Search results for: production scheduling optimization

Authors: Ali Mohammadi Bolban Abad, Fariborz Ahmadi

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Optimization in manufacture is a method to use limited resources to obtain the best performance and reduce waste. In this paper a new algorithm based on eurygaster life is introduced to obtain a plane in which task order and completion time of resources are defined. Evaluation results show our approach has less make span when the resources are allocated with some products in comparison to genetic algorithm.

Keywords: evolutionary computation, genetic algorithm, particle swarm optimization, NP-Hard problems, production scheduling

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Authors: Wenqian Shi, Xie He, Ziyin Huang, Zi Yu

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The dramatic changes in the global economic situation have produced dramatic changes to companies’ supply chain systems. A variety of opportunities and challenges make the traditional manufacturing industry feel pressured, and the manufacturing industry must seek a new way out as soon as possible. This paper presents a case study of the advanced planning and scheduling technology problem encountered by an electrical and electronics manufacturer. The objective is to seek the minimum cost of production planning and order management. Digitalization is applied to the problem, and the results demonstrate that significant production performances can be achieved in the face of the existing production of each link and order management systems to analyze and optimize. This paper can also provide some practical implications in various manufacturing industries. Finally, future research directions are discussed.

Keywords: advanced planning and scheduling, case study, production planning, supply chain optimization

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Authors: M. Ndeley

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The performance of global manufacturing supply chains depends on the interaction of production and transport processes. Currently, the scheduling of these processes is done separately without considering mutual requirements, which leads to no optimal solutions. An integrated scheduling of both processes enables the improvement of supply chain performance. The integrated production and transport scheduling problem (PTSP) is NP-hard, so that heuristic methods are necessary to efficiently solve large problem instances as in the case of global manufacturing supply chains. This paper presents a heuristic scheduling approach which handles the integration of flexible production processes with intermodal transport, incorporating flexible land transport. The method is based on a graph that allows a reformulation of the PTSP as a shortest path problem for each job, which can be solved in polynomial time. The proposed method is applied to a supply chain scenario with a manufacturing facility in South Africa and shipments of finished product to customers within the Country. The obtained results show that the approach is suitable for the scheduling of large-scale problems and can be flexibly adapted to different scenarios.

Keywords: production and transport scheduling problem, graph based scheduling, integrated scheduling

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Authors: Guilherme Gorgulho, Carlos Roberto Camello Lima

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Due to the competitive market in which companies are currently engaged, the constant changes require companies to react quickly regarding the variability of demand and process. The changes are caused by customers, or by demand fluctuations or variations of products, or the need to serve customers within agreed delivery taking into account the continuous search for quality and competitive prices in products. These changes end up influencing directly or indirectly the activities of the Planning and Production Control (PPC), which does business in strategic, tactical and operational levels of production systems. One area of concern for organizations is in the short term (operational level), because this planning stage any error or divergence will cause waste and impact on the delivery of products on time to customers. Thus, this study aims to optimize the efficiency of production scheduling, using different sequencing strategies in an automotive company. Seeking to aim the proposed objective, we used the computer simulation in conjunction with lean manufacturing to build and validate the current model, and subsequently the creation of future scenarios.

Keywords: computational simulation, lean manufacturing, production scheduling, sequencing strategies

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Authors: Guilherme Baldo Carlos

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The flexible job-shop scheduling problem (FJSP) is an NP-hard combinatorial optimization problem, which can be applied to model several applications in a wide array of industries. This problem will have its importance increase due to the shift in the production mode that modern society is going through. The demands are increasing and for products personalized and customized. This work aims to apply a meta-heuristic called a genetic algorithm (GA) to solve this problem. A GA is a meta-heuristic inspired by the natural selection of Charles Darwin; it produces a population of individuals (solutions) and selects, mutates, and mates the individuals through generations in order to find a good solution for the problem. The results found indicate that the GA is suitable for FJSP solving.

