Analysis of partial setup strategies for solving the operational planning problem in parallel machine electronic assembly systems

In this paper, we analyse the operational planning problem in an electronic assembly system with multiple placement machines operating in parallel. The partial setup strategy is proposed as an effective methodology for this problem. This strategy attempts to determine the balance between processing time and changeover time during system operation. The Tour primary issues are determining the assignment of products to machines, the sequence of products on each machine, the assignment of components to feeder locations for each product, and the component placement sequence for each product. Four solution procedures for unique and partial setup strategies are developed and tested. The computation results show that for low to medium volume high mix environments, the partial setup procedures offer significant improvement over the unique setup strategies. The results also show that no single fixed strategy dominates in all scenarios, and therefore, an adaptable procedure that will choose the best solution for each set of requirements is needed.     

Hierarchical production control for a flow shop with dynamic setup changes and random machine breakdowns

In this paper, we study a manufacturing system consisting of two machines separated by two intermediate buffers, and capable of producing two different products. Each product requires a constant processing time on each of the machines. Each machine requires a constant non-negligible setup change time from one product to the other. The demand rate for each product is considered to be piecewise constant. Each machine undergoes failure and repair. The time-to-failure and time-to-repair are exponentially distributed random variables. The setup change and processing operations are resumable. We model our system as a continuous time, continuous flow process. An optimal control problem is formulated for the system to minimize the total expected discounted cost over an infinite horizon. To determine the optimal control policy structure, a discrete version of the problem is solved numerically using a dynamic programming formulation with a piecewise linear penalty function. A real-time control algorithm is then developed with the objective of maintaining low work-in-process inventory and keeping the production close to the demand. The algorithm uses a hierarchical control structure to generate the loading times for each product on each machine in real time and to respond to random disruptions in the system. The system is simulated using this algorithm to study its performance. The performance of the algorithm is also compared to alternative policies.     

Workload allocation in multi-product, multi-facility production systems with setup times

In this article, we model the problem of assigning work to M heterogeneous servers (machines), which arises from exogenous demands for N products, in the presence of nonzero setup times. We seek a workload allocation which minimizes the total expected Work-in-Progress (WIP) inventory. Demands are assumed to arrive according to independent Poisson processes, but the setup and the processing times can have arbitrary distributions. Whenever a machine produces more than one product type, production batch sizes are determined by a group scheduling policy; which is also known as the cyclic-exhaustive polling policy. We formulate the workload allocation problem as a nonlinear optimization problem and then provide several insights gleaned from first order necessary conditions, from numerical examples, and from a close examination of the objective function. For example, we show that increasing either the load or the number of products assigned to a machine, or both, does not necessarily increase its contribution to total WIP. These insights are then used to devise a heuristic workload allocation as well as a lower bound. The heuristic allocation is further refined using a nonlinear optimization algorithm.     

GA-based adaptive setup planning toward process planning and scheduling integration

Setup planning of a part for more than one available machine is a typical combinatorial optimisation problem under certain constraints. It has significant impact not only on the whole process planning but also on scheduling, as well as on the integration of process planning and scheduling. Targeting the potential adaptability of process plans associated with setups, a cross-machine setup planning approach using genetic algorithms (GA) for machines with different configurations is presented in this paper. First, based on tool accessibility analysis of different machine configurations, partially sequenced machining features can be grouped into certain setups; then by responding to the requirements from a scheduling system, optimal or near-optimal setup plans are selected for certain criteria, such as cost, makespan and/or machine utilisation. GA is adopted for the combinatorial optimisation, which includes gene pool generation based on tool accessibility examination, setup plan encoding and fitness evaluation, and optimal setup plan selection through GA operations. The proposed approach is implemented in a GA toolbox, and tested using a sample part. The results demonstrate that the proposed approach is applicable to machines with varying configurations, and adaptive to different setup requirements from a scheduling system due to machine availability changes. It is expected that this approach can contribute to process planning and scheduling integration when a process plan is combined with setups for alternative machines during adaptive setup planning.     

Iterative algorithms for batching and scheduling to minimise the total job tardiness in two-stage hybrid flow shops

This study considers the batching and scheduling problem in two-stage hybrid flow shops in which each job with a distinct due-date is processed through two serial production stages, each of which has identical machines in parallel. Under the fundamental trade-off that large batch sizes with less frequent changeovers may reduce setup costs and hence increase machine utilisation, while small batch sizes may reduce job flow times and hence improve scheduling performance, the problem is to determine the number of batches, the batch compositions, the allocation of batches to the parallel machines at each stage, and the sequence of the batches allocated to each machine for the objective of minimising the total job tardiness. A mixed integer programming model is developed for the reduced problem in which the number of batches is given, and then, three iterative algorithms are proposed in which batching and scheduling are done repeatedly until a good solution is obtained. To show the performance of the algorithms, computational experiments were done on a number of test instances, and the results are reported. In particular, we show that the number of batches decreases as the ratio of the batch setup time to the job processing time increases.     

