Complexities and algorithms for synchronized scheduling of parallel machine assembly and air transportation in consumer electronics supply chain

In this paper, we study the problem of synchronized scheduling of assembly and air transportation to achieve accurate delivery with minimized cost in consumer electronics supply chain. This problem was motivated by a major PC manufacturer in consumer electronics industry. The overall problem is decomposed into two sub-problems, which consist of an air transportation allocation problem and an assembly scheduling problem. The air transportation allocation problem is formulated as an integer linear programming problem with the objective of minimizing transportation cost and delivery earliness tardiness penalties. The assembly scheduling problem seeks to determine a schedule ensuring that the orders are completed on time and catch the flights such that the waiting penalties between assembly and transportation is minimized. The problem is formulated as a parallel machine scheduling problem with earliness penalties. The computational complexities of the two sub-problems are investigated. The air transportation allocation problem with split delivery is shown to be solvable. The parallel machine assembly scheduling problem is shown to be NP-complete. Simulated annealing based heuristic algorithms are presented to solve the parallel machine problem.     

A dynamic programming based heuristic for the assembly line balancing problem

The simple assembly line balancing problem is the simplification of a real problem associated to the assignment of the elementary tasks required for assembly of a product in an assembly line. This problem has been extensively studied in the literature for more than half a century. The present work proposes a new procedure to solve the problem we call Bounded Dynamic Programming. This use of the term Bounded is associated not only with the use of bounds to reduce the state space but also to the reduction of such space based on heuristics. This procedure is capable of obtaining an optimal solution rate of 267 out of 269 instances, which have been used in previous works, thus obtaining the best-known performance for the problem. These results are an improvement from any previous procedure found in the literature even when using smaller computing times.     

Scheduling flexible machining and assembly systems

Most scheduling papers consider flexible machining and assembly systems as being independent. In this paper, a heuristic two-level scheduling algorithm for a system consisting of a machining and an assembly subsystem is developed. It is shown that the upper level problem is equivalent to the two machine flow shop problem. The algorithm at the lower level schedules jobs according to the established product and part priorities. Related issues, such as batching, due dates, process planning and alternative routes, are discussed. The algorithm and associated concepts are illustrated on a number of numerical examples.     

A heuristic approach to a single stage assembly problem with transportation allocation

Determining assembly scheduling and transportation allocation are two practical problems that industries face, such as the electronics and health products industries. Problems associated with assembly scheduling mainly focus on how to determine the orders’ processing sequence on the assembly line in order to minimize the waiting times before they are flown to their destinations. Problems associated with transportation allocation arise in the system of assigning processed orders to transport modes with the purpose of minimizing penalties from earliness and tardiness. To minimize overall delivery costs, businesses should decide on assembly scheduling and transportation allocation decision simultaneously. However, since simultaneously making these two decisions is not an easy task, most of the works done on them usually deal with these two problems separately. Apart from previous works, this paper establishes a mixed integer programming model that deals with these problems simultaneously. Due to the computational complexity of the problem, this paper develops a hybrid heuristic algorithm to solve this problem, and we evaluate the performance of the presented heuristic algorithm with the well-known GAMS/BARON and Lingo commercial software, which tests the heuristic algorithm on randomly-generated problems. The presented heuristic algorithm is shown to perform well compared with well-known commercial software.     

Designing a mixed-model,open-station assembly line using mixed-integer programming

An open-station assembly line that manufactures mixed models of sheet metal cabinets is considered in this research. The problem minimizes the total cost of the idle and utility times incurred in an assembly line with different line parameters (such as launch interval, station length, starting point of work, upstream walk, locus of the operator's movement, etc.) and operation sequences of the mixed models. An open-station system plays a significant controlling role in determining the optimal line parameters that minimize the total cost of idle and utility times in a mixed-model assembly line. Thus, a mixed-integer programming model for an open-station system is developed here to determine line parameters optimally. The model is tested on a three-station mixed-model line, which is a partial representation of a complete long assembly line. This research obtained a set of line parameters that minimize the total cost of idle and utility times optimally. Results indicate that the minimum total cost of idle and utility times in an open-station system decreases with line length. Other results pertinent to the line design are also demonstrated.     

