Timothy L. Smunt

Stochastic unpaced line design: Review and further experimental results

Abstract Previous design studies of unpaced assembly lines that exhibit stochastic task times indicate that an unbalanced allocation of task times results in optimal output rates. In this article, we present a comprehensive review of the previous literature on this topic and discuss the results of simulation experiments that test the bowl distribution for unbalancing unpaced lines. The simulation experiment was designed to test the bowl distribution in more realistic environments than previously tested and illustrates that a balanced line configuration is as good as or better than an unbalanced line configuration when task times are modeled with more typical values of variance. Stochastic unpaced assembly line research employs both simulation and analytical approaches to test the allocation of buffer capacity and task times to work stations. Analytical models are utilized to investigate simple line designs with exponential or Erlang task time distributions. Simulation is used for longer lines and for normal task time distributions. From the review of the previous research using both approaches, we note five major findings: 1) unbalancing task time allocation is optimal when task time variation is large; 2) unbalanced allocation of buffer storage capacity improves line output rate when task time variation is large; 3) output rate of an unpaced line decreases as the number of sequential workstations increases; 4) output rate increases as more buffer storage capacity is available; and 5) output rate decreases as the task time variation increases. Most of the previous research on unpaced lines investigated lines with few workstations and large task time variation. Empirical research by Dudley (6) suggests that variation of task times in practice is much less than variations employed in previous unpaced line studies. We present the results from simulation experiments that model longer unpaced lines with lower levels of task time variance of the magnitude that is likely to occur in practice. The results of our simulation experiments verify the benefits of using the bowl distribution for task time allocation when line lengths are short and task times experience large variance. However, when line lengths are extended or task time variation is reduced, the use of the bowl distribution for unbalancing the line degrades the lines efficiency. In these situations, the optimal task time allocation is a balanced line. Two important implications for managers follow from the results of our experiments: 1) that unpaced line output rate is relatively insensitive to moderate variations from optimal task time allocations when buffer storage is limited; and 2) that perfectly balanced line designs are optimal for most cases in practice.

The Effects of Learning on Optimal Lot Sizes: Further Developments on the Single Product Case

Abstract This paper reviews the previous research on the problem of determining optimal lot sizes when production costs decrease on a log-linear function. Problems due to simplifying assumptions of the previous work are discussed and modifications of previous models are presented to address more realistic conditions. Using a dynamic programming approach, the new results for two cases of learning, total transmission of learning (from lot to lot) and partial transmission, indicate that optimal lot sizes are increasing in the long-run and long transient states exist, contrary to conclusions of prior papers. The effect of forgetting indicates that operations managers should consider longer production runs for many processes. The revised model formulation presented in this study is also capable of handling demand characteristics of variance, growth and seasonality, significantly extending the application possibilities of the previous models which were limited to a continuous, deterministic demand pattern.

Optimal Acquisition of Automated Flexible Manufacturing Processes

We formulate the problem of converting a labor-intensive batch production process to one that incorporates flexible automation as a finite-state Markov decision process. Interest rates and the level of automated technology influence both operating and acquisition costs and are treated as random variables. The model specifies the optimal level of capacity to convert to flexible automation. The optimization criterion is the minimization of the sum of expected, discounted costs incurred over a finite planning horizon. The optimal acquisition strategy depends upon the time period, the current interest rate, the current level of technology, and a measure of the remaining capacity that is not automated. We investigate the structure of optimal acquisition strategies using mathematical analysis and simulation. Our objective is to illustrate the qualitative characteristics of optimal strategies for acquiring flexible automation. As a step toward the implementation of the model, we examine the qualitative consequences associated with specifying classes of inventory and acquisition cost functions.

The impact of worker forgetting on production scheduling

Numerous articles suggest using the Japanese manufacturing strategy of minimizing inventories by producing small lot sizes. However, few studies actually have investigated the relative advantages or disadvantages of such a strategy. Worker productivity improvements during production of a batch (learning)and the loss of productivity improvements due to the breaks between batches (forgetting)both influence the optimal lot size for a product. The results of this study indicate that worker forgetting in a batch production environment can substantially increase optimal lot sizes. Since forgetting causes a type of setup cost by penalizing breaks in production, it is intuitive to expect an increase in optimal lot size for forgetting. This study confirms the expectation. What is interesting, however, is that only a small amount of forgetting is required to substantially increase the optimal lot size. The conditions under which lot sizes need to be significantly increased are discussed and illustrated. The results...

Log-linear and non-log-linear learning curve models for production research and cost estimation

The empirical evidence supporting the use of learning curves for planning is well documented in the literature, although there still exists some misunderstandings on the use and accuracy of the various types of learning curve models currently used in production research and cost estimation. In this paper, we examine the continuous learning approach for log-linear learning curve models and its use in analysing productivity trends in manufacturing databases. In particular, we present the derivation of the mid-unit model, a continuous form of the log-linear learning curve, which can accurately provide production cost estimates from either cumulative average costs or unit costs. The formulation of the model requires negligible computational capabilities to accomplish even the most difficult learning curve projections, allowing for reasonable computation times when using regression analysis on large manufacturing databases. Further, we show that the ability to accurately project batch costs on a one or two slo...

