Customer Order Scheduling Problem Research Articles

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.

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.

A novel BRKGA for the customer order scheduling with missing operations to minimize total tardiness

We introduce a new variant of the customer order scheduling problem with missing operations to minimize total tardiness. This problem arises in the pharmaceutical industry, more specifically in physical–chemical analysis processes. Since each sample must be processed in some specific machines, we have missing operations. Given the NP-hardness of the problem, we present approximate algorithms to solve large-sized instances. First, we propose an innovative size-reduction matheuristic for a scheduling problem with due dates. This approach is based on partitioning the decision variables considering due dates and a dispatch rule. Furthermore, we develop a novel Biased Random Key Genetic Algorithm (BRKGA) that considers an efficient local search as 2-opt best improvement with swap neighborhood and a parameter-free restart procedure which restarts the search if the quality of the worst and best solutions were equal, minimizing the amount of parameters to be defined by the BRKGA. We perform computational experiments on 640 test instances to evaluate the proposed solution approaches. The results indicate the superiority of BRKGA compared to the competitive algorithms for order scheduling and its recent variants. In all set of instances, the novel BRKGA performed better than benchmarking methods and mathematical programming models, with average relative deviation index regarding best results as lower as 0.15%. Computational results point to the capacity of the proposed approaches to solve large-sized problems. • We introduce the customer order scheduling with missing operations. • We propose mixed-integer linear programming and constraint programming models. • We propose a new matheuristic named size reduction with partitions (SR-Q). • We develop an innovative BRKGA with a robust improvement procedure and a parameter-free restart operator. • We perform extensive computational tests with 640 randomly generated test instances.

A Genetic Hyper-Heuristic for an Order Scheduling Problem with Two Scenario-Dependent Parameters in a Parallel-Machine Environment

Studies on the customer order scheduling problem have been attracting increasing attention. Most current approaches consider that either component processing times for customer orders on each machine are constant or all customer orders are available at the outset of production planning. However, these assumptions do not hold in real-world applications. Uncertainty may be caused by multiple issues including a machine breakdown, the working environment changing, and workers’ instability. On the basis of these factors, we introduced a parallel-machine customer order scheduling problem with two scenario-dependent component processing times, due dates, and ready times. The objective was to identify an appropriate and robust schedule for minimizing the maximum of the sum of weighted numbers of tardy orders among the considered scenarios. To solve this difficult problem, we derived a few dominant properties and a lower bound for determining an optimal solution. Subsequently, we considered three variants of Moore’s algorithm, a genetic algorithm, and a genetic-algorithm-based hyper-heuristic that incorporated the proposed seven low-level heuristics to solve this problem. Finally, the performances of all proposed algorithms were evaluated.

Robust Scheduling of Two-Agent Customer Orders with Scenario-Dependent Component Processing Times and Release Dates

Although some uncertainty factors can occur in many practical environments, customer order scheduling problems involving two agents in such uncertain environments have not received attention in the current literature. Motivated by this observation, we address a two-agent customer order scheduling problem where various customer orders have scenario-dependent component processing times and release dates in order to find an appropriate schedule to minimize the maximum of the total completion time of the customer orders that belong to one agent and are subject to a constraint with the other agent. In order to solve this problem, a lower bound and six dominant properties are derived and used to propose a branch-and-bound algorithm to find an exact optimal solution. Afterward, three local search heuristics and two variants of a simulated annealing hyper-heuristic are proposed and empirically evaluated in order to find approximate solutions. Finally, we conclude the paper with a summary of our findings and some directions for future research.

Iterated greedy algorithms for customer order scheduling with dedicated machines

The customer order scheduling problem has received much attention recently due to its relevance to real world applications. In this study, the minimization of the total completion time of customer orders is studied in a dedicated machine environment, i.e. each order consists of one job on each machine. Two iterated greedy algorithms are presented that make use of problem properties and apply a new local search as well as a new construction function. In a computational experiment, both algorithms outperform two state-of-the-art approaches and prove their suitability to solve the customer order scheduling problem with dedicated machines.

