Economic lot sizing with learning and continuous time discounting: Is it significant?

Learning curves are a means of representing continuous improvement in firms. Such improvements bring savings in production costs. This may also allow smaller batches to be produced more frequently and hence bring further savings in holding costs. Earlier research advocated that for more realistic modelling of inventory problems, the holding cost should be evaluated means of the internal discount rate of the firm (C. Van Deft, J.P. Vail, International Journal of Production Economics 44 (1996) 255–265). This paper examines whether, when learning is considered, it is reasonable to ignore the effect of continuous time discounting of costs by investigating the effect of learning and time discounting both on the economic manufacturing quantity and minimum total inventory cost. Numerical examples are provided to illustrate the solution procedure for the mathematical model developed. Although the analysis yields different economic order quantities, the difference in cost from the quantities derived using Wilson lot size formula is not significant.