An efficient discrete event model of assembly/disassembly production networks

This paper develops a discrete event simulation model of assembly/disassembly (AD) production networks with finite buffers and unreliable machines. The model is an extension of a previous continuous flow model, which simulates the system only when a machine's production rate is altered. The events causing changes in the production rates are: a machine fails or is repaired and a buffer becomes full, empty, not full, or not empty. During operation between two events the system runs deterministically. Thus, given the state of the system (machine cumulative production, buffer levels and their statistics) at the time of occurrence of some event, the corresponding state variables upon the occurrence of the next event can be updated using analysis. The proposed model does not use repair, not-full, and not-empty events. This is achieved by considering the machine downtimes as transient times in which no parts are produced and by developing more complex state equations. Numerical results show that the model combines speed and accuracy.     

Capacity estimation of a multi-product unreliable production line

This paper addresses the problem of capacity estimation of a multi-product production line composed of m unreliable workstations and ( m - 1) intermediate buffers. A simulation-based experimental design methodology is proposed to improve the performance of this flexible production line, which is expressed as the cycle time. The modelling approach integrates, in a more representative manner, the many parameters that impact the capacity of the manufacturing system. These are: workstation failure, repair, and set-up as product type changes. An experimental optimization to judiciously locate/allocate buffers between workstations is used to determine the maximum contribution of buffers on the overall performance of this serial manufacturing system. A case study is presented to show the modelling steps and to assess the contribution of each buffer. Analysis of the results shows the trade-offs between the different levels of buffers and the cycle time of the production line. The results present the percentage of workstations' operation, set-up, downtime, blocking and starving. In addition, for each combination of buffer sizes, the bottleneck workstation is identified. Changing a buffer size impacts directly the cycle time and, in some cases, a new bottleneck workstation evolves. The results provide insights into the performance of the system, including detection of important interactions and critical parameters. Considering various design scenarios, our methodology helps to identify the best strategy of buffer location/allocation that ensures a minimum cycle time, while considering other criteria. This could be achieved with less experimental effort and the manager could make the selection of the best design scenario. An analysis of the dynamic behaviour of buffers and their effectiveness is also given and commented upon.     

Queuing network analysis approach for estimating the sizes of the time buffers in Theory of Constraints-controlled production systems

The present paper describes an open queuing network modelling approach to estimate the size of the time buffers in production systems controlled by the Theory of Constraints philosophy. Workstations in the production network are modelled as GI/G/m queues and a queuing network analysis multiproduct open queuing network modelling method is used to estimate the average flow time to the time buffer origin and the standard deviation of flow time. Using these two values together with an assumption of normally distributed flow times and a chosen service level, the final time buffer length is determined. The queuing network analysis method has been modified to enable the modelling of production networks with machine failures, batch service and varying transfer batch sizes. The modelling approach has also been incorporated in a computerized tool that uses product specific information such as bill-of-material and routing data, and production network information such as resource data to estimate the sizes and location of the necessary time buffers for each product. Simulation experiments indicate that the procedure is sufficiently accurate to provide an initial quick estimate of the needed time buffer lengths at the design stage of the line.     

Joint optimization of maintenance,buffers and machines in manufacturing lines

This article considers a series manufacturing line composed of several machines separated by intermediate buffers of finite capacity. The goal is to find the optimal number of preventive maintenance actions performed on each machine, the optimal selection of machines and the optimal buffer allocation plan that minimize the total system cost, while providing the desired system throughput level. The mean times between failures of all machines are assumed to increase when applying periodic preventive maintenance. To estimate the production line throughput, a decomposition method is used. The decision variables in the formulated optimal design problem are buffer levels, types of machines and times between preventive maintenance actions. Three heuristic approaches are developed to solve the formulated combinatorial optimization problem. The first heuristic consists of a genetic algorithm, the second is based on the nonlinear threshold accepting metaheuristic and the third is an ant colony system. The proposed heuristics are compared and their efficiency is shown through several numerical examples. It is found that the nonlinear threshold accepting algorithm outperforms the genetic algorithm and ant colony system, while the genetic algorithm provides better results than the ant colony system for longer manufacturing lines.     