Forecasting using partially known demands

Abstract Most forecasting models for building a master schedule do not use information from orders that have been received for future delivery. We propose two basic algorithms that forecast the total demand by making use of information on orders already received. We test these algorithms using actual demand data from a printing firm. The behavior of the algorithms under special conditions like price promotions and shocks is also illustrated. We conclude that the proposed algorithms perform relatively better than exponential smoothing when partially known demand data is available.

Improving operations planning with learning curves: overcoming the pitfalls of ‘messy’ shop floor data

Abstract While most of the previous research on learning and experience curves examines cost improvements at the product level, we investigate the use of learning curve analysis at the detailed component part production level. Using extensive shop floor data from a medium-sized commercial firm, we discovered that the ‘messy’ data (i.e. high level of data variance) at the detailed levels often lead to reduced decision maker confidence in the estimates of the learning rates. However, we also found that by applying simple aggregation methods, we could better determine the accuracy of the predicted learning curve rates. Increased confidence in the learning curve estimates is made possible by comparison of regression estimates made at the detailed data level to those made at various aggregated data levels. Based upon our analysis of the empirical data, we are able to provide insights into the practical use of learning curve analysis and associated data aggregation with ‘messy’ shop floor data.

Stochastic unpaced line design: A reply

Executive Summary In the May 1985 issue of the Journal of Operations Management, we published a paper containing two major segments ( Smunt and Perkins (1985) ). The first segment provided a comprehensive review of previously published research on unpaced assembly lines. Two of the primary references in this review were path-breaking studies by Hillier and Boling (1966) and Hillier and Boling (1979) . These studies introduced the idea of the “bowl phenomenon,” which suggests that line output can be increased (compared to a balanced line) by unbalancing the line with high service times placed at the beginning and end of the line and low service times placed in the middle of the line. This pair of studies also verified the existence of the bowl phenomenon for exponential and Erlang service times with line lengths up to five stations and buffer capacities between stations from zero to four units. The second segment of our 1985 paper reported on a set of experiments to investigate the “robustness” of the bowl phenomenon under varying service time and buffer capacity assumptions. We tested and confirmed three primary hypotheses: 1. The use of the bowl distribution to unbalance an assembly line will not significantly increase the output rate as compared to a balanced configuration when normally-distributed work station service times are employed with less variance than the exponential distribution. 2. Minimal increases of buffer storage capacity will significantly reduce or will negate the benefit of using the bowl distribution. 3. Output rate is not highly sensitive to moderate variations from optimal task time allocation for stochastic unpaced lines. In other words, we found that the bowl distribution does not have advantages over a balanced line if either more realistic normally-distributed service times are used or larger buffer capacities are available. Thus the bowl phenomenon, while interesting, does not appear to exist in most real world unpaced lines. In the “Note” which immediately precedes this “Reply,” the authors take issue with our conclusions, based primarily on their view that our 1985 experiments were “flawed.” While the “Note” authors provide some valuable arguments and correctly point out a weakness concerning the number of simulation repetitions in our 1985 study, in general it is their arguments that are “flawed,” as we will establish in this paper. In responding to the preceding “Note,” we have conducted a very extensive simulation experiment—much larger than either our 1985 study or the small study conducted as part of the preceding paper. The results of this enhanced study provide strong support for the conclusions of our 1985 paper.

Rough cut capacity planning in a learning environment

The area of capacity planning is receiving increased emphasis in the management of operations due to the financial benefits of efficiently utilizing capacity and to the importance of accurate capacity plans for use with material requirements planning (MRP) and other information-oriented planning systems. Most of the prior research in capacity planning has been limited to improving capacity management techniques that assume a constant level of productivity. But it has been shown in past empirical research that many firms exhibit productivity improvements, or learning, as more units are produced. These productivity improvements are usually associated with a learning process-human, technological, or organizational-and have been measured by logarithmic functions known as learning curves. When companies exhibit this learning process in the use of their capital or human resources, the capacity planning methodology used should consider the effects of future productivity improvements on capacity utilization. This paper presents an overview learning curve analysis (LCA) for rough-cut capacity planning and illustrates the effective use of learning curves for capacity planning through a comparison of traditional approaches with ones that incorporate the learning curve concept.

Processes with nearly-sequential routings: a comparative analysis

Abstract Recent advances in automated technology have made it possible to incorporate many of the benefits of flow lines in the production of low-to-medium volume products found in a batch environment. The use of automated technology and cellular manufacturing tends to induce flows that are nearly sequential—the level of flow dominance is high, but it is not as high as the level associated with a pure flow shop. While a number of prior research studies have examined the performance of specific process configurations, such as those associated with cellular manufacturing, group technology and flexible manufacturing systems, ours is the first to analyze the effects of flow dominance in a more general setting. In this paper, we study the effect on process performance of slight departures from purely-sequential flows. To obtain generalizable results, we use a full factorial simulation experiment to examine both the main and interaction effects of product attributes, such as the number of products and job size, and of process attributes, such as operation-time variance, setup time, parallel processing capability and flow dominance. Our results provide insights into the performance of a wide variety of batch production processes, including, as special cases, cellular manufacturing, jobs shops, and flow shops. We show that the performance of such systems, as measured by average flow times and flow time variance, can be substantially improved by eliminating even a small number of remaining non-standard routings, particularly when setup times are moderate-to-high or operation-time variation is low-to-moderate.