Order Scheduling Problem Research Articles

New model to streamline customer order scheduling

The Customer Order Scheduling (COS) problem involves organizing a set of orders, each characterized by a release time, a due date, and a processing time, with the objective of minimizing the costs associated with delivery delays. This study introduces an innovative approach, the Streamline COS, which integrates order scheduling optimization with improved resource utilization and a reduction in production inefficiencies. We present a model aimed at minimizing an objective function that encompasses delay penalties and the optimization of resource usage. Additionally, we introduce an optimized COS algorithm, named SCOS (Streamline COS), designed to find the optimal solution. The efficacy of this approach is validated through experiments with several datasets of varying sizes and instances, demonstrating that the Streamline COS method significantly enhances resource management, reduces delays, and optimizes order scheduling, while offering flexible priority management. This approach provides a practical and effective solution to complex scheduling problems and opens new research avenues, particularly in integrating dynamic constraints and leveraging optimization and machine learning techniques for further performance improvements.

Minimizing total tardiness for the single-machine identical-jobs order scheduling problem with a learning effect

Minimizing total tardiness for the single-machine identical-jobs order scheduling problem with a learning effect

Bayesian analysis of multi-fidelity modeling in the stochastic simulations

Multi-fidelity surrogate modeling has received intensive attention owing to its strong applicability to engineering design problems. Generally, unknown parameters in a surrogate model are estimated using simulation data, introducing parameter estimation uncertainty into the model prediction. This uncertainty can be further aggravated by the presence of random noise in stochastic simulations. To tackle this issue, this paper develops a novel Bayesian meta-modeling method for multi-fidelity simulations in stochastic situations. Utilizing prior information about the parameters and Bayesian posterior inference, a new closed-form predictive distribution is derived within the autoregressive cokriging framework. This formula explicitly accounts for both parameter estimation uncertainty and measurement error in response without requiring time-consuming Markov chain Monte Carlo methods. Numerical experiments conducted on the classic Borehole function and a stochastic customer order scheduling problem illustrate the performance of the proposed method. Results demonstrate that the proposed method surpasses existing methods and maintains robust predictive performance under heterogeneous stochastic circumstances with varying noise levels.

Minimizing the earliness–tardiness for the customer order scheduling problem in a dedicated machine environment

The customer order scheduling problem has garnered considerable attention in the recent scheduling literature. It is assumed that each of several customer orders consists of several jobs, and each customer order is completed only if each job of the order is completed. In this paper, we consider the customer order scheduling problem in a machine environment where each customer places exactly one job on each machine. The objective is to minimize the earliness–tardiness, where tardiness is defined as the time an order is finished past its due date, and earliness is the time a job is finished before its due date or the completion time of the corresponding order, whichever is later. Even though the earliness–tardiness criterion is an important objective for just-in-time production, this problem has not been studied in the context of the customer order scheduling problem. We provide a mixed-integer linear programming (MILP) formulation for this problem and derive multiple problem properties. Furthermore, we develop six different heuristics for this problem configuration. They follow the structure of the iterated greedy algorithm and additionally use a refinement function in which they differ. In a computational experiment, the algorithms were compared with each other and outperformed a solver solution of the MILP, which proves their ability to efficiently solve the problem configuration.

A dynamic programming algorithm for order picking in robotic mobile fulfillment systems

AbstractThe order scheduling and rack sequencing problem deals with the order picking process in robotic mobile fulfillment systems: automated guided vehicles lift and transport movable storage racks to picking stations to supply items requested by customer orders which are put together in cardboard boxes on a workbench of limited capacity. To efficiently operate the station, the sequence in which racks visit the station one after another and the intervals at which customer orders are scheduled must be coordinated. We present a dynamic programming algorithm for the order scheduling and rack sequencing problem at a single picking station minimizing the number of rack visits. Despite monolithic mixed integer linear programming formulations, our approach appears to be the first combinatorial solution method for the problem in literature. A computational study demonstrates the effectiveness of the approach.