Impact of sequence-dependent setup time on job shop scheduling performance

In a production system using multi-purpose and flexible machines, reducing setup time is an important task for better shop performance. Numerous cases were reported about successful reduction of setup times by standardization of setup procedures. However, setup times have not been eliminated and remain an important element of real production problems for production systems such as commercial printing, plastics manufacturing, metal processing, etc. It is especially critical when the setup time is sequence dependent. In this situation, shop performance cannot be effectively improved without the aid of an appropriate scheduling procedure. Review of the past studies shows that there has not been a significant amount of research done on the scheduling procedure for a dynamic job shop with sequence dependent setup times. This paper investigates the job shop scheduling problems that are complicated by sequence-dependent setup times. The study classifies and tests scheduling rules by considering whether setup time and/or due date information is employed. These scheduling rules are evaluated in dynamic scheduling environments defined by due date tightness, setup times and cost structure. A simulation model of a nine machine job shop is used for the experiment. A hypothetical, asymmetric, setup time matrix is applied to the nine machines.     

MIP-based fix-and-optimise algorithms for the parallel machine capacitated lot-sizing and scheduling problem

This paper examines the capacitated lot-sizing and scheduling problem (CLSP) with sequence-dependent setup times, time windows, machine eligibility and preference constraints. Such a problem frequently arises in the semiconductor manufacturing industry by which this paper is motivated. A mixed integer programming (MIP) model is constructed for the problem. Two MIP-based fix-and-optimise algorithms are proposed in which the binary decision variables associated with the assignment of machines are first fixed using the randomised least flexible machine (RLFM) rule and the rest of the decision variables are settled by an MIP solver. Extensive experiments show that the proposed algorithms outperform the state-of-the-art MIP-based fix-and-optimise algorithms in the literature, especially for instances with high machine flexibility and high demand variation.     

Development of a simulation-based optimisation for controlling operation allocation and material handling equipment selection in FMS

Flexible manufacturing system (FMS) is described as a set of computerised numerical controlled machines, input–output buffers interconnected by automated material handling devices. This paper develops a bi-objective operation allocation and material handling equipment selection problem in FMS with the aim of minimising the machine operation, material handling and machine setup costs and maximising the machine utilisation. The proposed model is solved by a modified chaotic ant swarm simulation based optimisation (CAS²O) while applying pre-selection and discrete recombination operators is surveyed a capable method to simulate different experiments of FMS problems. A test problem is selected from the literature to evaluate the performance of the proposed approach. The results validate the effectiveness of the proposed method to solve the FMS scheduling problem.     

Family-based scheduling of shops with functional layouts

Simulation studies of job shop scheduling have typically assumed that either setup times are zero (subsumed within the processing time), or that every part has such a unique setup that no setup advantages can be gained by better scheduling policies. These studies also assume that the shop has exactly one copy of every machine. Some researchers have proposed heuristics that explicitly consider setup times and parallel machines in the context of a one stage shop with static arrivals. In contrast, family-based scheduling centred around setup time reduction has been credited with achieving economic savings in batch production industries where GT is employed. We motivate this study by the case of an existing realworld semi-conductor testing facility that has family setups, parallel machines and dynamic job arrival. Using this setting, we investigate whether benefits can still be obtained by using a family-based scheduling philosophy in those environments which do not permit the physical creation of cellular layouts due to the presence of process related or other constraints. We propose and evaluate two new dispatching procedures in a functional job shop that is modelled after the semiconductor testing facility. Results show that a family-based scheduling philosophy centred around coordinating machine setups is advantageous at relatively high setup to processing time ratios, while classic job shop rules suffice otherwise. Based on these results, we present recommendations for managing such environments. We also suggest future research directions in this area.     

An adaptive scheduling algorithm for a parallel machine problem with rework processes

The development of a scheduling methodology for a parallel machine problem with rework processes is presented in this paper. The problem is to make a schedule for parallel machines with rework probabilities, due-dates, and sequence dependent setup times. Two heuristics are developed based on a dispatching algorithm and problem-space-based search method. In order to evaluate the efficacy of the proposed algorithms, six performance indicators are considered: total tardiness, maximum lateness, mean flow-time, mean lateness, the number of tardy jobs, and the number of reworks. This paper shows how these algorithms can adaptively capture the characteristics of manufacturing facilities for enhancing the performance under changing production environments. Extensive experimental results show that the proposed algorithms give very efficient performance in terms of computational time and each objective value.     