A station model for continuous materials flow production systems

This study develops a station model for continuous flow production systems. The most prominent use of the model is as a building block for a general and flexible decomposition method to analyse and design continuous materials flow production systems. Station breakdown and a finite capacity buffer are considered. Station inference caused by the blocking and starving phenomena is included in the station model. We assume that the time to station breakdown and station repair are exponentially distributed while the buffer is neither empty nor full. No restrictive assumptions are made about the distributions of the station breakdown and repair times when the station is blocked or starved, that is, while the buffer remains empty or remains full. The production rate and the expected level of the buffer are given in closed form. Numerical results that show the effects of the input parameters on the production rate along with an overview of the decomposition methods are presented.     

An algorithm for optimal buffer placement in reliable serial lines

The optima] allocation of buffer capacity in unbalanced production lines with reliable but variable workstations is a complex and little-researched topic. Analytic formulas for the throughput of these lines do not exist, so simulation is the only practical alternative for estimating throughput. Exhaustive search over all possible buffer allocations quickly becomes impractical beyond short lines and few buffers. Thus an algorithm is needed to efficiently find optimal or near-optimal allocations. We develop a simple search algorithm for determining the optimal allocation of a fixed amount of buffer capacity in an n-station serial line. The algorithm, which is an adaptation of the Spendley-Hext and Nelder-Mead simplex search algorithms, uses simulation to estimate throughput for every allocation considered. An important feature of the algorithm is that the simulation run length is adjusted during the running of the algorithm to save simulation run time when high precision in throughput estimates is not needed, and 10 ensure adequate precision when it is needed. We describe the algorithm and show that it can reliably find the known optimal allocation in balanced lines. Then we test the ability of the algorithm to find optimal allocations in unbalanced lines, first for cases in which the optimal allocation is known, and subsequently for cases in which the optimal allocation is not known. We focus particularly on lines with multiple imbalances in means and variances. In general, our algorithm proves highly efficient in finding a near-optimal allocation with short simulation run times. It also usually finds the true optimal allocation, but it is in the nature of this problem that many buffer allocations differ in throughput by small amounts that are difficult to resolve even with long simulation runs.     

Approximation of Flow Lines with Integrally Controlled Buffers

Production lines with integral control limits are studied in this paper. The behaviour of such lines can be shown to be approximated by that of flow lines with local buffers. The reduction of an integrally controlled line to a locally controlled one is computationally simple and accurate in the estimation of such performance measures as throughput, probabilities of buffers being full or empty and throughput time.

The advantage of such a reduction is that good techniques are available for estimating the performance of flow lines with local buffers only. Furthermore, a direct method is described for obtaining an estimate of the throughput of lines with integrally controlled buffers only. In the model used here, the product flow is continuous and the production units are unreliable. Both lifetimes and repair times of machines are distributed exponentially.     

A new method for the placement of buffers in serial production lines

The placement of buffers in a production line is an old and well-studied problem in industrial engineering/operations research that is still relevant today. Decisions regarding the amount and placement of buffers in a production line occur repeatedly in system design. In this paper we document a new buffer placement method for serial production lines that operate under a variety of assumptions. The method uses information generated in a production line simulation, whose conceptual representation of job flow and workstation interaction can be described with a network, to place buffers in order to maximise throughput. This buffer placement method is very efficient and can be implemented in a spreadsheet. We demonstrate the effectiveness of the method by comparing our results against those produced by a genetic algorithm for buffer placement. Experiments are conducted on a variety of test cases. This new buffer placement optimisation method will permit designers to quickly and effectively evaluate many design alternatives and thus improve final production system performance.     

Scheduling manufacturing systems with work-in-process inventory control: single-part-type systems

A real-time algorithm is developed for scheduling single-part-type production lines with work-in-process inventory buffers. We consider three classes of activities: operations, failures and repairs, and starvation and blockage. The scheduling objectives are to keep the actual production close to the demand, the work-in-process (WIP) inventory level low, and the cycle time short. A three-level hierardhical controller is constructed to regulate the production. At the top level, we determine the desirable buffer sizes and the target production level for each operation. At the middle level is a production flow rate controller that recalculates the production rates whenever a machine fails or is starved or blocked. The loading times for individual parts are determined at the bottom level of the hierarchy. The production scheduling algorithm is evaluated by using computer simulations for a variety of cases. Compared with a transfer line policy, a significant improvement in system performance is observed.     