Keywords: genetic algorithm, evolutionary algorithm, scheduling, flexible job-shop scheduling

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Authors: Fahad Y. Al-dawish

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The current trend by a large number of organizations and individuals to use cloud computing. Many consider it a significant shift in the field of computing. Cloud computing are distributed and parallel systems consisting of a collection of interconnected physical and virtual machines. With increasing request and profit of cloud computing infrastructure, diverse computing processes can be executed on cloud environment. Many organizations and individuals around the world depend on the cloud computing environments infrastructure to carry their applications, platform, and infrastructure. One of the major and essential issues in this environment related to allocating incoming tasks to suitable virtual machine (cloud task scheduling). Cloud task scheduling is classified as optimization problem, and there are several meta-heuristic algorithms have been anticipated to solve and optimize this problem. Good task scheduler should execute its scheduling technique on altering environment and the types of incoming task set. In this research project a cloud task scheduling methodology based on ant colony optimization ACO algorithm, we call it ACO-TS Ant Colony Optimization for Task Scheduling has been proposed and compared with different scheduling algorithms (Random, First Come First Serve FCFS, and Fastest Processor to the Largest Task First FPLTF). Ant Colony Optimization (ACO) is random optimization search method that will be used for assigning incoming tasks to available virtual machines VMs. The main role of proposed algorithm is to minimizing the makespan of certain tasks set and maximizing resource utilization by balance the load among virtual machines. The proposed scheduling algorithm was evaluated by using Cloudsim toolkit framework. Finally after analyzing and evaluating the performance of experimental results we find that the proposed algorithm ACO-TS perform better than Random, FCFS, and FPLTF algorithms in each of the makespaan and resource utilization.

Keywords: cloud Task scheduling, ant colony optimization (ACO), cloudsim, cloud computing

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Authors: Yitao Lei, Xingxiang Zhai, Burra Venkata Durga Kumar

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As the quantity and complexity of computing in large-scale software systems increase, distributed system computing becomes increasingly important. The distributed system realizes high-performance computing by collaboration between different computing resources. If there are no efficient resource scheduling resources, the abuse of distributed computing may cause resource waste and high costs. However, resource scheduling is usually an NP-hard problem, so we cannot find a general solution. However, some optimization algorithms exist like genetic algorithm, ant colony optimization, etc. The large scale of distributed systems makes this traditional optimization algorithm challenging to work with. Heuristic and machine learning algorithms are usually applied in this situation to ease the computing load. As a result, we do a review of traditional resource scheduling optimization algorithms and try to introduce a deep reinforcement learning method that utilizes the perceptual ability of neural networks and the decision-making ability of reinforcement learning. Using the machine learning method, we try to find important factors that influence the performance of distributed system computing and help the distributed system do an efficient computing resource scheduling. This paper surveys the application of deep reinforcement learning on distributed system computing resource scheduling proposes a deep reinforcement learning method that uses a recurrent neural network to optimize the resource scheduling, and proposes the challenges and improvement directions for DRL-based resource scheduling algorithms.

Keywords: resource scheduling, deep reinforcement learning, distributed system, artificial intelligence

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Authors: Majid Khalili, Hamed Tayebi

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This paper considers a stochastic flexible job-shop scheduling (SFJSS) problem in the presence of production disruptions, and reactive scheduling is implemented in order to find the optimal solution under uncertainty. In this problem, there are two main disruptions including machine failure which influences operation time, and modification or cancellation of the order delivery date during production. In order to decrease the negative effects of these difficulties, two derived strategies from reactive scheduling are used; the first one is relevant to being able to allocate multiple machine to each job, and the other one is related to being able to select the best alternative process from other job while some disruptions would be created in the processes of a job. For this purpose, a Mixed Integer Linear Programming model is proposed.

