Chrissoleon T. Papadopoulos

A simulated annealing approach for buffer allocation in reliable production lines

We describe a simulated annealing approach for solving the buffer allocation problem in reliable production lines. The problem entails the determination of near optimal buffer allocation plans in large production lines with the objective of maximizing their average throughput. The latter is calculated utilizing a decomposition method. The allocation plan is calculated subject to a given amount of total buffer slots in a computationally efficient way.

Large production line optimization using simulated annealing

We present a robust generalized queuing network algorithm as an evaluative procedure for optimizing production line configurations using simulated annealing. We compare the results obtained with our algorithm to those of other studies and find some interesting similarities but also striking differences between them in the allocation of buffers, numbers of servers, and their service rates. While context dependent, these patterns of allocation are one of the most important insights which emerge in solving very long production lines. The patterns, however, are often counter-intuitive, which underscores the difficulty of the problem we address. The most interesting feature of our optimization procedure is its bounded execution time, which makes it viable for optimizing very long production line configurations. Based on the bounded execution time property, we have optimized configurations of up to 60 stations with 120 buffers and servers in less than five hours of CPU time.

Analysis and Design of Discrete Part Production Lines

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Stochastic algorithms for buffer allocation in reliable production lines

The allocation of buffers between workstations is a major optimization problem faced by manufacturing systems designers. It entails the determination of optimal buffer allocation plans in production lines with the objective of maximizing their throughput. We present and compare two stochastic approaches for solving the buffer allocation problem in large reliable production lines. The allocation plan is calculated subject to a given amount of total buffer slots using simulated annealing and genetic algorithms. The throughput is calculated utilizing a decomposition method.

Exact analysis of a discrete material three-station one-buffer merge system with unreliable machines

In this paper, a model of a discrete material flow line consisting of three unreliable machines and one buffer of limited capacity is analysed. A similar system, but with continuous flow of material was examined by Helber and Mehrtens (2001) and Tan (2001). In our system it is assumed that the buffer has two immediate preceding machines, performing the same operations and one immediate succeeding machine that receives material from the buffer. For the case where the buffer reaches its own capacity, one of the two preceding machines has priority over the other to dispose its processed part into the buffer. Processing times are assumed to be deterministic and identical for all machines and are taken as the time unit. Geometrically distributed operation dependent failures at the machines are assumed. All possible transition equations for the examined model are derived and a recursive algorithm that generates the transition matrix for any value N of the storage level is developed. Once the transition matrix is known the performance measures of the model under consideration can be easily evaluated. This model may be used as a building block in a decomposition method to evaluate large production systems with split/merge operations (for example, flow lines with quality inspections and rework loops).

A dynamic programming algorithm for the buffer allocation problem in homogeneous asymptotically reliable serial production lines

In this study, the buffer allocation problem (BAP) in homogeneous, asymptotically reliable serial production lines is considered. A known aggregation method, given by Lim, Meerkov, and Top (1990), for the performance evaluation (i.e., estimation of throughput) of this type of production lines when the buffer allocation is known, is used as an evaluative method in conjunction with a newly developed dynamic programming (DP) algorithm for the BAP. The proposed algorithm is applied to production lines where the number of machines is varying from four up to a hundred machines. The proposed algorithm is fast because it reduces the volume of computations by rejecting allocations that do not lead to maximization of the lines throughput. Numerical results are also given for large production lines.

Approximate analysis of serial flow lines with multiple parallel-machine stations

This paper studies serial flow lines, in which each station consists of multiple identical reliable parallel machines. The parallel machines of different work stations are not necessarily identical, viz., station processing times are assumed to be exponentially distributed with non-identical mean service rates. Initially, a model consisting of two stations with multiple parallel machines and an intermediate buffer is solved analytically, by developing a recursive algorithm that generates the transition matrix for any value of the intermediate buffer capacity. This model is used as a decomposition block for solving larger lines. More specifically, the decomposition block is solved via exact Markovian analysis and then the decomposition equations and an algorithm that simultaneously solves them are derived in order to evaluate the performance measures of large production systems with multiple parallel-machine stations. Numerical results are provided for large production lines with up to 1000 workstations. These results are compared against simulation and the average percentage error is found to be very small.