A stochastic model of an unreliable kanban production system

We analyze a stochastic model of a production line withk stations (machines) in series. There are finitecapacity buffers between the machines and at the end of the line. The movement of the workpieces through the line is demand-driven, i.e. we deal with a pull (kanban) production system. Processing times are assumed to be deterministic and constant. There are two sources of randomness in the model: Demand for workpieces from outside is stochastic, and the machines may break down (and then be repaired) with a given probability. A demand from outside is lost if the final buffer is empty. This system is described by a discrete-time Markov chain. The steadystate distribution is given for k=1. This is the basis of a decomposition algorithm which approximates the throughput of the line and the percentage of satisfied demand for arbitraryk. A comparison with simulation results shows that this algorithm is very accurate.     

A linear programming approach to capacity estimation of automated production lines with finite buffers

This paper considers a highly automated manufacturing line which consists of a sequence of workstations. Relatively small buffers are assigned between workstations in order to guarantee a small manufacturing interval and quick feedback in the event of process failure to make acceptable product. These small buffers could lead to a noticeable loss of line capacity due to the phenomenon of blocking and starvation. We show by means of simple examples how the buffer sizes and the mix and loading sequence of different types of jobs could significantly affect the production rate of the line. A linear programming based method is then developed to estimate the line capacity for a given configuration of machines and buffers sizes and for a given job mix and sequence. This method also gives the expected machine utilizations, the time machines are blocked/starved and, more importantly, the reason for this lost production capacity. By judiciously interpreting this information, one or more of the following steps can be taken to improve the production rate: (a) change the loading sequence, (b) increase the buffer space selectively, (c) make the products in smaller or larger batches, and (d) add new machines.     

Manufacturing lines under surplus-based control: multiple products and bounded buffers

Challenged by the scheduling complexity for production flow processes in industrial facilities, we study the performance of multi-product producing lines. We analyse the performance of multi-product lines that consist a number of machines and bounded buffers with preselected base stock levels. It is assumed that each manufacturing machine in the line is capable of working with several product types, but only operate on one product at a time. The network is operated under a surplus-based production control policy in the presence of perturbations and production demand fluctuations. We derive bounds on the demand tracking accuracy for each product type, regardless its flow direction in the multi-product line. In addition, for a multi-product line with unidirectional product flow, we obtain a quantitative relation between demand tracking accuracy, its inventory levels, numbers of product types, buffer capacity limits and perturbations. The accuracy of the obtained demand tracking bounds is illustrated by numerical simulations. By means of simulation experiments, we show that the obtained results have a valuable meaning and can be used as a reference tool in practice.     

Mixed integer programming for scheduling surface mount technology lines

This paper presents new mixed integer programming formulations for blocking scheduling of SMT (Surface Mount Technology) lines for printed wiring board assembly. The SMT line consists of several processing stages in series, separated by finite intermediate buffers, where each stage has one or more identical parallel machines. A board that has completed processing on a machine may remain there and block the machine until a downstream machine becomes available for processing. The objective is to determine an assembly schedule for a mix of board types so as to complete the boards in a minimum time. Scheduling with continuous or with limited machine availability is considered. Numerical examples and some computational results are presented to illustrate applications of the models proposed.     

A tabu search approach for buffer allocation in production lines with unreliable machines

The optimal allocation of buffers is an important research issue in designing production lines. In this study, a tabu search (TS) algorithm is proposed to find near-optimal buffer allocation plans for a serial production line with unreliable machines. The main objective is to maximize the production rate, i.e. throughput, of the line. The efficiency of the proposed method is also tested to solve buffer allocation problems with the objective of total buffer size minimization. To estimate the throughput of the line with a given specific buffer allocation, an analytical decomposition approximation method is used. The performance of the tabu search algorithm is demonstrated on existing benchmark problems. The results obtained by the TS algorithm are clearly encouraging, as the TS algorithm is much better than the other algorithms for all considered benchmark problems.     