A reactive GRASP and Path Relinking for balancing reconfigurable transfer lines

A line balancing problem for reconfigurable transfer lines with sequence-dependent setup times and parallel machines was studied. These lines are paced and serial, i.e. a part to be machined passes through a sequence of stations. Stations are composed of CNC (Computer Numerical Control) machines. At least one CNC machine is installed at each station. These CNC machines are mono-spindle head machines, hence setup times between operations have to be taken into account. The origins of setup times are various, for example, the necessity to rotate the part, change and displace the tool, etc. Because of setup times, the station workload depends on the sequence in which the operations are assigned to the station. In addition, accessibility constraints have to be considered. The objective consists of assigning a given set of operations as well as machines to a sequence of workstations in order to minimise the total cost of the line. Keeping in mind the industrial importance of this problem and the lack of available methods in the literature tackling it efficiently, we propose a new heuristic based on GRASP combined with Path Relinking. A MIP approach is used to select the sequences of operations on workstations. Numerical experiments are presented and show that the proposed heuristic can provide good solutions even for large-sized instances while requiring a computational time that is fully compatible with a practical application. An industrial case study is also described.     

Minimizing the makespan for the two-machine scheduling problem with a single server: Two algorithms for very large instances

This article considers the problem of scheduling a given set of n jobs on two identical parallel machines with a single server. Each job must be processed on one of the machines. Before processing, the server has to set up the relevant machine. The objective is to minimize the makespan. For this unary NP-hard problem, two fast constructive algorithms with a complexity of O(n²) are presented. The performance of these algorithms is evaluated for instances with up to 10,000 jobs. Computational results indicate that the algorithms have an excellent performance for very large instances so that the obtained objective function values are very close to a lower bound, and in many cases even an optimal solution is achieved. Superiority over all existing algorithms is obtained by sequencing the jobs on the two machines so that the machine idle time and the server waiting time are minimized. In doing so, the characteristics of an optimal solution resulting from its relevant lower bound are taken into account.     

辊板式铝塑泡罩包装机的开发

目的 铝塑泡罩包装机分为DPA系列(辊辊型)、DPP(B)系列(平板或板板型)、DPH(T)系列(辊板型)3种类型,针对过去的泡罩包装机存在着一些如封合后会弯曲、影响美观以及效率低下等问题,需要加大力度对泡罩包装机进行设计开发,使其达到国际先进水平。方法 DPH(T)系列辊板式铝塑泡罩包装机在辊辊式和平板式铝塑泡罩包装机的技术基础上优化并组合,DPH(T)系列辊板式铝塑泡罩包装机采用平板式吹塑成型(也叫正压成型)和辊式封合技术;新研发的DPH辊板型铝塑泡罩包装机采用摆线运动规律来改善凸轮的动力特性。结果 DPH(T)系列铝塑泡罩包装机生产效率高、运行平稳、结构合理、操作简单、性能可靠、消除了刚性和柔性冲击;DPH(T)系列铝塑泡罩包装机广泛用于药品、食品等的包装。结论 DPH(T)系列铝塑泡罩包装机综合性能得到了改善和提高,并且有些机型目前已经达到了国际先进水平。     

Sequencing n Products Involving m Independent Jobs on m Machines

This article considers the problem of scheduling n products over m distinct machines. Every product consists of a set of jobs, each requiring a known processing time on a designated machine. There are no precedence constraints, and simultaneous processing of jobs requiring different machines within a product is allowed. The object of scheduling is to minimize a regular measure of performance associated with the products. It is shown that there exists an optimal schedule with the “no passing property.” Branch and bound routines are developed for finding the optimal solution for the two measures of performance: (1) total penalty cost; and (2) sum of product completion times. Comparisons between the optimal solution and solutions obtained using dispatching rules are given in the penalty cost case.     