Markovian analysis of a discrete material manufacturing system with merge operations, operation-dependent and idleness failures

This paper examines a discrete material manufacturing system consisting of three machines that are subject to breakdown and one buffer of finite capacity. It is assumed that the buffer has two immediate preceding machines performing the same operations and one immediate succeeding machine receiving material from the buffer. When the buffer reaches its own capacity, one of the two preceding machines has priority over the other to dispose its processed part into the buffer.It is also assumed that there is a new way of the machines reaching failure, by allowing the machines to fail not only when they are operational but also when are either blocked or starved. The latter gives rise to the possibility of modeling the production of more than one part types. The model is solved analytically by developing a recursive algorithm that generates the transition matrix for any value C of the intermediate buffer capacity. Then various performance measures of the system (e.g., throughput) can be easily evaluated. Numerical results for the throughput are also given and these are compared against simulation. The proposed model may be used as a decomposition block to solve large flow lines with merge/ split operations (for example, flow lines with quality inspections and rework loops) and multiple part types.

A DSS for the buffer allocation of production lines based on a comparative evaluation of a set of search algorithms

In the design of production lines, the classical approach to the buffer allocation problem (BAP) is to use a search algorithm in association with an evaluative algorithm to obtain the mathematical optimum of the specified objective function. In practice, a choice often has to be made regarding which search algorithm to use for the efficient solution of the BAP. This paper gives the results of a carefully selected set of experiments on short (K = number of stations = 3, 4, , 11 stations), medium length (K = 12, 13, , 30 stations) and long lines (K = 40, 50, , 100 stations) and, within each line, small N (N = total number of buffer slots = K/2 if K is even; = (K – 1)/2 if K is odd), medium N (N = K + 1) and large N (N = 2K) to evaluate the effectiveness of the following five search algorithms: simulated annealing, genetic, tabu search, myopic and complete enumeration (where possible). The production lines are balanced and the single exponential machine at each station is perfectly reliable. All the experiments were run on a readily available desktop PC with the following specifications: Windows XP Professional Version 2002 Service Pack 3, Pentium® Dual-Core CPU E5300@2.60 GHz, 2.00 GB RAM. The measures of performance used are CPU time required and closeness to the maximum throughput achieved. The five search algorithms are ranked in respect to these two measures and certain findings regarding their performance over the experimental set are noted. The distributions of buffer slots to storage areas for the algorithm(s) leading to maximum throughput are examined and certain patterns are found, leading to indications for design rules. Based on the results of the above experiments, two additional sets of experiments were carried out, one using the simulated annealing algorithm for production lines of K = 3 to 20 and N = 1 to 20 (accounting for a total number of 360 different production lines) and another using the myopic algorithm for production lines of K = 3 to 80 and N = 1 to 120 (accounting for a total number of 9360 different production lines). These results may be used as references for comparison purposes in the international literature. Using the results from all sets of experiments, a decision support system (DSS) is designed and implemented which, as is illustrated, may assist production line designers in making decisions regarding the most appropriate of the five search algorithms tested to use for the BAP-A (the dual problem) and the BAP-B (the primal problem) for a wide class of production lines (consisting of K = 3 to 80 and N = 1 to 120).

Stochastic modeling of manufacturing systems : advances in design, performance evaluation, and control issues

Factory Design.- Dilemmas in factory design: paradox and paradigm.- Unreliable Production Lines.- Lean buffering in serial production lines with non-exponential machines.- Analysis of flow lines with Cox-2-distributed processing times and limited buffer capacity.- Performance evaluation of production lines with finite buffer capacity producing two different products.- Automated flow lines with shared buffer.- Integrated quality and quantity modeling of a production line.- Stochastic cyclic flow lines with blocking: Markovian models.- Queueing Network Models of Manufacturing Systems.- Performance analysis of multi-server tandem queues with finite buffers and blocking.- An analytical method for the performance evaluation of echelon kanban control systems.- Closed loop two-echelon repairable item systems.- A heuristic to control integrated multi-product multi-machine production-inventory systems with job shop routings and stochastic arrival, set-up and processing times.- Performance analysis of parallel identical machines with a generalized shortest queue arrival mechanism.- A review and comparison of hybrid and pull-type production control strategies.- Stochastic Production Planning and Assembly.- Planning order releases for an assembly system with random operation times.- A multiperiod stochastic production planning and sourcing problem with service level constraints.