Formulations and heuristic for the long-term preventive maintenance order scheduling problem

This paper studies the long-term preventive maintenance order scheduling problem (LTPMOSP). The problem consists of deciding which maintenance should be scheduled, assigning each maintenance simultaneously to a team and a machine over the planning horizon, and determining when each maintenance should be performed. The goal of the problem is to minimize the number of teams activated and the sum of penalties for maintenance not scheduled. This paper presents two new formulations for the problem, where the first formulation is based on time-indexed variables, and the second formulation combines time-indexed variables with precedence variables. Furthermore, to solve large-size instances, an algorithm based on the GRASP metaheuristic is proposed. The results of the computational experiments show that the new formulations significantly outperform the literature formulation by finding new optimal solutions for some instances with up to 600 maintenance orders. The second formulation stands out by finding a more significant number of optimal solutions. The results also show a superiority of the GRASP algorithm over heuristic methods in the literature, generating better upper bounds in expressively less time, resulting in a schedule with a greater percentage of maintenance planned to be performed.

Comparison of MOEAs in an Optimization-Decision Methodology for a Joint Order Batching and Picking System

This paper investigates the performance of a two-stage multi-criteria decision-making procedure for order scheduling problems. These problems are represented by a novel nonlinear mixed integer program. Hybridizations of three Multi-Objective Evolutionary Algorithms (MOEAs) based on dominance relations are studied and compared to solve small, medium, and large instances of the joint order batching and picking problem in storage systems with multiple blocks of two and three dimensions. The performance of these methods is compared using a set of well-known metrics and running an extensive battery of simulations based on a methodology widely used in the literature. The main contributions of this paper are (1) the hybridization of MOEAs to deal efficiently with the combination of orders in one or several picking tours, scheduling them for each picker, and (2) a multi-criteria approach to scheduling multiple picking teams for each wave of orders. Based on the experimental results obtained, it can be stated that, in environments with a large number of different items and orders with high variability in volume, the proposed approach can significantly reduce operating costs while allowing the decision-maker to anticipate the positioning of orders in the dispatch area.

A novel implicit decision variable classification approach for high-dimensional robust multi-objective optimization in order scheduling

This paper efficiently addresses the high-dimensional robust order scheduling problem. A novel algorithm named dynamic cooperative coevolution based on an implicit decision variable classification approach (DCC/IDVCA) is developed to search for robust order schedules. To significantly reduce the computational resources required for solving the high-dimensional robust order scheduling problem, we propose decomposing the original decision variables through implicit classification methods. First, a novel estimation method is introduced to evaluate the weighted contribution of variables to robustness. This method utilizes historical information, including the variation of the overall mean effective fitness and the frequency of variables being classified into highly robustness-related subcomponents in previous cycles, for evaluating their weighted contribution to robustness. Then, based on the corresponding weighted robustness contributions, the original variables are classified into highly and weakly robustness-related variables. Finally, these two types of variables are decomposed into highly and weakly robustness-related subgroups within a dynamic cooperative coevolution framework and optimized separately. In the experimental section, the proposed algorithm is applied to two practical order scheduling problems in discrete manufacturing industry. The experimental results demonstrate that the proposed algorithm achieves competitive outcomes compared to state-of-the-art high-dimensional robust multi-objective optimization algorithms.

Bi-Objective Job-Shop Scheduling Considering Human Fatigue in Cobotic Order Picking Systems: A Case of an Online Grocer

Increasing online retail has resulted in increased automation in order picking systems, leading to new challenges and opportunities in task scheduling. The job-shop scheduling problem is an optimization problem essential in such systems, but existing JSP literature often overlooks workplace fatigue, which harms employees’ well-being and costs U.S. employers up to €127 billion annually. In this work, we propose fatigue consideration in the job-shop scheduling problem in a cobotic order picking system to mitigate its negative effects. We present a new bi-objective mixed integer nonlinear programming problem formulation that considers worker fatigue and productivity during schedule optimisation. To put the results of simulated optimisation in perspective, we experimentally validate the fatigue model and scheduling results in a real operation. The mathematical model finds solutions that conventional single-objective optimisation cannot, allowing fractional fatigue distribution improvements more than 4x larger than the decrease in productivity they require in 53% of the considered virtual cases. The experiments show that our predictive fatigue model has an average RMSE of 2.20 kcal/min in estimating energy expenditure rates compared to heart rate measurements. It also shows a low correlation, meaning it is unfit for application. On the other hand, fatigue-conscious schedules show no clear benefit regarding measured and perceived fatigue. However, the scheduling model could also use heart rate measurements that do not show these inaccuracies. Our study highlights the need to further develop and validate the mathematical formulation and fatigue model and extend to other human factors and indirect fatigue effects.