An imperialist competitive algorithm for multi-objective U-type assembly line design

Many assembly lines are now being designed as U-type assembly lines rather than straight lines because of the pressure of the just-in-time (JIT) manufacturing concept. Since any type of an assembly line balancing problem is known to be NP-hard, there has been a growing tendency toward using evolutionary algorithms to solve such a hard problem. This paper proposes a new population-based evolutionary algorithm, namely imperialist competitive algorithm (ICA) inspired by the process of socio-political evolution, to address the multi-objective U-type assembly line balancing problem (UALBP). Two considered objectives are to minimize the line efficiency and minimize the variation of workload. Furthermore, the Taguchi design is applied to tune the effective parameters of the proposed ICA. To demonstrate the efficiency of the proposed algorithm, the associated results are compared against an efficient genetic algorithm (GA) in the literature over a large group of benchmarks taken from the literature. The computational results show that the proposed ICA outperforms GA.     

Simple heuristics for the assembly line worker assignment and balancing problem

We propose simple heuristics for the assembly line worker assignment and balancing problem. This problem typically occurs in assembly lines in sheltered work centers for the disabled. Different from the well-known simple assembly line balancing problem, the task execution times vary according to the assigned worker. We develop a constructive heuristic framework based on task and worker priority rules defining the order in which the tasks and workers should be assigned to the workstations. We present a number of such rules and compare their performance across three possible uses: as a stand-alone method, as an initial solution generator for meta-heuristics, and as a decoder for a hybrid genetic algorithm. Our results show that the heuristics are fast, they obtain good results as a stand-alone method and are efficient when used as a initial solution generator or as a solution decoder within more elaborate approaches.     

Supply chain models for an assembly system with preprocessing of raw materials

In this paper, we investigate the material procurement and delivery policy in a production system where raw materials enter into the assembly line from two different flow channels. The system encompasses batch production process in which the finished product demand is approximately constant for an infinite planning horizon. Two distinct types of raw materials are passed through the assembly line before to convert them into the finished product. Of the two types of raw materials, one type requires preprocessing inside the facility before the assembly operation and other group is fed straightway in the assembly line. The conversion factors are assigned to raw materials to quantify the raw material batch size required. To analyze such a system, we formulate a nonlinear cost function to aggregate all the costs of the inventories, ordering, shipping and deliveries. An algorithm using the branch and bound concept is provided to find the best integer values of the optimal solutions. The result shows that the optimal procurement and delivery policy minimizes the expected total cost of the model. Using a test problem, the inventory requirements at each stage of production and their corresponding costs are calculated. From the analysis, it is shown that the rate and direction change of total cost is turned to positive when delivery rates per batch reaches close to the optimal value and the minimum cost is achieved at the optimal delivery rate. Also, it is shown that total incremental cost is monotonically increasing, if the finished product batch size is increased, and if, inventory cost rates are increased. We examine a set of numerical examples that reveal the insights into the procurement-delivery policy and the performance of such an assembly type inventory model.     

Stochastic cyclic scheduling problem in synchronous assembly and production lines

In this paper we address the stochastic cyclic scheduling problem in synchronous assembly and production lines. Synchronous lines are widely used in the production and assembly of various goods such as automobiles or household appliances. We consider cycle time minimisation (or throughput rate maximisation) as the objective of the scheduling problem with the assumption that the processing times are independent random variables. We first discuss the two-station case and present a lower bounding scheme and an approximate solution procedure for the scheduling problem. For the general case of the problem, two heuristic solution procedures are presented. An extension of the two-station lower bound to the general case of the problem is also discussed. The performance of the proposed heuristics on randomly generated problems is documented, and the impact of scheduling decisions on problems with different levels of variability in processing times are analysed. We also analyse the problem of sequence determination when the available information is limited to the expected values of individual processing times.     

