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.     

Optimal buffer allocation strategy for minimizing work-in-process inventory in unpaced production lines

Several researchers have previously studied the problem of allocating buffer storage to maximize the throughput of a production line for a given total amount of buffer space. In this paper we study the optimal buffer allocation problem of minimizing the average work-in-process subject to a minimum required throughput and a constraint on the total buffer space. Although these two buffer allocation problems are closely related, our results show, surprisingly, that their optimal buffer allocations have very different patterns. Specifically, we show that the optimal buffer allocations for the problem considered here generally exhibit a monotonically increasing property where an increasing amount of buffer space is assigned toward the end of the line. This monotonically increasing property generally holds for both the balanced and unbalanced lines. On the basis of our empirical results, we develop a good heuristic for selecting the optimal buffer allocations.     

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.     

Characterizing the optimal allocation of storage space in production line systems with variable processing times

We consider the optimal allocation of buffer storage spaces in unpaced production lines with variable processing times. It is known that for a fixed total number of buffer spaces, the production rate can often be improved by deliberately unbalancing the buffer allocations in an inverted bowl pattern (the storage bowl phenomenon), with more storage space allocated to the internal stations than to the end stations. It has been hypothesized that if the total number of buffer spaces is also a decision variable, then for a reasonable cost model the optimal allocation would have one additional storage space at each of the internal stations. This paper uses a cost model to show that the optimal allocation is more complicated than this. For balanced lines, the inverted bowl pattern is typically optimal, but the bowl shape becomes more and more pronounced (in an absolute sense) with larger numbers of buffer spaces. However, the relative shape of the bowl stays fairly constant. However, if the workload is unbalanced, the buffer space pattern deviates from the bowl pattern by reducing the number of buffer spaces in buffers that are not adjacent to the bottleneck machine.     

A note on resource allocation scheduling with group technology and learning effects on a single machine

In this article, single-machine group scheduling with learning effects and convex resource allocation is studied. The goal is to find the optimal job schedule, the optimal group schedule, and resource allocations of jobs and groups. For the problem of minimizing the makespan subject to limited resource availability, it is proved that the problem can be solved in polynomial time under the condition that the setup times of groups are independent. For the general setup times of groups, a heuristic algorithm and a branch-and-bound algorithm are proposed, respectively. Computational experiments show that the performance of the heuristic algorithm is fairly accurate in obtaining near-optimal solutions.     

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.     

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 segmentation approach for solving buffer allocation problems in large production systems

Buffer space allocation is an important step in production line design. In this paper, we focus on maximising the profit rate of a line subject to a production rate constraint. We describe a newly observed property of production line optimisation. The property is that the production rate constraint, if it is effective, allows an original line to be decoupled into several short lines for optimisation. An approximation method is developed from this property. Instead of optimising a long line, the method divides it into several short lines, optimises them separately and combines their optimal buffer distributions to find the optimal or near optimal buffer distribution of the original line. The method greatly improves the computation efficiency for solving buffer allocation problem for long lines, while ensuring the accuracy of the optimal buffer distribution. A heuristic explanation is proposed. Numerical experiments are provided to show the accuracy and efficiency of the method. The effect of the number and length of line segments on the performance of the method is discussed.     

Buffer capacity allocation for a desired throughput in production lines

In this study, we are concerned with finding the minimum-total-buffer allocation for a desired throughput in production lines with phase-type processing times. We have implemented a dynamic programming algorithm that uses a decomposition method to approximate the system throughput at every stage. We provide numerical examples to show the buffer allocation and compare the corresponding simulated throughput and its bounds with the desired throughput.     

Allocation of tasks to stations in small-batch assembly with learning: basic concepts

Conventional line balancing deals with the processing of large batches with fixed operation times, such that the throughput rate is maximized. Solution procedures are predicted upon equal allocation of work to stations along the line. When batches are small, operation times exhibit learning effects, and not all stations are employed at the beginning and end of the batch process. Thus a totally different approach must be taken. The objective is to minimize the throughput time of a finite batch. In this article we show that optimal solutions are based upon allocation of work to stations in decreasing proportions, so that more work is allocated to the first station than to the last. A number of theorems are presented to support and illustrate the decreasing proportions principle; and two heuristics, one based upon simplified linear programming model, and the other on the geometric mean ratio of successive task times, are developed to find task-to-station allocations that yield minimum throughput times for the small-batch problem. A comparison with equal allocation of work (under learning conditions) is made, and the properties of the task allocations and resultant schedules are discussed.     

Analysis of serial production lines: characterisation study and a new heuristic procedure for optimal buffer allocation

Buffer allocation in serial production lines is one of the important design issues, and hence it has been studied extensively in the literature. In this paper, we analyse the problem to characterise the optimal buffer allocation; specifically, we study the cases with single and multiple bottleneck stations under various experimental conditions. In addition, we develop an efficient heuristic procedure to allocate buffers in serial production lines to maximise throughput. The results of the computational experiments indicate that the proposed algorithm is very efficient in terms of both solution quality and CPU time requirements. Moreover, the characterisation study yields interesting findings that may lead to important practical implications. A comprehensive bibliography is also provided in the paper.     

