Convex resource allocation scheduling in the no-wait flowshop with common flow allowance and learning effect

ABSTRACTIn this article, the two-machine no-wait permutation flowshop scheduling problem with common due window assignment, learning effect and resource allocation is considered, wherein learning effect and resource allocation mean that the processing time of a job is a function of its position in a sequence and its amount of resource allocation. According to the common due window assignment method, each job is associated with a common due window, which is a decision variable. The goal is to determine the sequence of jobs, common due window starting time, due window size and resource allocation such that the linear weighted sum of job earliness, tardiness, due window size and resource cost is minimized. This article shows that the scheduling problem can be solved in polynomial time.

This paper studies a multiple common due date assignment problem on a single machine. The job-dependent due dates are obtained based on common flow allowance criteria. We assume that the processing time of a job is controllable by the resource amount assigned to it. The objective is to find the optimal multiple common dues, the set of jobs assigned to each due date, the sequence of jobs and resource allocation scheme to minimize a total cost based on earliness and tardiness of jobs, the common dues and resource cost. We propose an optimal algorithm to solve the problem.

This paper studies a due-window assignment problem on a single machine. The job-dependent due-windows are obtained by the common flow allowance criterion. We assume that the processing time of a job is a linear function of its starting time and decreasing function of the resource amount assigned to it. The objective is to find the optimal size and location of the due-windows, the sequence of jobs and resource allocation scheme to minimize a cost function based on the window size and location, the earliness and tardiness of jobs and resource cost. We propose an algorithm to solve the problem.

In this paper, the no-wait flow shop scheduling problem under makespan and flowtime criteria is addressed. The no-wait flowshop is a variant of the well-known flowshop scheduling problem where all processes follow the previous one without any interruption for operations of a job. Owing to the problem is known to be NP-hard for more than two machines, a hybrid meta-heuristic algorithm based on ant colony optimization (ACO) and simulated annealing (SA) algorithm is improved. First, at each step, due to the characteristic of ACO algorithm that include solution construction and pheromone trail updating, some different areas of search space are checked and best solution is selected. Then, to enhance the quality and diversity of the solution and finding best neighbor of this solution, a novel SA is presented. Moreover, a new principle is applied for global pheromone update based on the probability function like SA algorithm. The proposed approach solution is compared with several the state-of-the-art algorithms in the literature. The reported results show that the proposed algorithms are effective and the new approach for local search in ACO algorithm is efficient for solving the no-wait flow shop problem. Then, we employed another hybrid ACO algorithm based on hybridization of ACO with variable neighborhood search (VNS) and compare the results given by two proposed algorithms. These results show that our new hybrid provides better results than ACO-VNS algorithm.

Single-machine due-window assignment scheduling with delivery times and variable processing times is investigated, where the variable processing time of a job means that the processing time is a function of its position in a sequence and its resource allocation. Currently, there are multiple optimization objectives for the due-window assignment problem, and there is a small amount of research on optimization problems where the window starting time, the rejected cost and the optimal scheduling are jointly required. The goal of this paper is to minimize the weighed sum of scheduling cost, resource consumption cost and outsourcing measure under the optional job outsourcing (rejection). Under two resource allocation models (i.e., linear and convex resource allocation models), the scheduling cost is the weighted sum of the number of early–tardy jobs, earliness–tardiness penalties and due-window starting time and size, where the weights are positional-dependent. The main contributions of this paper include the study and data simulation of single-machine scheduling with learning effects, delivery times and outsourcing cost. For the weighed sum of scheduling cost, resource consumption cost and outsourcing measure, we prove the polynomial solvability of the problem. Under the common and slack due-window assignments, through the theoretical analysis of the optimal solution, we reveal that four problems can be solved in O(n6) time, where n is the number of jobs.

Scheduling with learning effects has received growing attention nowadays. A well-known learning model is called ‘position-based learning’ in which the actual processing time of a job is a non-increasing function of its position to be processed. However, the actual processing time of a given job drops to zero precipitously as the number of jobs increases. Motivated by this observation, we propose two truncated learning models in single-machine scheduling problems and two-machine flowshop scheduling problems with ordered job processing times, respectively, where the actual processing time of a job is a function of its position and a control parameter. Under the proposed learning models, we show that some scheduling problems can be solved in polynomial time. In addition, we further analyse the worst-case error bounds for the problems to minimize the total weighted completion time, discounted total weighted completion time and maximum lateness.

In industries machine maintenance is used in order to avoid untimely machine fails as well as to improve production effectiveness. This research regards a permutation flow shop scheduling problem with aging and learning effects considering maintenance process. In this study, it is assumed that each machine may be subject to at most one maintenance activity during the planning horizon. The objectives aim to minimize the makespan, tardiness of jobs, tardiness cost while maximizing net present value, simultaneously. Due to complexity and Np-hardness of the problem, two Pareto-based multi-objective evolutionary algorithms including non-dominated ranked genetic algorithm (NRGA) and non-dominated sorting genetic algorithm (NSGA-II) are proposed to attain Pareto solutions. In order to demonstrate applicability of the proposed methodology, a real-world application in polymer manufacturing industry is considered.