A size-reduction algorithm for the order scheduling problem with total tardiness minimization

We investigated a variant of the customer order scheduling problem taking into consideration due dates to minimize the total tardiness. Since the problem under study is NP-hard, we propose an efficient size reduction algorithm (SR). We perform an extensive computational experience and compare our proposition with JPO-20 matheuristic, the best existing algorithm for the problem under study. We use the Relative Deviation Index (RDI) and the Success Rate (SRa) as the statistical indicators for the performance measure. We must emphasize that SR presented the lowest average RDI (around 15.5 %), whereas the JPO-20 presented an average RDI approximately three times higher (around 52.5 %). Furthermore, the proposed SR presented a higher average SRa (around 66.9%), whereas the JPO-20 presented a lower average success (around 25.7%). Our proposal used a lower computational effort, resulting in a reduction for the computation times of approximately 22%. The obtained results point to the superiority of the proposed SR in comparison with the JPO-20.

A differential evolution algorithm for the customer order scheduling problem with sequence-dependent setup times

Although the customer order scheduling problem to minimize the total completion time has received a lot of attention from researchers, the literature has not considered so far the case where there are sequence-dependent setups between jobs belonging to different orders, a case that may occurs in real-life scenarios. For this NP-hard problem we develop a novel efficient approximate solution procedure. More specifically, we develop an innovative discrete differential evolution algorithm where differential mutations are performed directly in the permutation space and that uses a novel, parameter-free, restart procedure. The so-obtained solutions are improved by two proposed local search mechanisms that employ problem-specific, heuristic dominance relations. We carry out an extensive computational experience with randomly generated test instances to compare our proposal with existing algorithms from related problems. In these experiments, the proposed algorithm obtains the best results in terms of their average relative percentage deviation and success rate. Furthermore, an analysis of variance test, followed by a Tukey’s test, confirms the excellent performance of the algorithm proposed.

A learning-based two-stage optimization method for customer order scheduling

This paper addresses the customer order scheduling problem in parallel production environment commonly appearing in the pharmaceutical and paper industries. The problem aims to minimize the total completion time of the orders with their jobs processed on dedicated machines in parallel. To deal with the computational challenge of large-scale problems, we propose a learning-based two-stage optimization method consisting of a learned dispatching rule in the first stage and an adaptive local search in the second stage. The new dispatching rules are automatically generated by the proposed feature-enhanced genetic programming method in an off-line learning manner. Based on the high-quality initial solutions provided by the learned dispatching rule, we develop an adaptive local search to further improve the solution quality. Numerical results indicate the superiority of the learned dispatching rule and show the proposed two-stage optimization method significantly outperforms state-of-the-art methods in the literature.

Stochastic customer order scheduling on heterogeneous parallel machines with resource allocation consideration

This study considers a stochastic customer order scheduling and resource allocation problem in an unrelated parallel machine environment. Customer orders dynamically arrive at a machine station, and each consists of multiple product types with random workloads. Speeds of the machines are controllable through the allocation of limited resources such as overtime or dedicated manpower. The objective is to minimize the long run expected order cycle time by optimizing workload schedule and resource allocation. The impacts of workload variance, product similarity and machine speed are evaluated, and several optimal properties are explored. Three heuristic algorithms are proposed based on the theoretical results developed. The effectiveness of the proposed algorithms is demonstrated through extensive numerical experiments. This study brings new perspectives to resource allocation problems in stochastic environment, and provides insights into the relationship between resource allocation decisions and overall production efficiency.

Customer order scheduling with job-based processing on a single-machine to minimize the total completion time

This study considers a customer order scheduling (COS) problem in which each customer requests a variety of products (jobs) processed on a single flexible machine, such as the computer numerical control (CNC) machine. A sequence-independent setup for the machine is needed before processing each product. All products in a customer order are delivered to the customer when they are processed. The product ordered by a customer and completed as the last product in the order defines the customer order’s completion time. We aim to find the optimal schedule of the customer orders and the products to minimize the customer orders’ total completion time. We have studied this customer order scheduling problem with a job-based processing approach in which the same products from different customer orders form a product lot and are processed successively without being intermingled with other products. We have developed two mixed-integer linear programming models capable of solving the small and medium-sized problem instances optimally and a heuristic algorithm for large-sized problem instances. Our empirical study results show that our proposed tabu search algorithm provides optimal or near-optimal solutions in a very short time. We have also compared the job-based and order-based processing approaches for both setup and no-setup cases and observed that the job-based processing approach yields better results when jobs have setup times.

