A genetic algorithm for robotic assembly line balancing

Flexibility and automation in assembly lines can be achieved by the use of robots. The robotic assembly line balancing (RALB) problem is defined for robotic assembly line, where different robots may be assigned to the assembly tasks, and each robot needs different assembly times to perform a given task, because of its capabilities and specialization. The solution to the RALB problem includes an attempt for optimal assignment of robots to line stations and a balanced distribution of work between different stations. It aims at maximizing the production rate of the line. A genetic algorithm (GA) is used to find a solution to this problem. Two different procedures for adapting the GA to the RALB problem, by assigning robots with different capabilities to workstations are introduced: a recursive assignment procedure and a consecutive assignment procedure. The results of the GA are improved by a local optimization (hill climbing) work-piece exchange procedure. Tests conducted on a set of randomly generated problems, show that the Consecutive Assignment procedure achieves, in general, better solution quality (measured by average cycle time). Further tests are conducted to determine the best combination of parameters for the GA procedure. Comparison of the GA algorithm results with a truncated Branch and Bound algorithm for the RALB problem, demonstrates that the GA gives consistently better results.     

Multi-degree cyclic scheduling of a no-wait robotic cell with multiple robots

This paper addresses cyclic scheduling of a no-wait robotic cell with multiple robots. In contrast to many previous studies, we consider r-degree cyclic (r > 1) schedules, in which r identical parts with constant processing times enter and leave the cell in each cycle. We propose an algorithm to find the minimal number of robots for all feasible r-degree cycle times for a given r (r > 1). Consequently, the optimal r-degree cycle time for any given number of robots for this given r can be obtained with the algorithm. To develop the algorithm, we first show that if the entering times of r parts, relative to the start of a cycle, and the cycle time are fixed, minimizing the number of robots for the corresponding r-degree schedule can be transformed into an assignment problem. We then demonstrate that the cost matrix for the assignment problem changes only at some special values of the cycle time and the part entering times, and identify all special values for them. We solve our problem by enumerating all possible cost matrices for the assignment problem, which is subsequently accomplished by enumerating intervals for the cycle time and linear functions of the part entering times due to the identification of the special values. The algorithm developed is shown to be polynomial in the number of machines for a fixed r, but exponential if r is arbitrary.     

无重叠区的双抓钩周期性排序问题的求解

在当今的自动化制造系统中，计算机控制的抓钩的排序直接影响系统的生产率。本文研究了产品在系统的一边装载、而在另一边卸载的电镀线周期性排序问题。工件在每个工作站的处理时间在给定时间范围内，工作站之间没有缓冲槽，相同轨道上的两个抓钩用于工作站之间工件的运送，目标是对运送进行排序以极小化生产周期。为了求解这个问题，本文提出一个求解方法，所提出的方法首先将生产线分为两个无重叠的区域，并且为每个区域分配一个抓钩，然后，提出了一个给定抓钩分配下的混合整数线性规划模型。通过求解不同抓钩分配下模型的最优解，并且选择这些解中最好的一个，以便得到最优解，一个标杆示例被运行，以表明该方法的应用。另外，给出有多重处理槽工序问题的模型和求解方法。     

Parallel Integer Optimization for Crew Scheduling

Performance aspects of a Lagrangian relaxation based heuristic for solving large 0-1 integer linear programs are discussed. In particular, we look at its application to airline and railway crew scheduling problems. We present a scalable parallelization of the original algorithm used in production at Carmen Systems AB, Göteborg, Sweden, based on distributing the variables. A lazy variant of this approach which decouples communication and computation is even useful on networks of workstations. Furthermore, we develop a new sequential active set strategy which requires less work and is better adapted to the memory hierarchy properties of modern RISC processors. This algorithm is also suited for parallelization on a moderate number of networked workstations.     

