and show that they induce additional implicit constraints, which can be represented by linear inequalities and incorporated into linear optimization models for master production scheduling. In a numerical study, we evaluate the approach and show, that it can significantly reduce sequencing violations compared to existing approaches.

MILP performance improvement strategies for short-term batch production scheduling: a chemical industry use case

This paper presents the development and mathematical implementation of a production scheduling model utilizing mixed-integer linear programming (MILP). A simplified model of a real-world multi-product batch plant constitutes the basis. The paper shows practical extensions to the model, resulting in a digital twin of the plant. Apart from sequential arrangement, the final model contains maintenance periods, campaign planning and storage constraints to a limited extend. To tackle weak computational performance and missing model features, a condensed mathematical formulation is introduced at first. After stating that these measures do not suffice for applicability in a restrained time period, a novel solution strategy is proposed. The overall non-iterative algorithm comprises a multi-step decomposition approach, which starts with a reduced scope and incrementally complements the schedule in multiple subproblem stages. Each of those optimizations holds less decision variables and makes use of warmstart information obtained from the predecessor model. That way, a first feasible solution accelerates the subsequent improvement process. Furthermore, the optimization focus can be shifted beneficially leveraging the Gurobi solver parameters. Findings suggest that correlation may exist between certain characteristics of the scheduling scope and ideal parameter settings, which yield potential for further investigation. Another promising area for future research addresses the concurrent multi-processing of independent MILPs on a single machine. First observations indicate that significant performance gains can be achieved in some cases, though sound dependencies were not discovered yet.

Capacity planning and production scheduling integration: improving operational efficiency via detailed modelling

Successful capacity planning and production scheduling is built on the understanding of market opportunities and the costs of capacity, production, sourcing, inventory, and distribution over the planning horizon. Increasingly, companies attempt to integrate capacity planning and production scheduling to improve upon the commonly used sequential decision process, but most related research works fail to capture the granularity of actual operational decisions and therefore may overlook potential cost-saving opportunities. The contributions of this study include: (1) a detailed integrated capacity and production scheduling model with multiple discrete and continuous options for varying short and medium-term capacity, (2) a heuristic algorithm that exploits the problem structure to solve the nonlinear mixed integer problem, (3) an evaluation of the value of the integrated model relative to traditional practice and its sensitivity to parameters, (4) a review of past contributions to integrated planning, particularly focused on IJPR, and (5) a case study originated from a world-class automobile manufacturer illustrating how the model can be applied and confirming its value relative to hierarchical and less detailed modelling approaches.

Integrated Parametric Graph Closure and Branch-and-Cut Algorithm for Open Pit Mine Scheduling under Uncertainty

Open pit mine production scheduling is a computationally expensive large-scale mixed-integer linear programming problem. This research develops a computationally efficient algorithm to solve open pit production scheduling problems under uncertain geological parameters. The proposed solution approach for production scheduling is a two-stage process. The stochastic production scheduling problem is iteratively solved in the first stage after relaxing resource constraints using a parametric graph closure algorithm. Finally, the branch-and-cut algorithm is applied to respect the resource constraints, which might be violated during the first stage of the algorithm. Six small-scale production scheduling problems from iron and copper mines were used to validate the proposed stochastic production scheduling model. The results demonstrated that the proposed method could significantly improve the computational time with a reasonable optimality gap (the maximum gap is 4%). In addition, the proposed stochastic method is tested using industrial-scale copper data and compared with its deterministic model. The results show that the net present value for the stochastic model improved by 6% compared to the deterministic model.

Reinforcement learning approach to scheduling of precast concrete production

The production scheduling of precast concrete (PC) is essential for successfully completing PC construction projects. The dispatching rules, widely used in practice, have the limitation that the best rule differs according to the shop conditions. In addition, mathematical programming and the metaheuristic approach, which would improve performance, entail more computational time with increasing problem size, let alone its models being revised as the problem size changes. This study proposes a PC production scheduling model based on a reinforcement learning approach, which has the advantages of a general capacity to solve various problem conditions with fast computation time and good performance in real-time. The experimental study shows that the proposed model outperformed other methods by 4–12% of the total tardiness and showed an average winning rate of 77.0%. The proposed model could contribute to the successful completion of off-site construction projects by supporting the stable progress of PC construction.