A robust customer order scheduling problem along with scenario-dependent component processing times and due dates

The customer’s order (CO) issues have received growing attention in the scheduling research community. In the CO design, a customer’s order consists of several components, and the processed orders are assigned to m parallel machines. The completion time of an order is assumed at the time at which all components in a customer’s order are finished. In the published articles, the processing times of all components were considered as fixed and known numbers in customer order scheduling problems. This assumption is indeed at odds in many real practical productions in which there exist a lot of relevant uncertainty factors; for example, machine may break down, the working situation may change, some operator’s performance may become instability, and so on. In such a situation, the processing times of given jobs are impropriate assumed as fixed and constant numbers. Thus, this article introduces a customer’s order scheduling problem on m parallel machines along with scenario-dependent processing times of all components and scenario-dependent due dates. Based on the worse case, the measurement rule is to find an appropriate policy to minimize the maximum total tardiness of given n customer’s orders across the possible scenarios among all possible schedules. In this study we derive several dominant rules and lower bounds used in a branch-and-bound method searching for exact solutions. Subsequently, we propose several heuristics and an iterated greedy algorithm with and without a population-based for finding approximate solutions. Finally, the computational results of all proposed algorithms are tested and reported.

Customer order scheduling problem to minimize makespan with sequence-dependent setup times

In this paper, we study a variant of the customer order scheduling problem when sequence-dependent setup times cannot be ignored. The performance measure adopted is the makespan minimization. The existence of sequence-dependent setup times makes this problem to be NP-hard. Furthermore, the solution encoding usually employed for other variants of the customer order scheduling problem does not guarantee finding optimal solutions. For this problem, we present some properties and develop two Mixed Integer Linear Programming (MILP) formulations to analyze the structure of the solutions. Using these properties and models, we propose two matheuristics based on fixing some integer decision variables in the MILP models, denoted as Fixed Variable List Algorithm (FVLA) and Clustering Sequence Algorithm (CSA), respectively. The computational experiments carried out prove the ability of these matheuristics to find high-quality solutions in reasonable CPU time. More specifically, the FVLA matheuristic stands out as the most efficient for the problem.

Spatial and temporal optimization for smart warehouses with fast turnover

With the rapid development of e-commerce and the new retail, the same-day or even same-half day delivery service is provided to compete for market share. Recently, an increased number of e-commerce companies implement the unmanned smart warehouses to improve the logistics efficiency. In order to further reduce the demand response time, a novel picking strategy is designed to firstly split the orders, and then assign the partial orders to different pickers. After all the order segments have been collected, it is shipped to the customer. Due to the inherent complexity of the problem, a two stage optimization model is introduced. In the first stage, an order splitting and batching strategy based on spatial measure is proposed. And a MIP model is constructed to minimize the total picking distance, which is then solved via a column generation based algorithm. In the second stage, the newly formed batches are considered as a priori inputs, which are then assigned to automatic pickers. The picking process is modeled as a special parallel machine scheduling problem with multiple due dates for a single item, which could reduce to a customer order scheduling problem on parallel machines, and it is unary NP-complete. A heuristic method is proposed to obtain an approximate solution. Although the order splitting technique is not new in the logistics industry, the split orders are picked according to a vehicle routing problem, which fails to address the kitting issue for fast turnovers. In the numerical analysis section, the proposed algorithm is validated through extensive testing on various scales of instances. It is observed that the optimality gap for our algorithm is within 9%, and the computation time is around 5 min. Also, the average turnover rate increases by approximately 50% in comparison with the no-splitting policy. In most cases, the average order tardiness decreases by 90% compared with order splitting and no-kitting policy.