Bees Algorithm for constrained fuzzy multi-objective two-sided assembly line balancing problem

Bees Algorithm is one of the swarm intelligence based heuristics which tries to model natural behaviour of honey bees in food foraging and used to solve optimization problems. On the other hand, Two-sided Assembly Line Balancing Problem is a generalization of simple Assembly Line Balancing Problem where different assembly tasks are carried out on the same product in parallel at both left and right sides of the line. Two-sided assembly lines are generally employed for the assembly of large-sized products such as buses and trucks. Furthermore, many real life problems contain imprecise objectives and Fuzzy Multi-objective Programming gives an opportunity to handle such situations. In this study, Two-sided Assembly Line Balancing Problem is considered more realistically by employing positional, zoning and synchronous task constraints and by utilizing fuzzy approaches so as to maximize work slackness index and line efficiency, and minimize total balance delay. For solving this problem Bees Algorithm is used as a search mechanism for obtaining good solutions and extensive computational results are presented.     

Bicriteria sequencing methods for the mixed-model assembly line in just-in-time production systems

A mixed-model manufacturing facility operating in a pull production environment can be controlled by setting a production schedule only for the last process in the facility which is usually an assembly line of mixed-model type. In the mixed-model sequencing problems, two major goals are considered: (1) smoothing the workload on each workstation on the assembly line, and (2) keeping a constant rate of usage of all parts used on the assembly line. In this study, first, some well-known solution approaches with goal 2 are analyzed through minimizing the sum-of-deviations of actual production from the desired amount. The approaches that are found to be performing better than the others are extended for the bicriteria problem considering goals 1 and 2, simultaneously. It is also shown that the bicriteria problem with the sum-of-deviations type objective function can also be formulated as an assignment problem, and the optimal solution to the small-sized problems can thus be obtained by solving the assignment problem. Finally, the conditions when it is important to take the workload-smoothing goal into consideration are analyzed.     

Application of robust optimization to automated test assembly

In automated test assembly (ATA), 0-1 linear programming (0-1 LP) methods are applied to select questions (items) from an item bank to assemble an optimal test. The objective in this 0-1 LP optimization problem is to assemble a test that measures, in as precise a way as possible, the ability of candidates. Item response theory (IRT) is commonly applied to model the relationship between the responses of candidates and their ability level. Parameters that describe the characteristics of each item, such as difficulty level and the extent to which an item differentiates between more and less able test takers (discrimination) are estimated in the application of the IRT model. Unfortunately, since all parameters in IRT models have to be estimated, they do have a level of uncertainty to them. Some of the other parameters in the test assembly model, such as average response times, have been estimated with uncertainty as well. General 0-1 LP methods do not take this uncertainty into account, and overestimate the predicted level of measurement precision. In this paper, alternative robust optimization methods are applied. It is demonstrated how the Bertsimas and Sim method can be applied to take this uncertainty into account in ATA. The impact of applying this method is illustrated in two numerical examples. Implications are discussed, and some directions for future research are presented.     

A branch and bound algorithm for the two-stage assembly scheduling problem

This paper develops a branch and bound algorithm for the two-stage assembly scheduling problem. In this problem, there are m machines at the first stage, each of which produces a component of a job. When all m components are available, a single assembly machine at the second stage completes the job. The objective is to schedule the jobs on the machines so that the maximum completion time, or makespan, is minimized. A lower bound based on solving an artificial two-machine flow shop problem is derived. Also, several dominance theorems are established and incorporated into the branch and bound algorithm. Computational experience with the algorithm is reported for problems with up to 8000 jobs and 10 first-stage machines.     