Cash-flow-oriented buffer allocation in stochastic flow lines

This paper defines the problem of buffer space allocation in flow lines as an investment problem. A model is developed and solution techniques are described that can be used to determine buffer allocations that maximize the expected net present value of the investment, including machines, buffers and inventory. Production rates and inventory levels are explicitly linked to projected cash flow to assess the economic consequences of the buffer allocation. Several examples of linear flow lines as well as assembly/disassembly systems and flow lines with rework loops are analysed numerically. These examples demonstrate the importance of the buffer allocation problem and provide intuition with respect to the structure of optimized solutions. A result is that as product quality in a system with a rework loop improves, an optimally designed system can receive more buffer spaces and may use more inventory. This possibly counterintuitive result is due to the economic perspective on the buffer allocation problem.     

Simulation of unbalanced buffer allocation in unreliable unpaced production lines

This article presents the results of a study investigating the performance of unpaced unreliable production lines (i.e. subject to breakdown) that are unbalanced in terms of their buffer storage sizes. Simulation is carried out for five, eight and 10 station lines with mean buffer space set at two, four and six units. Buffer capacity is allocated in different configurations for each of these lines. Performance indicators on throughput, idle time and average buffer level are analysed using a range of statistical tools, and relationships between the independent and dependent variables are determined. Overall results show that the best patterns for unreliable lines in terms of generating higher throughput rates (or lower idle times) as compared to a balanced line are those where total available buffer capacity is allocated as evenly as possible between workstations. In contrast, concentrating more buffer capacity towards the end of the line gives best average buffer level results.     

A PREDICTIVE MODEL FOR THE THROUGHPUT OF UNBALANCED, UNBUFFERED THREE-STATION SERIAL LINES

The three-station serial line is a fundamental building block of many complex production systems. In this paper we develop methods for predicting the throughput of unbalanced three-station serial lines. We model the variability of processing times using a variety of probability distributions that spans the range of variabilities encountered in practice. We develop procedures for approximating throughput, for any allocation of total mean processing time, based on the throughput of a small number of easily analyzed cases.     

A heuristic for production scheduling and inventory control in the presence of sequence-dependent setup times

The consideration of sequence-dependent setup times is one of the most difficult aspects of production scheduling problems. This paper reports on the development of a heuristic procedure to address a realistic production and inventory control problem in the presence of sequence-dependent setup times. The problem considers known monthly demands, variable production rates, holding costs, minimum and maximum inventory levels per product, and regular and overtime capacity limits. The problem is formulated as a Mixed-Integer Program (MIP), where subtour elimination constraints are needed to enforce the generation of job sequences in each month. By relaxing the subtour elimination constraints, the MIP formulation can be used to find a lower bound on the optimal solution. CPLEX 3.0 is used to calculate lower bounds for relatively small instances of this production problem, which are then used to assess the merit of a proposed heuristic. The heuristic is based on a simple short-term memory tabu search method that coordinates linear programming and traveling salesperson solvers in the search for optimal or near-optimal production plans.     

Buffer sizing models for end-of-aisle order picking systems

We study an end-of-aisle order picking system with inbound and outbound buffer positions. The system is referred to as a miniload system with a horse-shoe front-end configuration, and is modeled as a two-stage cyclic queueing system with limited capacity. We analyze the system by utilizing known queueing results. Closed form expressions are developed for system performance measures, including the steady-state probability and system throughput. To provide some decision criteria in the design of buffer capacity, we examine the effect of the buffer size on system throughput. We give examples to illustrate how the results developed can be applied to solving real world problems. It is also shown that under heavy retrieval system demand, the system naturally achieves its optimal operating condition in the long run and it always performs dual command cycles.     

Research on scheduling with job-dependent learning effect and convex resource-dependent processing times

We study resource allocation scheduling with job-dependent learning effect on a single machine with or without due date assignment considerations. For a convex resource processing time function, we provide a polynomial time algorithm to find the optimal job sequence, and resource allocations that minimise the schedule criterion (the total compression cost) subject to the constraint that the total compression cost (the schedule criterion) is less than or equal to a fixed amount.     

面向多媒体业务的无线ATM多址接入协议

基于MDR-TDMA（Multi-service Dynamic Reservation-TDMA）的无线ATM多址接入控制协议包括两个主要的过程，即请求报文的信息时隙的分配过程，对于前者，通过基于帧的自适应伪贝叶斯ALOHA算法，在保证请求报文最优吞吐率的条件下，实现了不同优先级的请求报文接入。对于后者，着重分析了以视频会议为模型的VBR业务的带宽分配，提出了一种新的带宽分配方法-Minmax算法，并将它的仿真结果与线性比例算法进行比较。     

Optimal buffer allocation in production lines

The optimal allocation of buffers in production lines is an important research issue in the design of a manufacturing system. We present a new hybrid algorithm for this complex design problem: the hybrid Nested Partitions (NP) and Tabu Search (TS) method. The Nested Partitions method is globally convergent and can utilize many of the existing heuristic methods to speed up its convergence. In this paper, we incorporate the Tabu Search heuristic into the NP framework and demonstrate through numerical examples that using the hybrid method results in superior solutions. Our numerical results illustrate that the new algorithm is very efficient for buffer allocation problems in large production lines.