Geometallurgical prediction models of processing plant indicators for stochastic mine production scheduling

This article presents a new geometallurgical framework that builds empirical prediction models of key performance indicators of the processing plant and integrates them into a simultaneous stochastic optimization model for mine production scheduling. The prediction models are created by tracking blended rock properties and matching them with observed responses from the operating processing plant. Several applied case studies in a gold mining complex are presented building prediction models of ball mill throughput, steel ball consumptions, and reagent consumptions from collected data in a gold leaching operation. Finally, the integration of these geometallurgical prediction models into stochastic mine production scheduling is demonstrated to monetize the gained insights. Compared with conventional planning, the resulting mine plans increase yearly profit and are more likely to align with production targets.

Integrated optimization of batch production process scheduling based on USEBCTM and explicit model predictive control

An integration model of batch process production scheduling and control is established by using synchronous method, which generates mixed integer dynamic (MIDO) problem. In order to solve the online computing burden of MIDO problem, explicit model predictive control (E-MPC) is applied to solve the online implementation of scheduling and control integration problem. Using the method based on USEBCTM to establish the scheduling level constraints, and used the MPT toolbox in MATLAB to solve the E-MPC dynamic problem. The explicit control solution was converted into the control level constraint, then with scheduling level constrain optimization objective together.

Multiobjective Lot Sizing and Scheduling of Multiproduct Switching Production in the Process Industry Considering Uncertain Market Information Under Mass Customization

With the gradual diversification of customer demand, to improve the rapid response ability of enterprises, this paper fully considers uncertain market information under the background of mass customization and establishes a new process industry multi-product switching production lot sizing and scheduling model with the goal of minimizing the maximum completion time and total switching cost. Fuzzy chance-constrained programming is used to explicitly incorporate market demand with uncertain quantities into the model. Starting from reality, this paper considers the switching cost of equipment when processing multiple varieties of products and skillfully integrates the conversion rate of materials during processing into the novel model, making the entire production system closer to the real state. It provides a new concept to consider cost reduction for actual workshop scheduling management. In addition, this paper proposes an improved multi-objective genetic particle swarm optimization (SMOPSO-IIs) algorithm to simulate and solve the model. The operation results show that the Pareto solution obtained by the SMOPSO-IIs algorithm is better overall. Finally, the model is solved by example simulation, and the operation results are analyzed along with a scheduling Gantt chart to verify its applicability and effectiveness. The model presented in this paper can be used to further shorten the gap between production theory and practical application and improve the current workshop scheduling management system of the process industry.

A Production Scheduling Method for Resolving Multiple Equipment Operation Conflicts in Lithium Battery Mills

Due to the wide variety of production orders and complex processes in the lithium battery cell rolling shop, it is easy to cause conflict deadlock problems when multiple devices are operating at the same time, thus blocking the tasks and affecting productivity. In this paper, we build a task scheduling framework for the rolling shop by combining the production process of lithium battery cells, and establish a production scheduling model for the rolling shop by considering the scheduling rules of order splitting and order prioritization. An improved genetic algorithm is proposed to solve the model with the completion time and delay time as the optimization objectives. First, heuristic rules are combined with GLR initialization methods to generate initial populations to improve population quality. Secondly, a simulated annealing algorithm with an elite retention strategy is introduced to screen the new population, and a neighborhood exchange strategy based on order priority ranking is proposed to overcome the problem that the iterative process is prone to illegal solutions. Finally, the encoding method and mutation repair mechanism are improved, and adaptive crossover and mutation operations are used to improve the search capability of the algorithm. The experimental results show that the improved genetic algorithm is feasible and effective in solving the optimization problem of rolling operation shop scheduling, and the algorithm has certain application value in improving the efficiency of smart shop operation.

Joint optimization of demand-side operational utility and manufacture-side energy consumption in a distributed parallel machine environment

Previous production scheduling models often set optimization objectives from the perspective of manufacturers, such as makespan, tardiness and energy consumption. However, none of the objectives can reflect the extent to which the scheduling plan affects the demand side. In fact, the delivery time of orders will directly affect the equipment utilization or project schedule on the demand side. In this paper, we focus on a new objective named total operational utility of all distributed equipment from the demand side, and integrate it into an energy-efficient production scheduling model based on the distributed parallel machine environment, in which the total energy consumption of manufacture side including processing energy consumption and transportation energy consumption is another objective. The orders are the spare parts used to replace the deteriorated components of distributed equipment based on forecasting information. Based on the scheduled delivery time fed back from the scheduling plan, the relationship among operating speed, deterioration rate and operating efficiency is used, and an optimal speed adjustment strategy is developed for each equipment to improve the operational utility. A memetic algorithm (NMA) based on the structure of NSGA-Ⅱ is presented for the model. A list scheduling heuristic and a problem-dependent heuristic are designed to generate initial population. Two problem-dependent local search operators are developed to enhance the searching ability. By performing extensive experiments and comparing NMA with some well-known algorithms, the effectiveness and superiority of NMA are demonstrated.