Resource level minimization in the discrete–continuous scheduling

A discrete–continuous problem of non-preemptive task scheduling on identical parallel processors is considered. Tasks are described by means of a dynamic model, in which the speed of the task performance depends on the amount of a single continuously divisible renewable resource allotted to this task over time. An upper bound on the completion time of all the tasks is given. The criterion is to minimize the maximum resource consumption at each time instant, i.e., the resource level. This problem has been observed in many industrial applications, where a continuously divisible resource such as gas, fuel, electric, hydraulic or pneumatic power, etc., has to be distributed among the processing units over time, and it affects their productivity. The problem consists of two interrelated subproblems: task sequencing on processors (discrete subproblem) and resource allocation among the tasks (continuous subproblem). An optimal resource allocation algorithm for a given sequence of tasks is presented and computationally tested. Furthermore, approximation algorithms are proposed, and their theoretical and experimental worst-case performances are analyzed. Computer experiments confirmed the efficiency of all the algorithms.     

Operations planning for a multi-stage kanban system

A multi-stage production line which operates under a just-in-time production philosophy with linear demand is considered here. The first workstation processes the raw materials after receiving them from suppliers, a kanban mechanism between the workstations transports the work-in-process to the succeeding workstation, and after processing them, delivers the finished products to a buyer or a warehouse. The problem is to find optimally the number of raw material orders, kanbans circulated between workstations, finished goods shipments to the buyers, and the batch size for each shipment (lot). A cost function is developed based on the costs incurred due to the raw materials, the work-in-process between workstations, and the finished goods. Optimal number of raw material orders that minimizes the total cost is obtained, which is then used to find the optimal number of kanbans, finished goods shipments, and the batch sizes for shipments. Numerical examples are used to demonstrate the computations of optimal parameters, and to configure the kanban mechanism on a timescale. Several avenues for future research are also indicated.     

A special case of transfer lines balancing by graph approach

A balancing problem for paced production lines with workstations in series and blocks of parallel operations at the workstations is considered. Operations of each workstation are partitioned into blocks. All operations of the same block are performed simultaneously by one spindle head. All blocks of the same workstation are also executed simultaneously. The relations of the necessity of executing some operations at the same workstation, the possibility of combining the blocks at the same workstation as well as precedence constraints are given. The operation time of the workstation is the maximal value among operation times of its blocks. The line cycle time is the maximal workstation time. The problem is to choose blocks from a given set and allocate them to workstations in such a way that (i) all the operations are assigned, (ii) the above constraints are satisfied, (iii) a given cycle time is not exceeded, and (iv) the line cost is minimal. A method for solving the problem is based on its transformation to a constrained shortest path problem.     

Increasing flexibility and productivity in Industry 4.0 production networks with autonomous mobile robots and smart intralogistics

Manufacturing flexibility improves a firm’s ability to react in timely manner to customer demands and to increase production system productivity without incurring excessive costs and expending an excessive amount of resources. The emerging technologies in the Industry 4.0 era, such as cloud operations or industrial Artificial Intelligence, allow for new flexible production systems. We develop and test an analytical model for a throughput analysis and use it to reveal the conditions under which the autonomous mobile robots (AMR)-based flexible production networks are more advantageous as compared to the traditional production lines. Using a circular loop among workstations and inter-operational buffers, our model allows congestion to be avoided by utilizing multiple crosses and analyzing both the flow and the load/unload phases. The sensitivity analysis shows that the cost of the AMRs and the number of shifts are the key factors in improving flexibility and productivity. The outcomes of this research promote a deeper understanding of the role of AMRs in Industry 4.0-based production networks and can be utilized by production planners to determine optimal configurations and the associated performance impact of the AMR-based production networks in as compared to the traditionally balanced lines. This study supports the decision-makers in how the AMR in production systems in process industry can improve manufacturing performance in terms of productivity, flexibility, and costs. 