Keywords: flexible job-shop scheduling, reactive scheduling, stochastic environment, mixed integer linear programming

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Authors: Carolina Silva, João Nuno Oliveira, Rui Sousa, João Paulo Silva

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This study uses genetic algorithms to solve a job scheduling problem in a weaving factory. The underline problem regards an NP-Hard problem concerning unrelated parallel machines, with sequence-dependent setup times. This research uses real data regarding a weaving industry located in the North of Portugal, with a capacity of 96 looms and a production, on average, of 440000 meters of fabric per month. Besides, this study includes a high level of complexity once most of the real production constraints are applied, and several real data instances are tested. Topics such as data analyses and algorithm performance are addressed and tested, to offer a solution that can generate reliable and due date results. All the approaches will be tested in the operational environment, and the KPIs monitored, to understand the solution's impact on the production, with a particular focus on the total number of weeks of late deliveries to clients. Thus, the main goal of this research is to develop a solution that allows for the production of automatically optimized production plans, aiming to the tardiness minimizing.

Keywords: genetic algorithms, textile industry, job scheduling, optimization

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Authors: C. E. Nugraheni, L. Abednego

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This paper is concerned with minimization of mean tardiness and flow time in a real single machine production scheduling problem. Two variants of genetic algorithm as meta-heuristic are combined with hyper-heuristic approach are proposed to solve this problem. These methods are used to solve instances generated with real world data from a company. Encouraging results are reported.

Keywords: hyper-heuristics, evolutionary algorithms, production scheduling, meta-heuristic

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Authors: Asma Rebaya, Imen Amari, Kaouther Gasmi, Salem Hasnaoui

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Over these last years, the number of cores witnessed a spectacular increase in digital signal and general use processors. Concurrently, significant researches are done to get benefit from the high degree of parallelism. Indeed, these researches are focused to provide an efficient scheduling from hardware/software systems to multicores architecture. The scheduling process consists on statically choose one core to execute one task and to specify an execution order for the application tasks. In this paper, we describe an efficient scheduler that calculates the optimal number of cores required to schedule an application, gives a heuristic scheduling solution and evaluates its cost. Our proposal results are evaluated and compared with Preesm scheduler results and we prove that ours allows better scheduling in terms of latency, computation time and number of cores.

Keywords: computation time, hardware/software system, latency, optimization, multi-cores platform, scheduling

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Authors: Su Xiaohan, Jin Chicheng, Liu Yijing, Burra Venkata Durga Kumar

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Energy-aware scheduling in real-time systems aims to minimize energy consumption, but issues related to resource reservation and timing constraints remain challenges. This study focuses on analyzing two scheduling algorithms, Fair-Share Scheduling (FFS) and Priority-Driven Preemptive Scheduling (PDPS), for solving these issues and energy-aware scheduling in real-time systems. Based on research on both algorithms and the processes of solving two problems, it can be found that Fair-Share Scheduling ensures fair allocation of resources but needs to improve with an imbalanced system load, and Priority-Driven Preemptive Scheduling prioritizes tasks based on criticality to meet timing constraints through preemption but relies heavily on task prioritization and may not be energy efficient. Therefore, improvements to both algorithms with energy-aware features will be proposed. Future work should focus on developing hybrid scheduling techniques that minimize energy consumption through intelligent task prioritization, resource allocation, and meeting time constraints.

Keywords: energy-aware scheduling, fair-share scheduling, priority-driven preemptive scheduling, real-time systems, optimization, resource reservation, timing constraints

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Authors: Jens Ehm

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Manufacturing in supply chains requires an efficient organisation of production and transport processes in order to guarantee the supply of all partners within the chain with the material that is needed for the reliable fulfilment of tasks. If one partner is not able to supply products for a certain period, these products might be missing as the working material for the customer to perform the next manufacturing step, potentially as supply for further manufacturing steps. This way, local disruptions can influence the whole supply chain. In order to avoid material shortages, an efficient scheduling of tasks is necessary. However, the occurrence of unexpected disruptions cannot be eliminated, so that a modification of the schedule should be arranged as fast as possible. This paper discusses the challenges for the implementation of real-time scheduling and control methods and presents a graph-based approach that enables the integrated scheduling of production and transport processes for multiple supply chain partners and offers the potential for quick adaptations to parts of the initial schedule.