The Pareto set reduction in bicriteria customer order scheduling on a single machine with setup times

A bicriteria customer order scheduling problem is investigated in the context of the axiomatic approach of the Pareto set reduction proposed by V. Noghin. We construct families of the instances with various structures of the Pareto set and theoretically analyze the Pareto set reduction.

Tailoring customer order scheduling search algorithms

Customer Order Scheduling Problem (COSP) with minimisation of the total completion time as the objective is NP-Hard. COSP has many applications that include the pharmaceutical and the paper industries. However, most existing COSP algorithms struggle to find very good solutions in large-sized problems. One key reason behind is that those algorithms are based on generic templates and as such lack problem specific structural knowledge. In this paper, we capture such knowledge in the form of heuristics and then embed those heuristics within constructive and perturbative search algorithms. In the proposed deterministic constructive search algorithm, we use processing times in various ways to obtain initial dispatching sequences that are later used in prioritising customer orders during search. We also augment the construction process with solution exploration. In the proposed stochastic perturbative search, we intensify its diversification phase by prioritising rescheduling of customer orders that are affected badly. Our tailoring of the search in this case is to make informed decisions when the search has lost its direction. On the contrary to that, in the intensification phase, we then take diversifying measures and use multiple neighbourhood operators randomly so that the search does not get stuck very quickly. Our experimental results show that the proposed algorithms outperform existing state-of-the-art COSP algorithms.

Using heuristic and iterative greedy algorithms for the total weighted completion time order scheduling with release times

Abstract The customer order scheduling problem is becoming a major topic in the research community, but the research regarding customer order scheduling problems with ready times remains relatively limited. This study examined an order scheduling problem with ready times where the measurement criterion was minimizing the total weighted completion time of all the given orders. To solve this intractable problem, we first derived several dominance rules and two lower bounds to use in a branch-and-bound method for finding an exact solution. We then modified five existing heuristics and adopted an iterative greedy (IG) algorithm to determine a near-optimal solution. Specifically, we used a fixed proportion of destruction and a linear function of destruction in the IG algorithm. Pairwise improvement was applied to all the proposed heuristics to achieve high-quality solutions, and we performed one-way analysis of variance and Fisher's least significant difference tests to evaluate and compare the performance of all the proposed algorithms.

Tardiness minimisation for a customer order scheduling problem with sum-of-processing-time-based learning effect

During solving scheduling problems in a manufacturing system, the processing time of a job is commonly assumed to be independent of its position in a scheduling sequence. However, this independence assumption may not adequately reflect many real manufacturing situations. In fact, the job processing time usually steadily decreases as the process proceeds when the same task is performed repeatedly and the efficiency is, therefore, gradually increased. Inspired by these observations, this study addressed a customer order scheduling problem with sum-of-processing-time-based learning effect on multiple machines. The objective was to search an optimal schedule to minimise total tardiness of the orders. A branch-and-bound algorithm incorporating several dominance rules and a lower bound was first proposed for searching the optimal schedule. Four heuristics and three metaheuristics were then developed for searching near-optimal schedules. Extensive computational experiments were finally tested to evaluate the performances of all the proposed algorithms.

An integrated weighted fuzzy multi-objective model for supplier selection and order scheduling in a supply chain

This paper presents a new weighted fuzzy multi-objective model to integrated supplier selection, order quantity allocation and customer order scheduling problem to prepare a responsive and order-oriented supply chain in a make-to-order manufacturing system. Total cost and quality of purchased parts as well as the reliability of on-time delivery of customer orders are regarded as the objectives of the model. On the other hand, flexible suppliers can contribute to the responsiveness and flexibility of entire supply chain in the face of uncertain customer orders. Therefore, a mathematical measure is developed for evaluating the volume flexibility of suppliers and is considered as the other objective of the model. Furthermore, by considering the effect of interdependencies between the selection criteria and to handle inconsistent and uncertain judgments, a fuzzy analytic network process method is used to identify top suppliers and consider as the last objective. In order to optimise these objectives, the decision-maker needs to decide from which supplier to purchase parts needed to assemble the customer orders, how to allocate the demand for parts between the selected suppliers, and how to schedule the customer orders for assembled products over the planning time horizon. Numerical examples are presented and computational analysis is reported.