     

A Genetic Algorithm for the Allocation of Buffer Storage Capacities in a Production Line with Unreliable Machines

In this paper, we consider a flow-line manufacturing system organized as a series of workstations separated by finite buffers. The failure and repair times of machines are supposed to be exponentially distributed. The production rate of each machine is deterministic, and different machines may have different production rates. The buffer allocation problem consists in determining the buffer capacities with respect to a given optimality criterion, which depends on the average production rate of the line, the buffer acquisition and installation cost, and the inventory cost. For this problem we propose a genetic algorithm where the tentative solutions are evaluated with an approximate method based on the Markov-model aggregation approach.     

A faster algorithm for 2-cyclic robotic scheduling with a fixed robot route and interval processing times

Consider an m-machine production line for processing identical parts served by a mobile robot. The problem is to find the minimum cycle time for 2-cyclic schedules, in which exactly two parts enter and two parts leave the production line during each cycle. This work treats a special case of the 2-cyclic robot scheduling problem when the robot route is given and the operation durations are to be chosen from prescribed intervals. The problem was previously proved to be polynomially solvable in O(m⁸log m) time. This paper proposes an improved algorithm with reduced complexity O(m⁴).     

A polynomial algorithm for 2-cyclic robotic scheduling: A non-Euclidean case

In this paper we consider the problem of no-wait cyclic scheduling of identical parts in an m-machine production line in which a robot is responsible for moving each part from a machine to another. The aim is to find the minimum cycle time for the so-called 2-cyclic schedules, in which exactly two parts enter and two parts leave the production line during each cycle. The earlier known polynomial-time algorithms for this problem are applicable only under the additional assumption that the robot travel times satisfy the triangle inequalities. We lift this assumption on robot travel times and present a polynomial-time algorithm with the same time complexity as in the metric case, O(m⁵logm).     

Tabu search algorithms for an industrial multi-product and multi-objective assembly line balancing problem,with reduction of the task dispersion

This paper presents a real-world industrial application of the multi-product and multi-objective assembly line balancing problem, for a company involved in the production of four models of a white goods product. The problem solved is a GALBP-2, with 10 workstations and multiple objectives (to maximize the production rate in order to deal with an increase of the demand forecasted, to reach an equal cycle time of all the models and an equal workload of the different workstations, and finally, to minimize the dispersion of worker tasks on each one of the different models—the common tasks of the different models at the same workstation). The paper presents an integrated approach based on four heuristics cited in the literature and: (1) an improvement procedure based on tabu search, with the objective of minimizing the cycle time; and, subsequently, (2) a second tabu search in order to increase the uniformity of the tasks performed at each workstation (the common tasks at the same workstation).     

Review and comparison of three methods for the solution of the car sequencing problem

The car sequencing problem is the ordering of the production of a list of vehicles which are of the same type, but which may have options or variations that require higher work content and longer operation times for at least one assembly workstation. A feasible production sequence is one that does not schedule vehicles with options in such a way that one or more workstations are overloaded. In variations of the problem, other constraints may apply. We describe and compare three approaches to the modeling and solution of this problem. The first uses integer programming to model and solve the problem. The second approaches the question as a constraint satisfaction problem (CSP). The third method proposes an adaptation of the Ant Colony Optimization for the car sequencing problem. Test-problems are drawn from CSPLib, a publicly available set of problems available through the Internet. We quote results drawn both from our own work and from other research. The literature review is not intended to be exhaustive but we have sought to include representative examples and the more recent work. Our conclusions bear on likely research avenues for the solution of problems of practical size and complexity. A new set of larger benchmark problems was generated and solved. These problems are available to other researchers who may wish to solve them using their own methods.     

Tabu search for discrete–continuous scheduling problems with heuristic continuous resource allocation

Problems of scheduling non-preemptable, independent jobs on parallel identical machines under an additional continuous renewable resource to minimize the makespan are considered. Each job simultaneously requires for its processing a machine and an amount (unknown in advance) of the continuous resource. The processing rate of a job depends on the amount of the resource allotted to this job at a time. The problem is to find a sequence of jobs on machines and, simultaneously, a continuous resource allocation that minimize the makespan. A heuristic procedure for allocating the continuous resource is used. The tabu search metaheuristic to solve the considered problem is presented. The results produced by tabu search are compared with optimal solutions for small instances, as well as with the results generated by simple search methods – multi-start iterative improvement and random sampling for larger instances.     