Keywords: production, logistics, integrated scheduling, real-time scheduling

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Authors: Norhayati Mohd Rasip, Abd. Samad Hasan Basari , Nuzulha Khilwani Ibrahim, Burairah Hussin

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The allocation of working schedule especially for shift environment is hard to fulfill its fairness among them. In the case of nurse scheduling, to set up the working time table for them is time consuming and complicated, which consider many factors including rules, regulation and human factor. The scenario is more complicated since most nurses are women which have personnel constraints and maternity leave factors. The undesirable schedule can affect the nurse productivity, social life and the absenteeism can significantly as well affect patient's life. This paper aimed to enhance the scheduling process by utilizing the particle swarm optimization in order to solve nurse scheduling problem. The result shows that the generated multiple initial schedule is fulfilled the requirements and produces the lowest cost of constraint violation.

Keywords: nurse scheduling, particle swarm optimisation, nurse rostering, hard and soft constraint

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Authors: Christian Meinecke, Bernd Scholz-Reiter

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The integrated problem of production and distribution scheduling is relevant in many industrial applications. Thus, many heuristics to solve this integrated problem have been developed in the last decade. Most of these heuristics use a sequential working principal or a single decomposition and integration approach to separate and solve sub-problems. A heuristic using a multi-step decomposition and integration approach is presented in this paper and evaluated in a case study. The result show significant improved results compared with sequential scheduling heuristics.

Keywords: production and outbound distribution, integrated planning, heuristic, decomposition, integration

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Authors: Zouhair Issa Ahmed, Ahmed Abdulrasool Ahmed, Falah Hassan Abdulsada

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This paper presents a layout of a factory using Pro-Model simulation by choosing the best layout that gives the highest productivity and least work in process. The general problem is to find the best sequence in which jobs pass between the machines which are compatible with the technological constraints and optimal with respect to some performance criteria. The best simulation with Pro-Model program increased productivity and reduced work in process by balancing lines of production compared with the current layout of factory when productivity increased from 45 products to 180 products through 720 hours.

Keywords: scheduling, Pro-Model, simulation, balancing lines of production, layout planning, WIP

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Authors: Mohsen Ziaee

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Almost all existing researches on the flowshop scheduling problems focus on the permutation schedules and there is insufficient study dedicated to the general flowshop scheduling problems in the literature, since the modeling and solving of the general flowshop scheduling problems are more difficult than the permutation ones, especially for the large-size problem instances. This paper considers the general flowshop scheduling problem with the objective function of the makespan (F//Cmax). We first find the optimal solution of the problem by solving a mixed integer linear programming model. An efficient heuristic method is then presented to solve the problem. An ant colony optimization algorithm is also proposed for the problem. In order to evaluate the performance of the methods, computational experiments are designed and performed. Numerical results show that the heuristic algorithm can result in reasonable solutions with low computational effort and even achieve optimal solutions in some cases.

Keywords: scheduling, general flow shop scheduling problem, makespan, heuristic

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Authors: Arshad Mehmood Ch, Riaz Ahmad, Imran Ali Ch, Waqas Durrani

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This study deals with the application of Ant Colony Optimization (ACO) approach to solve no-wait flowshop scheduling problem (NW-FSSP). ACO algorithm so developed has been coded on Matlab computer application. The paper covers detailed steps to apply ACO and focuses on judging the strength of ACO in relation to other solution techniques previously applied to solve no-wait flowshop problem. The general purpose approach was able to find reasonably accurate solutions for almost all the problems under consideration and was able to handle a fairly large spectrum of problems with far reduced CPU effort. Careful scrutiny of the results reveals that the algorithm presented results better than other approaches like Genetic algorithm and Tabu Search heuristics etc; earlier applied to solve NW-FSSP data sets.