This paper addresses multi-degree cyclic scheduling of two robots in a no-wait flowshop, where exactly r(r > 1) identical parts with constant processing times enter and leave the production line during each cycle, and transportation of the parts between machines is performed by two robots on parallel tracks. The objective is to minimize the cycle time. The problem is transformed into enumeration of pairs of overlapping moves that cannot be performed by the same robot. This enumeration is accomplished by enumerating intervals for some linear functions of decision variables. The algorithm developed is polynomial in the number of machines for a fixed r, but exponential if r is arbitrary. Computational results with benchmark instances are reported. Note to Practitioners-This paper was motivated by the problem of cyclic scheduling of a no-wait production line, where a part must be processed without any interruption either on or between machines due to characteristics of the processing technology itself or the absences of storage capacity between operations of a part. Multi-degree schedules, in which multiple parts enter and leave the line during a cycle, usually have larger throughput rate than simple ones. This paper proposes an algorithm for multi-degree cyclic scheduling of a no-wait flowshop with two robots. Computational results show that the throughput rate can be really improved by using multi-degree schedules with two robots. However, we have not addressed the decision of the optimal value of the degree of the cycle. Furthermore, since we consider that the two robots travel along parallel tracks, the collision-avoidance constraints have been relaxed in the algorithm. In future research, we will address the two problems and generalize the algorithm to multi-robot cases.

This study considers a new flow shop scheduling problem with synchronous material movement. Specifically, we consider an automated machining centre that consists of a loading/unloading station, two CNC machining stations, and a material handling device. The material handling device is a rotary table that moves jobs between stations simultaneously. Given a set of jobs that need to be processed in the machining centre, the objective of the problem is to find the sequence that minimises the makespan. This problem can be shown to be NP-hard in the strong sense. A dynamic programming algorithm is proposed to obtain an optimal sequence for small- and medium- size problems. For large-scale problems, two heuristic algorithms are developed to obtain a near-optimal solution in a short time. Computational results for the proposed algorithms are provided.

This paper presents a predictive robust and stable approach for a two-machine flow shop scheduling problem with machine disruption and uncertain job processing time. Indeed, a general approach is proposed that can be used for robustness and stability optimization in an m-machine flow shop or job shop scheduling problem. The robustness measure is the total expected realized completion time. The expected sum of squared aberration between each jobs’ completion time in the realized and initial schedules is the stability measure. We proposed and compared two methods to deal with such an NP-hard problem; a method based on decomposing the problem into sub-problem and solving each sub-problem, and a theorem-based method. The extensive computational results indicated that the second method has a better performance in terms of robustness and stability, especially in large-sized problems. In other words, the second method is preferable because of the better manufacturer responsiveness to the customer and the production staff satisfaction enhancement.

In this paper we consider the flow shop scheduling problems with the effects of learning and deterioration. In this model the processing times of a job is defined as a function of its starting time and position in a sequence. The scheduling objective functions are makespan and total completion time. We prove that even with the introduction of learning effect and deteriorating jobs to job processing times, some special flow shop scheduling problems remain polynomially solvable.

Teaching resources in higher education are an important part of the talent cultivation system of higher education institutions. Dynamic management and optimal allocation of teaching resources are the focus of the construction of each school, which reflects the teaching, research, and management level of the school to a certain extent. In this paper, after combining the current situation and management problems of teaching resources in six schools in City A and putting forward constructive opinions, we further use data envelopment analysis to study the efficiency of teaching resource allocation in School H in City A and put forward the method of resource optimization.The input redundancy rate of School X1 in School H during the three years of 2021-2023 is 30.25%, 44.15%, and 55.26%, respectively. The data shows that the school has an excess of teacher inputs and there is a shortage of resources for teachers. For the current dynamic management and resource allocation problems of teaching resources in A city school, this paper argues that the management of school teaching resources is a long-term and complex organic whole, and needs to be reformed in terms of structure, resource integration and management, and to construct a high-quality and efficient management model. In terms of resource optimization and allocation, schools can optimize the talent resource allocation mechanism and other aspects to promote the full allocation of teaching resources in higher education.

We introduce a two-machine flow shop scheduling problem under linear constraints (2-FLC problem in short), in which the processing times of two stages of jobs are also decision variables and satisfy a system of linear constraints. The goal is to determine the processing times of each job, and to schedule the jobs to the two-machine flow shop such that the makespan, i.e., the completion time of all the jobs is minimized. This problem can find applications in various areas, such as industrial production and advertising planning. We study the computational complexity and algorithms for the 2-FLC problem. Particularly, we show that although the two-machine flow shop scheduling problem can be solved in polynomial time, the 2-FLC problem is generally NP-hard in the strong sense. Then we consider the design and analysis of algorithms on various settings of the 2-FLC problem. In particular, we propose a polynomial time algorithm for the 2-FLC problem when there is a fixed number of constraints. For the general case, we first propose a simple 2-approximation algorithm, and then design a polynomial time approximation scheme (PTAS).

This article considered the single machine scheduling with controllable processing time (resource allocation) and deterioration effect concurrently. It discussed the minimization of three objectives, which involve the weighted sum of the makespan and the total resource consumption cost, the total resource consumption cost under the condition that the makespan (total flow time) is restricted to a fixed constant and the optimal resource allocation and the optimal job sequence is what we need to make decision. Considering the makespan constraint, it proved that these problems can be solved in polynomial time. A special case of the last problem can be solved in polynomial time with respect to the total flow time constraint.

Scheduling of a Two-machine Flowshop with Travel Time Between Machines