Intelligent dynamic control of stochastic economic lot scheduling by agent-based reinforcement learning

This paper addresses a stochastic economic lot scheduling problem (SELSP) for a single machine make-to-stock production system in which the demands and the processing times for N types of products are random. The sequence-independent setup times and costs are explicitly considered and may have different values for various types of products. The SELSP is to decide when, what, and how much (the lot size) to produce so that the long-run average total cost, including setup, holding and backorder costs, is minimised. We develop a mathematical model and propose two reinforcement learning (RL) algorithms for real-time decision-making, in which a decision agent is assigned to the machine and improves the accuracy of its action-selection decisions via a ‘learning’ process. Specifically, one is a Q-learning algorithm for a semi-Markov decision process (QLS) and another is a Q-learning algorithm with a learning-improvement heuristic (QLIH) to further improve the performance of QLS. We compare the performance of QLS and QLIH with a benchmarking Brownian policy and the first-come-first-served policy. The numerical results show that QLIH outperforms QLS and both benchmarking policies.     

Production sequencing problem with re-entrant work flows and sequence dependent setup times

This paper addresses a shop scheduling problem where a set of n jobs needs to be scheduled on two machines for the side frame press shop in a truck manufacturing company. A most unusual aspect of the problem is that the setup times required for a job in the first machine depend not on the immediately preceding job but on the job which is two steps prior to it. Redefining the job elements, the problem is formulated into a general two machine flow shop problem which can be solved by dynamic programming with the objective of the minimum makespan. An optimal schedule is found utilizing the sequence dominance conditions and the decisiondelay scheme. Since the computational requirements of dynamic programming are impracticably demanding for large-sized problems, a genetic algorithm is developed and its performance is examined through a comparative study.     

A fuzzy logic modelling of dynamic scheduling in FMS

This paper is concerned with scheduling in flexible manufacturing systems (FMSs) using a fuzzy logic (FL) approach. Four fuzzy input variables: machine allocated processing time, machine priority, due date priority and setup time priority are defined. The job priority is the output fuzzy variable, showing the priority status of a job to be selected for next operation on a machine. The model will first select the machines and then assign operations based on a multi-criteria scheduling scheme. The performance of the approach is compared against established methods reported in the literature. The performance measures considered average machine utilisation, meeting due dates, setup times, work in process and mean flow times. The test results demonstrate the superiority of the fuzzy logic approach in most performance measures.     

Flow control of two-level assembly lines

The paper addresses the flow control problem in two-level assembly production lines composed of a unique assembly machine and multiple upper level machines. In order to obtain a finished product, the assembly machine needs components produced by different upper level machines. We assume that the production capacity of each machine is constant and the demand is known over the whole problem horizon. Backlogging is not allowed. The flow control problem consists of adjusting the production of the machines in order to minimize the total cost incurred by holding components and finished products. Properties of the optima) solutions are given. Based on these properties, we propose a simple analytical solution.     

Capacitated lot sizing with parallel machines,sequence-dependent setups,and a common setup operator

In this paper, we consider a special variant of a capacitated dynamic lot sizing problem which, despite its practical relevance, has not been treated sufficiently in the literature. In addition to the significant complexity introduced by the sequence dependency of setup times, the problem is further complicated by the fact that there is only one single setup operator which is responsible for all setups on all machines. Hence, the multi-machine problem cannot be decomposed into multiple single machine problems, as the setup operations must be coordinated among the different machines. In addition, lots are produced in batches whereby the processing time of a lot is a step-wise function of the number of batches per lot. Due to perishability and quarantine issues, time windows for the production are given. We formulate a big-bucket lot sizing model and apply MIP-based heuristics to two industrial data sets.     

Optimization-based manufacturing scheduling with multiple resources, setup requirements, and transfer lots

The increasing demand for on-time delivery of products and low production cost is forcing manufacturers to seek effective schedules to coordinate machines and operators so as to reduce costs associated with labor, setup, inventory, and unhappy customers. This paper presents the modeling and resolution of a job shop scheduling system for J. M. Products Inc., whose manufacturing is characterized by the need to simultaneously consider machines and operators, machines requiring significant setup times, operators of different capabilities, and lots dividable into transfer lots. These characteristics are typical for many manufacturers, difficult to handle, and have not been adequately addressed in the literature. In our study, an integer optimization formulation with a separable structure is developed where both machines and operators are modeled as resources with finite capacities. Setups are explicitly considered following our previous work with additional penalties on excessive setups. By analyzing transfer lot dynamics, transfer lots are modeled by using linear inequalities. The objective is to maximize on-time delivery of products, reduce inventory, and reduce the number of setups. By relaxing resource capacity constraints and portions of precedence constraints, the problem is decomposed into smaller subproblems that are effectively solved by using a novel dynamic programming procedure. The multipliers are updated using the recently developed surrogate subgradient method. A heuristic is then used to obtain a feasible schedule based on subproblem solutions. Numerical testing shows that the method generates high quality schedules in a timely fashion.