Keywords: no-wait, flowshop, scheduling, ant colony optimization (ACO), makespan

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Authors: Roshanak Khodabakhsh Jolfaei, Javad Akbari Torkestani

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As a cooperative environment for problem-solving, it is necessary that grids develop efficient job scheduling patterns with regard to their goals, domains and structure. Since the Grid environments facilitate distributed calculations, job scheduling appears in the form of a critical problem for the management of Grid sources that influences severely on the efficiency for the whole Grid environment. Due to the existence of some specifications such as sources dynamicity and conditions of the network in Grid, some algorithm should be presented to be adjustable and scalable with increasing the network growth. For this purpose, in this paper a job scheduling algorithm has been presented on the basis of learning automata in computational Grid which the performance of its results were compared with FPSO algorithm (Fuzzy Particle Swarm Optimization algorithm) and GJS algorithm (Grid Job Scheduling algorithm). The obtained numerical results indicated the superiority of suggested algorithm in comparison with FPSO and GJS. In addition, the obtained results classified FPSO and GJS in the second and third position respectively after the mentioned algorithm.

Keywords: computational grid, job scheduling, learning automata, dynamic scheduling

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Authors: Sanjay Kumar Parjapati, Ajai Jain

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This paper presents optimization of makespan for ‘n’ jobs and ‘m’ machines flexible job shop scheduling problem with sequence dependent setup time using genetic algorithm (GA) approach. A restart scheme has also been applied to prevent the premature convergence. Two case studies are taken into consideration. Results are obtained by considering crossover probability (pc = 0.85) and mutation probability (pm = 0.15). Five simulation runs for each case study are taken and minimum value among them is taken as optimal makespan. Results indicate that optimal makespan can be achieved with more than one sequence of jobs in a production order.

Keywords: flexible job shop, genetic algorithm, makespan, sequence dependent setup times

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Authors: Aydin Teymourifar, Gurkan Ozturk

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In this paper, a new hybrid particle swarm optimization algorithm is proposed for the multi-objective flexible job shop scheduling problem that is very important and hard combinatorial problem. The Pareto approach is used for solving the multi-objective problem. Several new local search heuristics are integrated into an algorithm based on the critical block concept to enhance the performance of the algorithm. The algorithm is compared with the recently published multi-objective algorithms based on benchmarks selected from the literature. Several metrics are used for quantifying performance and comparison of the achieved solutions. The algorithms are also compared based on the Weighting summation of objectives approach. The proposed algorithm can find the Pareto solutions more efficiently than the compared algorithms in less computational time.

Keywords: swarm-based optimization, local search, Pareto optimality, flexible job shop scheduling, multi-objective optimization

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Authors: R. Gupta, P. Jain, S. Das

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One way to approach construction scheduling optimization problem is to focus on the individual aspects of planning, which can be broadly classified as time scheduling, crew and resource management, and cost control. During the last four decades, construction planning has seen a lot of research, but to date, no paper had attempted to summarize the literature available under important heads. This paper addresses each of aspects separately, and presents the findings of an in-depth literature of the various planning techniques. For techniques dealing with time scheduling, the authors have adopted a rough chronological documentation. For crew and resource management, classification has been done on the basis of the different steps involved in the resource planning process. For cost control, techniques dealing with both estimation of costs and the subsequent optimization of costs have been dealt with separately.

Keywords: construction planning techniques, time scheduling, resource planning, cost control

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Authors: Sapan Tiwari, Namrata Ghosh

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In urban mass transit, crew scheduling always plays a significant role. It deals with the formulation of work timetables for its staff so that an organization can meet the demand for its products or services. The efficient schedules of a specified timetable have an enormous impact on staff demand. It implies that an urban mass transit company's financial outcomes are strongly associated with planning operations in the region. The research aims to demonstrate the state of the crew scheduling studies and its practical implementation in mass transit businesses in metropolitan areas. First, there is a short overview of past studies in the field. Subsequently, the restrictions and problems with crew scheduling and some models, which have been developed to solve the related issues with their mathematical formulation, are defined. The comments are completed by a description of the solution opportunities provided by computer-aided scheduling program systems for operational use and exposures from urban mass transit organizations. Furthermore, Bus scheduling is performed using the Hungarian technique of problem-solving tasks and mathematical modeling. Afterward, the crew scheduling problem, which consists of developing duties using predefined tasks with set start and end times and places, is resolved. Each duty has to comply with a set line of work. The objective is to minimize a mixture of fixed expenses (number of duties) and varying costs. After the optimization of cost, the outcome of the research is that the same frequency can be provided with fewer buses and less workforce.