An extension of the extended basic period approach for economic lot scheduling problems

This paper addresses the problem of choosing cyclical production patterns for several products which are produced on a common production facility. The extended basic period approach of Elmaghraby is extended by allowing more than two basic periods. The problem of dimensionality of the dynamic programming formulation is dealt with by aggregating the capacity data in different basic periods.The author is indebted to Dr. S. E. Elmaghraby for inspiring him to work on the economic lot scheduling problem and for many valuable suggestions. The author is also grateful to Mr. Z. Naman for carrying out the computer programming.     

Modelling transfer line design problem via a set partitioning problem

The design of a transfer line is considered. This line is used for a repetitive execution of a given set of operations to produce identical items. The line is composed of a sequence of workstations equipped with processing modules (blocks). Each block performs specific operations. The machined items move along the workstations in the same direction. There is the same cost associated with each workstation and different costs associated with diverse blocks. The problem is to determine the number of workstations, select a set of blocks and assign the selected blocks to the workstations so that, for each item, each operation is performed exactly once with total line cost to be minimized. The specificity of the problem is that all operations of the same workstation are performed in parallel. There are inclusion, exclusion, and precedence relations that restrict the assignment of blocks and operations to the same workstation and constrain the processing order of the operations on the transfer line. We suggest a reduction of this transfer line design problem to a simple set partitioning problem. This reduction is based on the concept of a locally feasible workstation.     

The coordination of transportation and batching scheduling

We study a coordinated scheduling problem of production and transportation in which each job is transported to a single batching machine for further processing. There are m vehicles that transport jobs from the holding area to the batching machine. Each vehicle can transport only one job at a time. The batching machine can process a batch of jobs simultaneously where there is an upper limit on the batch size. Each batch to be processed occurs a processing cost. The problem is to find a joint schedule of production and transportation such that the sum of the total completion time and the total processing cost is optimized. For a special case of the problem where the job assignment to the vehicles is predetermined, we provide a polynomial time algorithm. For the general problem, we prove that it is NP-hard (in the ordinary sense) and present a pseudo-polynomial time algorithm. A fully polynomial time approximation scheme for the general problem is obtained by converting an especially designed pseudo-polynomial dynamic programming algorithm.     

Simultaneously scheduling multiple turns for steel color-coating production

This paper investigates a large-scale scheduling problem in the iron and steel industry, called color-coating production scheduling (CCPS). The problem is to generate multiple production turns for the galvanized coils that dynamically arrive from upstream lines within a given scheduling horizon, and at the same time determine the sequence of these turns so that the productivity and product quality are maximized while the production cost and the number of generated turns are minimized. We formulate this problem as a mixed integer nonlinear program and propose a tabu search heuristic to obtain satisfactory solutions. Results on real production instances show that the presented model and heuristic are more effective and efficient with comparison to manual scheduling. A practical scheduling system for CCPS combining the model and heuristic has been developed and successfully implemented in a major iron and steel enterprise in China.     

Minimizing the weighted number of tardy jobs with due date assignment and capacity-constrained deliveries for multiple customers in supply chains

In this paper, an integrated due date assignment and production and batch delivery scheduling problem for make-to-order production system and multiple customers is addressed. Consider a supply chain scheduling problem in which n orders (jobs) have to be scheduled on a single machine and delivered to K customers or to other machines for further processing in batches. A common due date is assigned to all the jobs of each customer and the number of jobs in delivery batches is constrained by the batch size. The objective is to minimize the sum of the total weighted number of tardy jobs, the total due date assignment costs and the total batch delivery costs. The problem is NP-hard. We formulate the problem as an Integer Programming (IP) model. Also, in this paper, a Heuristic Algorithm (HA) and a Branch and Bound (B&B) method for solving this problem are presented. Computational tests are used to demonstrate the efficiency of the developed methods.