A joint optimization model for production scheduling and preventive maintenance interval

Machine maintenance is performed in production to prevent machine failure in order to maintain production efficiency and reduce failure costs. Due to the importance of maintenance in production, it is necessary to consider an integrated schedule for production and maintenance. Most of the literature on machine scheduling assumes that machines are always available. However, this assumption is unrealistic in many industrial applications. Preventive maintenance (PM) is often performed in a production system to prevent premature machine failure in order to maintain production efficiency. However, this assumption is inappropriate in real industrial cases. Machine maintenance plan is often performed in a production system to prevent premature machine failure in order to maintain production efficiency. Parallel machine layout is very common in modern production systems. Its performance sometime has a key impact on overall productivity. In this paper, a parallel machine scheduling problem with individual maintenance operations is considered. Then, a mathematical model is formulated including scheduling and maintenance operation optimization. The objective is to assign all jobs to machines so that the completion time and the average cost are minimized, jointly. Maintenance is considered in time intervals. To solve the proposed problem, a branch and bound (B&B) algorithm is adapted and proposed. The results show the applicability of the mathematical model in production systems and efficiency of the adapted B&B in comparison with Gams optimization software.

A Joint Optimization Model of Production Scheduling and Maintenance Based on Data Driven for a Parallel-Series Production Line

The maintenance of a production line is becoming more important with the development of demanding higher operational efficiency and safety in industrial system. However, a production line often operates under dynamically operational and environmental conditions and the production scheduling is also a very important factor for the maintenance of a production line. First, this paper proposes an integrated data-driven model that coordinates maintenance planning decisions with production scheduling decisions to solve the problem of scheduling and maintenance planning for a parallel-series production line. The degradation information is considered, and the total cost is to be minimized in the proposed model. Also, the total cost is related with production process and maintenance considering reliability of equipment. Then, in order to better describe the relationship between production and maintenance, the accumulative processing time of equipment is used as the input of its failure function. Also, an ability factor is developed to control its reduced level by adopting preventive maintenance. Finally, a case study is used to demonstrate the implementation and potential applications of the proposed model. The long-term wear test experiments are conducted at a research laboratory facility of Shanghai Pangyuan Machinery Co., Ltd. The result proves that the proposed method is feasible and efficient to solve the joint decision-making problem for a parallel-series production line with multivariety and small batch production. The proposed model in this paper is suitable for semiconductor manufacturing.

A Hyper Heuristic Algorithm Based Genetic Programming for Steel Production Scheduling of Cyber-Physical System-ORIENTED

Intelligent manufacturing is the trend of the steel industry. A cyber-physical system oriented steel production scheduling system framework is proposed. To make up for the difficulty of dynamic scheduling of steel production in a complex environment and provide an idea for developing steel production to intelligent manufacturing. The dynamic steel production scheduling model characteristics are studied, and an ontology-based steel cyber-physical system production scheduling knowledge model and its ontology attribute knowledge representation method are proposed. For the dynamic scheduling, the heuristic scheduling rules were established. With the method, a hyper-heuristic algorithm based on genetic programming is presented. The learning-based high-level selection strategy method was adopted to manage the low-level heuristic. An automatic scheduling rule generation framework based on genetic programming is designed to manage and generate excellent heuristic rules and solve scheduling problems based on different production disturbances. Finally, the performance of the algorithm is verified by a simulation case.

Application of CPLEX in beer production planning

In order to enhance the competitiveness of the industry, enterprises will continue to improve the production and operation management plan by means of reasonable allocation of internal and external resources, improving production technology, shortening the manufacturing cycle and reducing production costs. In this paper, a complex production planning problem of beer is introduced. Based on the production of beer enterprises, the production processes of beer are analyzed. The production scheduling model of beer enterprises is established, and the production plan is analyzed and solved by CPLEX solver.

Using a Genetic Algorithm, Integrated Preventive Maintenance Planning and Production Scheduling for a Single Machine

Although there is a relationship between preventive maintenance and production scheduling, almost all industrial units plan them separately; in other words, preventive maintenance is planned with the goal of maximizing machine availability, but the main goal is to maximize customer satisfaction by minimizing total weighted expected completion time. We propose realistic approaches for merging production scheduling and maintenance planning models in this research. Rafsanjan Arvand Wheel Co. was chosen to test this model. The results of model implementation on an industrial scale are depicted in detail. Apart from synchronizing production and maintenance operations, the data suggest that this strategy is highly effective. Calculations demonstrate a 42% improvement in overall weighted completion time of client orders, which has a significant impact on customer satisfaction.