Keywords: crew scheduling, duty, optimization of cost, urban mass transit

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Authors: Mohammadali Abedini Sanigy, Jiangang Fei

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In this paper, a mathematical optimization model was developed to maximize the profit in a vegetable production planning problem. It serves as a decision support system that assists farmers in land allocation to crops and harvest scheduling decisions. The developed model can handle different rotation rules in two consecutive cycles of production, which is a common practice in organic production system. Moreover, different production methods of the same crop were considered in the model formulation. The main strength of the model is that it is not restricted to predetermined production periods, which makes the planning more flexible. The model is classified as a mixed integer programming (MIP) model and formulated in PYOMO -a Python package to formulate optimization models- and solved via Gurobi and CPLEX optimizer packages. The model was tested with secondary data from 'Australian vegetable growing farms', and the results were obtained and discussed with the computational test runs. The results show that the model can successfully provide reliable solutions for real size problems.

Keywords: crop rotation, harvesting, mathematical model formulation, vegetable production

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Authors: John M. Ikome

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In the process of manufacturing, a machine breakdown usually forces a modified flow shop out of the prescribed state, this strategy reschedules part of the initial schedule to match up with the pre-schedule at some point with the objective to create a schedule that is reliable with the other production planning decisions like material flow, production and suppliers by utilizing a critical decision-making concept. We propose a rescheduling strategy and a match-up point that will have a determination procedure through an advanced feedback control mechanism to increase both the schedule quality and stability. These approaches are compared with alternative re-scheduling methods under different experimental settings.

Keywords: scheduling, heuristics, branch, integrated

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Authors: Hanife Merve Öztürk, Sıdıka Dalgan

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In this project, a capacity analysis study is done at TAT A. Ş. Maret Plant. Production capacity of products which generate 80% of sales amount are determined. Obtained data entered the LEKIN Scheduling Program and we get production schedules by using heuristic methods. Besides heuristic methods, as mathematical model, disjunctive programming formulation is adapted to flexible job shop problems by adding a new constraint to find optimal schedule solution.

Keywords: scheduling, flexible job shop problem, shifting bottleneck heuristic, mathematical modelling

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Authors: C. D. Papanikolaou, V. A. Giouvanis, E. A. Karatasiou, D. S. Dimakas, M. A. Sakellariou-Makrantonaki

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Irrigation is one of the most important cultivation practices for each crop, especially in areas where rainfall is enough to cover the crop water needs. In such areas, the farmers must irrigate in order to achieve high economical results. The precise irrigation scheduling contributes to irrigation water saving and thus a valuable natural resource is protected. Under this point of view, in the experimental field of the Laboratory of Agricultural Hydraulics of the University of Thessaly, a research was conducted during the growing season of 2012 in order to evaluate the growth, seed and oil production of sunflower as well as the water saving, by applying different methods of irrigation scheduling. Three treatments in four replications were organized. These were: a) surface drip irrigation where the irrigation scheduling based on the Penman-Monteith (PM) method (control); b) surface drip irrigation where the irrigation scheduling based on a soil moisture sensor (SMS); and c) surface drip irrigation, where the irrigation scheduling based on a soil potential sensor (WM).

Keywords: irrigation, energy production, soil moisture sensor, sunflower, water saving

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Authors: Aydin Teymourifar, Gurkan Ozturk

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In this paper, a new hybrid Hopfield neural network is proposed for the dynamic, flexible job shop scheduling problem. A new heuristic based and easy to implement energy function is designed for the Hopfield neural network, which penalizes the constraints violation and decreases makespan. Moreover, for enhancing the performance, several heuristics are integrated to it that achieve active, and non-delay schedules also, prevent early convergence of the neural network. The suggested algorithm that is designed as a generalization of the previous studies for the flexible and dynamic scheduling problems can be used for solving real scheduling problems. Comparison of the presented hybrid method results with the previous studies results proves its efficiency.