混流装配线平衡问题的多目标优化方法研究

针对混流装配线存在的工序作业多、平衡难度大等问题,以U型布置的混装线为研究对象,兼顾工作站平均负荷和瞬时负荷平衡,在最小化工作站数的基础上均衡了工作站间和工作站内不同产品的作业负荷,建立U型混流装配线多目标平衡优化模型,同时提出目标法解决联合目标中的目标函数兼容性问题。设计并运用改进的自适应遗传算法求解模型,考虑到交叉、变异操作的随机性,在变异阶段加入强制规则,并对新生成的子代个体进行基因冲突检测,以提高可行解的比率。算例研究的结果表明本文所提的多目标优化方法能够较好地解决混装线平衡问题。     

An adaptive search for the response time variability problem

The Response Time Variability Problem (RTVP) is an NP-hard combinatorial scheduling problem, which has recently been reported and formalised in the literature. This problem has a wide range of real-world applications in mixed-model assembly lines, multi-threaded computer systems, broadcast of commercial videotapes and others. The RTVP arises whenever products, clients or jobs need to be sequenced in such a way that the variability in the time between the points at which they receive the necessary resources is minimised. We propose a greedy but adaptive heuristic that avoids being trapped into a poor solution by incorporating a look ahead strategy suitable for this particular scheduling problem. The proposed heuristic outperforms the best existing methods, while being much faster and easier to understand and to implement.     

Heuristics and lower bounds for the simple assembly line balancing problem type 1: Overview,computational tests and improvements

Assigning tasks to work stations is an essential problem which needs to be addressed in an assembly line design. The most basic model is called simple assembly line balancing problem type 1 (SALBP-1). We provide a survey on 12 heuristics and 9 lower bounds for this model and test them on a traditional and a lately-published benchmark dataset. The present paper focuses on algorithms published before 2011.     

On the combinatorics of an origami model

We consider the problem of how the assembly process of an origami model, made up of similar pieces, can be completed given that at each step there are several choices. A result is given in the language of graphs that provides a sufficient condition under which assembly of the model will never fail.     

Scheduling just-in-time part supply for mixed-model assembly lines

With increasing cost competition and product variety, providing an efficient just-in-time (JIT) supply has become one of the greatest challenges in the use of mixed-model assembly line production systems. In the present paper, therefore, we propose a new approach for scheduling JIT part supply from a central storage center. Usually, materials are stored in boxes that are allotted to the consumptive stations of the line by a forklift. For such a real-world problem, a new model, a complexity proof as well as different exact and heuristic solution procedures are provided. Furthermore, a direct comparison with a simple two-bin kanban system is provided. Such a system is currently applied in the real-world industrial process that motivates our research. It becomes obvious that this policy is considerably outperformed according to the resulting inventory- and α-service levels. Moreover, at the interface between logistics and assembly operations, strategic management implications are obtained. Specifically, based on the new approach, it is the first time a statistical analysis is being made as to whether widespread Level Scheduling policies, which are well-known from the Toyota Production System, indeed facilitate material supply. Note that in the literature it is frequently claimed that this causality exists.     

Optimal workforce assignment to operations of a paced assembly line

We study a paced assembly line intended for manufacturing different products. Workers with identical skills perform non-preemptable operations whose assignment to stations is known. Operations assigned to the same station are executed sequentially, and they should follow the given precedence relations. Operations assigned to different stations can be performed in parallel. The operation’s processing time depends on the number of workers performing this operation. The problem consists in assigning workers to operations such that the maximal number of workers employed simultaneously in the assembly line is minimized, the line cycle time is not exceeded and the box constraints specifying the possible number of workers for each operation are not violated. We show that the general problem is NP-hard in the strong sense, develop conventional and randomized heuristics, propose a reduction to a series of feasibility problems, present a MILP model for the feasibility problem, show relation of the feasibility problem to multi-mode project scheduling and multiprocessor scheduling, establish computational complexity of several special cases based on this relation and provide computer experiments with real and simulated data.