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.
The use of the learning curve has been receiving increasing attention due to its applications in different operations management areas; e.g. inventory management. In general, learning is an important consideration whenever an operator begins production of a new product, changes to a new machine or restarts production after some delay. This implies that the time/cost needed to produce a product will reduce as the individual, or group of individuals, becomes more proficient.
The economic manufacturing quantity model with learning in production has been treated in Refs. [1], [2], [3], [4], [5], [6], [7], [8], [9], [10], [11], [12], [13], [14] and [15]. These researches concluded that in the presence of learning in production, the optimal lot size policies were to produce more lots of smaller sizes, and that resulted in substantial savings in total inventory costs. Traditional inventory models [16] and [17] do not account for the time-value of money. The effects of discounting may be considered when determining the economic manufacturing quantity [18], [19], [20], [21], [22] and [23].
The basis of this research stems from the principles discussed above. First, learning has economic implications for the design of inventory systems due to the continuous improvement in production capacity. Secondly, as advocated in [18], [19], [20], [21], [22] and [23], discounting effects should be considered for the realistic modelling of the economic lot size problem. However, none of these Refs. [1], [2], [3], [4], [5], [6], [7], [8], [9], [10], [11], [12], [13], [14], [15], [16], [17], [18], [19], [20], [21], [22] and [23] studied the combined effect of learning in production and continuous time discounting on the economic manufacturing quantity. That is the focus of this paper.
The rest of the paper is organised as follows: Section 2 presents an introduction to learning curve theory, Section 3 describes the mathematical model that is used, Section 4 discusses the numerical results drawn from the mathematical model developed in Section 3, and finally, Section 5 presents a summary and conclusions.