Multiobjective Differential Evolution Algorithm Balancing Multiple Stakeholders for Low-Carbon Order Scheduling in E-Waste Recycling

Order scheduling is an important part of the e-waste recycling process, which can influence the quantity and efficiency of the recycling. With the sustainable development of e-waste recycling, low-carbon order scheduling becomes a significant and challenging reverse logistics scheduling problem. However, it is difficult to obtain an effective low-carbon order schedule considering the conflicting interests of the multiple stakeholders, including enterprises, drivers, customers, and governments. To address this issue, a multi-objective order scheduling model (MOOSM) and a multi-objective differential evolution algorithm balancing multiple stakeholders (MODE-MS) are proposed in this paper. First, to embody the interests of different stakeholders, three time-dependent key variables are calculated by the road congestion and vehicle load, including the velocity, travelling time and carbon emission. Second, with the above key variables, a five-objective order scheduling model is formulated to describe the low-carbon order scheduling problem in e-waste recycling. Third, for solving the MOOSM, a multi-objective differential evolution algorithm based on an adaptive evolutionary search strategy is developed to obtain the low-carbon and stakeholders satisfied scheduling schemes. The experimental results validate the feasibility of MOOSM and the effectiveness of MODE-MS. By comparing with four state-to-art algorithms, the advantages of the proposed MODE-MS are further demonstrated in solving the low-carbon order scheduling.

Multi-Objective Order Scheduling via Reinforcement Learning

Order scheduling is of a great significance in the internet and communication industries. With the rapid development of the communication industry and the increasing variety of user demands, the number of work orders for communication operators has grown exponentially. Most of the research that tries to solve the order scheduling problem has focused on improving assignment rules based on real-time performance. However, these traditional methods face challenges such as poor real-time performance, high human resource consumption, and low efficiency. Therefore, it is crucial to solve multi-objective problems in order to obtain a robust order scheduling policy to meet the multiple requirements of order scheduling in real problems. The priority dispatching rule (PDR) is a heuristic method that is widely used in real-world scheduling systems In this paper, we propose an approach to automatically optimize the Priority Dispatching Rule (PDR) using a deep multiple-objective reinforcement learning agent and to optimize the weighted vector with a convex hull to obtain the most objective and efficient weights. The convex hull method is employed to calculate the maximal linearly scalarized value, enabling us to determine the optimal weight vector objectively and achieve a balanced optimization of each objective rather than relying on subjective weight settings based on personal experience. Experimental results on multiple datasets demonstrate that our proposed algorithm achieves competitive performance compared to existing state-of-the-art order scheduling algorithms.

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

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

Order acceptance and scheduling with delivery under generalized parameters

AbstractInspired by the concept of generalized due dates introduced by Hall (IIE Transactions, 18(2), 220–222), in this article we first define four new generalized parameters in machine scheduling: the generalized release dates (GRD), generalized processing times (GPT), generalized rejection costs (GRC), and generalized delivery times (GDT). We then study order acceptance and scheduling problems with delivery consideration under the generalized parameters of GRD, GPT, GRC, and GDT, respectively. The objective of each scheduling problem in consideration is to minimize the maximum delivery completion time of the accepted jobs plus the total rejection penalty cost of the rejected jobs. We show that two of the six problems studied in this article are weakly NP‐hard while the other four ones can be solved in polynomial time. For each NP‐hard problem, we provide a pseudo‐polynomial time algorithm, a 2‐approximation algorithm and a fully polynomial‐time approximation scheme.

An iterated local search for customer order scheduling in additive manufacturing

This paper studies the customer order scheduling problem in the context of additive manufacturing. The study discusses an integrated problem involving the nesting of parts as well as the scheduling of batches of nested parts onto unrelated parallel machines. A mixed-integer programming model is presented, based on existing formulations from the literature, that integrates different materials and sequence-dependent setup times. Additionally, a metaheuristic based on an iterated local search is proposed for the problem configuration under consideration. Focusing on minimizing the total weighted tardiness of orders, the efficiency of the heuristic approach is evaluated using comprehensive test data. Further, we show the importance of the considered order-related objective by using qualitative analysis.