Analysis of approximately balanced production lines

This paper develops two analytical formulas for estimating the throughput of a reliable production line with exponential service times and finite intermediate buffers. The formulas apply in the case of an approximately balanced line with identical buffers or near optimal buffer allocations, where the processing times of the machines are close to each other but not necessarily the same. The derivation of the formulas is based on the standard decomposition method. Moreover, it is proved that, in general cases, both formulas provide upper bounds for the throughput obtained by the decomposition method. Numerical experiments show that the proposed formulas achieve good accuracy for approximately balanced production lines. Finally, the formulas are applied to the buffer allocation problem, and two closed-form expressions are obtained for estimating the smallest buffer capacity which is necessary to achieve the desired throughput.     

Automated production line design with flexible unreliable machines for profit maximization

A model is presented for jointly determining the profit-maximizing configuration of machines (both type and number) and buffer capacities along an automated flexible production line. A heuristic solution procedure is developed for the general case of finite buffer capacities. The procedure combines an optimal solution algorithm for the case of infinite buffers with a heuristic algorithm which determines the finite buffer capacities.     

A scheduling problem in glass manufacturing

In this paper, a production scheduling problem in glass manufacturing is studied. The production facility consists of multiple identical production lines and each production line includes a number of serially arranged machines. The production is characterized by semi-ordered processing times in each product family, and the last machine in each production line is a bottleneck machine. Significant changeover times are required when products of different families are produced on a production line. The scheduling problem was modeled as a parallel no-delay flowshop scheduling problem (PNDFSP). The PNDFSP combines the parallel machine scheduling problem (PMSP) with the no-delay flowshop scheduling problem (NDFSP). While PMSP and NDFSP have received considerable attention in the literature, PNDFSP has not been well studied. A mixed-integer programming formulation is developed and an efficient heuristic algorithm is proposed. The sequential heuristic algorithm considers simultaneously the line changeover time, no-delay effect, and line utilization in assigning product families to the production lines. The computational results are reported.     

Allocation of buffers to serial production lines with bottlenecks

The optimal placement of a predetermined amount of buffer capacity in balanced serial production lines is a well-understood problem: in lines with moderate variability, the optimal allocation involves equal numbers of buffers at each site; in lines with severe variability, the equal allocation is modified slightly to place more buffers toward the center of the line. Buffering unbalanced lines is a much less well-understood problem. We study the problem of buffering serial lines with moderate variability and a single bottleneck; i.e., a single station with a larger mean processing time than all other stations. Our analysis shows that a bottleneck station draws buffers toward it, but the optimal allocation depends on the location and severity of the bottleneck, as well as the number of buffers available. Furthermore, relatively large imbalances in mean processing times are required to shift the optimal buffer allocation away from an equal allocation. Finally, line length appears to have a relatively small effect on the optimal allocation with a given bottleneck. These results suggest that, at least for the class of lines studied here, equal buffer allocations may be optimal except in severely unbalanced lines. Furthermore, in severely unbalanced lines, throughput appears to be insensitive to the allocation of buffers.     

Reducing energy consumption in serial production lines with Bernoulli reliability machines

This paper is devoted to developing an integrated model to minimise energy consumption while maintaining desired productivity in Bernoulli serial lines with unreliable machines and finite buffers. For small systems, such as three- and four-machine lines with small buffers, exact analysis to optimally allocate production capacity is introduced. For medium size systems (e.g. three- and four-machine lines with larger buffers, or five-machine lines with small buffers), an aggregation procedure to evaluate line production rate is introduced. Using it, optimal allocation of machine efficiency is searched to minimise energy consumption. Insights and allocation principles are obtained through the analyses. Finally, for larger systems, a fast and accurate heuristic algorithm is presented and validated through extensive numerical experiments to obtain optimal allocation of production capacity to minimise energy consumption while maintaining desired productivity.     

Performance evaluation of a make-tO-stock production line with a two-parameter-per-machine policy: the control point policy

This paper presents a decomposition method for evaluating the performance of a production line with finite buffers controlled by the Control Point Policy (CPP), a policy with two parameters per machine. (One parameter is the buffer size; the other is a local hedging point.) Policies with two parameters per machine show very good performance while remaining simple to use. However, decomposition methods have not yet been developed for their analysis. We consider a production line, with exponentially distributed processing, failure, and repair times, controlled by a CPP. We decompose this line into two-machine CPP-controlled lines, which considerably simplifies the decomposition equations. Furthermore, the information loops are then included in the building blocks, and can be solved numerically. A numerical study shows that the method is accurate.