Learning curves and lot sizing for independent and dependent demand

This paper explores the effect of learning curve behaviour, as opposed to linear, on lot-sizing. The first portion of the paper develops optimizing models for the independent demand situation. The second portion examines lot sizing for dependent demand, developing a lot sizing rule similar to Part Period Balancing. After examining the shortcomings of previous attempts at the independent demand lot sizing problem, two models are derived. Excluding material costs (for an assembly operation, the cost of all components), the optimal lot size is seen to vary linearly with demand and inversely with the carrying cost rate. When material costs are included a small optimal lot size is derived. The difference between the two, expressed as a fraction of the smaller lot size, equals the material/labour ratio of the last unit produced in the smaller lot size. For dependent demand, the incremental model developed by Freeland and Colley as an improvement on Part Period Balancing is used as a beginning concept. An analogous model, called Assembly Period Balancing, is developed for learning curve cost behaviour. The decision rule for combining lots is expressed as a comparison of the material/labour ratio of the lot considered for combining with another expression involving the carrying cost rate, relative lot size and the learning curve exponent. Finally, cost data from an electronics manufacturer are used to examine the cost penalties of failing to recognise learning curve cost behaviour. It is shown that optimal lot sizes for learning curve costs can be much larger than those obtained assuming linear costs. It is also shown that much larger lots can be economically combined in the dependent demand case when costs follow a learning curve.