Keywords: dynamic flexible job shop scheduling, neural network, heuristics, constrained optimization

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Authors: Kwan Hee Han

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External environment of enterprise is rapidly changing majorly by global competition, cost reduction pressures, and new technology. In these situations, production scheduling function plays a critical role to meet customer requirements and to attain the goal of operational efficiency. It deals with short-term decision making in the production process of the whole supply chain. The major task of production scheduling is to seek a balance between customer orders and limited resources. In manufacturing companies, this task is so difficult because it should efficiently utilize resource capacity under the careful consideration of many interacting constraints. At present, many computerized software solutions have been utilized in many enterprises to generate a realistic production schedule to overcome the complexity of schedule generation. However, most production scheduling systems do not provide sufficient information about the validity of the generated schedule except limited statistics. Process mining only recently emerged as a sub-discipline of both data mining and business process management. Process mining techniques enable the useful analysis of a wide variety of processes such as process discovery, conformance checking, and bottleneck analysis. In this study, the performance of generated production schedule is evaluated by mining event log data of production scheduling software system by using the process mining techniques since every software system generates event logs for the further use such as security investigation, auditing and error bugging. An application of process mining approach is proposed for the validation of the goodness of production schedule generated by scheduling software systems in this study. By using process mining techniques, major evaluation criteria such as utilization of workstation, existence of bottleneck workstations, critical process route patterns, and work load balance of each machine over time are measured, and finally, the goodness of production schedule is evaluated. By using the proposed process mining approach for evaluating the performance of generated production schedule, the quality of production schedule of manufacturing enterprises can be improved.

Keywords: data mining, event log, process mining, production scheduling

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Authors: Kamyar Tolouei, Ehsan Moosavi

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In open-pit mines, the long-term production scheduling optimization problem (LTPSOP) is a complicated problem that contains constraints, large datasets, and uncertainties. Uncertainty in the output is caused by several geological, economic, or technical factors. Due to its dimensions and NP-hard nature, it is usually difficult to find an ideal solution to the LTPSOP. The optimal schedule generally restricts the ore, metal, and waste tonnages, average grades, and cash flows of each period. Past decades have witnessed important measurements of long-term production scheduling and optimal algorithms since researchers have become highly cognizant of the issue. In fact, it is not possible to consider LTPSOP as a well-solved problem. Traditional production scheduling methods in open-pit mines apply an estimated orebody model to produce optimal schedules. The smoothing result of some geostatistical estimation procedures causes most of the mine schedules and production predictions to be unrealistic and imperfect. With the expansion of simulation procedures, the risks from grade uncertainty in ore reserves can be evaluated and organized through a set of equally probable orebody realizations. In this paper, to synthesize grade uncertainty into the strategic mine schedule, a stochastic integer programming framework is presented to LTPSOP. The objective function of the model is to maximize the net present value and minimize the risk of deviation from the production targets considering grade uncertainty simultaneously while satisfying all technical constraints and operational requirements. Instead of applying one estimated orebody model as input to optimize the production schedule, a set of equally probable orebody realizations are applied to synthesize grade uncertainty in the strategic mine schedule and to produce a more profitable and risk-based production schedule. A mixture of metaheuristic procedures and mathematical methods paves the way to achieve an appropriate solution. This paper introduced a hybrid model between the augmented Lagrangian relaxation (ALR) method and the metaheuristic algorithm, the Harris Hawks optimization (HHO), to solve the LTPSOP under grade uncertainty conditions. In this study, the HHO is experienced to update Lagrange coefficients. Besides, a machine learning method called Random Forest is applied to estimate gold grade in a mineral deposit. The Monte Carlo method is used as the simulation method with 20 realizations. The results specify that the progressive versions have been considerably developed in comparison with the traditional methods. The outcomes were also compared with the ALR-genetic algorithm and ALR-sub-gradient. To indicate the applicability of the model, a case study on an open-pit gold mining operation is implemented. The framework displays the capability to minimize risk and improvement in the expected net present value and financial profitability for LTPSOP. The framework could control geological risk more effectively than the traditional procedure considering grade uncertainty in the hybrid model framework.

Keywords: grade uncertainty, metaheuristic algorithms, open-pit mine, production scheduling optimization

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