Optimal production and maintenance scheduling for a degrading multi-failure modes single-machine production environment

Two important aspects of manufacturing systems are production scheduling and maintenance planning. These aspects are interdependent, but in most research work, this dependency is ignored. This paper proposed an integrated mathematical model for joint production scheduling and maintenance planning for a degrading multi-failure single-machine manufacturing system, in which the machine has discrete deterioration states. The machine is subject to different failure modes. The first failure mode is the machine’s full deterioration, which is detected at the end of a job’s processing, and the other failure mode is random breakdowns, which are detected at the time of failure. Two machine deterioration state-based thresholds are considered, and five different maintenance actions may carry out a replacement, preventive, and corrective perfect or imperfect maintenance. Since the machine’s states’ transitions follow an exponential distribution, a closed-form matrix-based mathematical model with probabilistic input parameters is presented. This paper aims to optimize the total system’s cost, including the maintenance cost, machine energy consumption cost as well as the makespan penalty for exceeding a pre-determined threshold. The proposed model determines the optimal jobs’ sequence as well as the machine’s deterioration state-based thresholds. Due to the complexity of the developed model, a genetic algorithm (GA), simulated annealing (SA) algorithm, and a teaching–learning-based optimization (TLBO) algorithm have been used to solve the presented model. The algorithms are validated using a full enumeration technique, and the model is validated by applying different maintenance strategies. Our results demonstrate the superiority of the GA compared to the other algorithms.

Applications of process and digital twin models for production simulation and scheduling in the manufacturing of food ingredients and products

Food Processing Industries are bound to increasingly adopt digital technologies in order to ensure product safety and quality, minimize costs in the face of low profit margins, shorten lead times and guarantee timely delivery of an increasing number of products despite production dead times and uncertainties. The concept of a digital twin put forward in the context of Industry 4.0 encompasses a digital model of the production model that mimics the physical system, interacts with it and can be used to design, monitor and optimize its performance. In this paper, the application of integrated process and digital twin models in food processing is discussed in the context of process simulation and production scheduling. The modeling challenges, opportunities and special characteristics that distinguish food from other process industries are also discussed. The potential benefits from implementing a digital modeling approach on a food process are presented with the help of a large-scale brewery case study.

Production Scheduling in a Flexible Hybrid Flow Shop in the Food Industry Based on the Theory of Constraints

This paper proposes a mathematical model for production scheduling, whose objective is to maximize the profits or Throughput of a company in the food sector through a Flexible Hybrid Flow, based on the theory of constraints. Considering the company's production configuration, which is a two-stage hybrid flow line, a mixed integer linear model programming (MILP) was formulated and programmed to adequately represent the real situation. The mathematical model developed in this study that is an easy and effective tool that helps to control the production process, by optimizing the quantities of each product to be produced, as well as establishing the sequence in which they must be carried out, which becomes an advantage against its competitors and also obtain a timely response to the needs of demand and compliance with the commitments made to its customers. The results obtained with the MILP, with reasonable computational times, allow for maximizing profits, considering the constraints of the problem.

Production Scheduling of Open Pit Mine Using Sequential Branch-and-Cut and Longest Path Algorithm: An Application from an African Copper Mine

Open pit mine production scheduling assigns mining blocks in different production periods for maximising profits after satisfying geotechnical and operational constraints. In this paper, two Open pit mine production scheduling models were applied in an African copper deposit. The first model is a traditional model with more tight resource constraints; the second model is a more robust model where resource constraints are relaxed by penalizing the objective function. Both the models were solved using two step algorithms: (a) year wise production scheduling using a sequential branch-and-cut algorithm; and (b) an iterative longest path algorithm to improve the solution generated from branch-and-cut. Results demonstrated that due to the tight constraints in Model 1, the optimizer was unable to generate a feasible solution after the first period, therefore the lower limit metal production constraint was eliminated to generate a feasible solution; however, Model 2 was able to generate a feasible solution for all periods. Results show that both the models generated nearly the same amount of ore, waste, metal content, and mine life. Model 2 generates relatively more net present value as compared to Model 1, whereas, the computational time required for solving the scheduling problem is relatively less for Model 1 than for Model 2.