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

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

A bi-level nested heuristic algorithm for divisional seru order acceptance and scheduling problems

This paper focuses on the order acceptance and scheduling problem with worker–operation assignment considering the precedence constraint in the divisional seru production system, which is a new production type derived from Japan and can achieve responsiveness, flexibility, and efficiency simultaneously. With limited production capacity and workers with different skill sets and skill levels, the problem considered in this paper includes three sub-problems: (i) assigning workers to each seru, (ii) making the order acceptance and scheduling plan, and (iii) allocating workers to operations for each order. Subsequently, a nonlinear integer programming model is established for improving the total net revenue, and a bi-level nested heuristic algorithm is designed due to its intractable computation. Computational experiments are made finally, and results show that the objective value obtained by the bi-level nested heuristic algorithm is 3% better than the bi-level genetic algorithm, and the running time is shortened by 99.23%. That is, the proposed bi-level nested heuristic algorithm can achieve better results and higher efficiency for divisional seru order acceptance and scheduling problems.

An Iterated Population-Based Metaheuristic for Order Acceptance and Scheduling in Unrelated Parallel Machines with Several Practical Constraints

This study considers order acceptance and scheduling problems in unrelated parallel machines with several practical constraints, including order release times, sequence-dependent setup times, machines’ unequal ready times, and preventive maintenance. In a make-to-order production environment, issues with order acceptance and scheduling are mainly caused by the limited production capacity of a factory, which makes it impossible to accept all orders. Consequently, some orders must be rejected in order to maximize profits and the accepted orders must be completed by the due date or no later than the deadline. An iterated population-based metaheuristic is proposed to solve the problems. The algorithm begins with an efficient initial solution generator to generate an initial solution, and then uses the destruction and construction procedure to generate a population with multiple solutions. Then, a solution is selected from the population, and a variable neighborhood descent search algorithm with several new reduced-size neighborhood structures is applied to improve the selected solution. Following the completion of the local search, a method for updating the members of the population was devised to enhance its diversity. Finally, the metaheuristic allows the populations to evolve for several generations until the termination condition is satisfied. To evaluate the performance of the proposed metaheuristic, a heuristic rule and an iterated local search algorithm are examined and compared. The computational experimental results indicate that the presented metaheuristic outperforms the other heuristics.

Integration of Discrete Simulation, Prediction, and Optimization Methods for a Production Line Digital Twin Design

The integration of discrete simulations, artificial intelligence methods, and the theory of probability in order to obtain a high flexibility of the production system is crucial. In this paper, the concept of a smart factory operation is proposed along with the idea of data exchange architecture, simulation creation, performance optimization, and predictive analysis of the production process conditions. A Digital Twin for a hybrid flow shop from the automotive industry is presented as a case study. In the paper, the Ant Colony Optimization (ACO) algorithm is developed for multi-criteria scheduling problems in order to obtain a production plan without delays and maximum resource utilization. The ACO is compared to the immune algorithm and genetic algorithm. The best schedules are achieved with low computation time for the Digital Twin. By predicting the reliability parameters of the limited resources of the Digital Twin, stable deadlines for the implementation of production tasks are achieved. Mean Time To Failure and Mean Time of Repair are predicted for a real case study of an electric steering gear production line. The presented integration and data exchange between the elements of the smart factory: a Digital Twin, a computing module including an optimization, prediction, and simulation methods fills the gap between theory and practice for Industry 4.0. The paper presents measurable benefits of integration of discrete simulation tools, historical data analysis, and optimization methods.

Service level and profit maximisation in order acceptance and scheduling problem with weighted tardiness

Traditional order acceptance and scheduling (OAS) problem focused on profit optimisation and the number of accepted orders has been only regarded as a constraint in the OAS model in a few research studies. The current paper investigates a bi-objective OAS problem to maximise profit and service level. There are two categories of regular and special orders in a single-machine environment. We have proposed a mixed integer linear program using goal programming. Due to the NP-hard nature of the problem, we have developed a simulated annealing-based heuristic to solve the problem, and a lower bound to assess its performance. Both single objective and bi-objective versions of the problem have been studied. Computational experiments demonstrate the ability of the proposed heuristic. The advantages and disadvantages of the proposed bi-objective OAS problem are discussed. Also, the relation between service level and profit objectives is studied in both problems with and without special orders.

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

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