This paper studies alternative methods for reducing lead time and their impact on the safety stock and the expected total costs of a (Q,s) continuous review inventory control system. We focus on a single-vendor–single-buyer integrated inventory model with stochastic demand and variable, lot size-dependent lead time and assume that lead time consists of production and setup and transportation time. As a consequence, lead time may be reduced by crashing setup and transportation time, by increasing the production rate, or by reducing the lot size. We illustrate the benefits of reducing lead time in numerical examples and show that lead time reduction is especially beneficial in case of high demand uncertainty. Further, our studies indicate that a mixture of setup time and production time reduction is appropriate to lower expected total costs.
Lead time plays an important role in today's logistics management. Defined as the time that elapses between the placement of an order and the receipt of the order into inventory (see Silver et al., 1998), lead time may influence customer service and impact inventory costs. As the Japanese example of just-in-time-production has shown, consequently reducing lead times may increase productivity and improve the competitive position of the company (see also Tersine and Hummingbird, 1995).
In the inventory management literature, lead time has often been treated as a decision variable that may be varied within given boundaries. If it is assumed that lead time can be decomposed into several components, such as setup time, process time, or queue time, for example (see Tersine, 2002), it can be assumed that each component may be reduced at a crashing cost. For example, one could restructure the production process or use a sophisticated factory information system to reduce setup time or increase setup accuracy (see Shingo, 1985 and Trovinger and Bohn, 2005), modify the production equipment to speed up the production process or implement a batch transfer policy to benefit from overlapping production cycles (see Hopp et al., 1990). Reducing lead times is especially important in situations where customer demand is uncertain, since long lead times put the company at a high risk of running out of stock before an order arrives. In this context, a variety of studies illustrate that reducing replenishment lead time may lower the safety stock, reduce the stock-out loss, and improve the customer service level, which results in lower expected total costs. Further, it has been shown that lead time is correlated with financial performance indicators, such as ROI or average profit (see Christensen et al., 2007), which underscores the importance of managing lead time.
One major drawback we identified when studying the literature on lead time reduction in inventory models is that the vast majority of authors assumed that lead time is independent of the lot size quantity and that a piecewise linear function is appropriate to describe the relationship between lead time reduction and lead time crashing costs. While the resulting models may be suitable to describe a variety of industries, lead times often vary with the manufacturing lot size in practice. Further, we may assume that the relationship between lead time reduction and lead time crashing costs is not necessarily linear in nature and that more complicated cost structures may be found in reality.
To close the research gap identified above and to provide both practitioners and researchers with a comparison of alternative methods for reducing lead time, this paper studies an inventory model with stochastic demand and variable, lot-size dependent lead time under different lead time reduction strategies. We assume that lead time consists of production and setup and transportation time, and that lead time may be reduced by shortening setup and transportation time and/or by increasing the production rate, which results in reduced production time. We explicitly focus on a two-stage production system with a manufacturer and a buyer to study the impact of individual decisions on the total expected costs of the system.
The paper is organized as follows: in the next two sections, the article reviews related literature and outlines the assumptions and definitions which are used in the remaining parts of the paper. Subsequently, we develop a formal model and propose a solution method to find an approximate optimal solution. Numerical examples and the results of a simulation study are presented in Section 5. Section 6 concludes the article.
In this paper, we extended previous models by allowing lead time to be varied either by reducing setup time or by increasing the production rate, which results in a reduced production time. We illustrated the behavior of our model in numerical examples and conducted a computational experiment to derive more general results. It has been shown that the system may react in a variety of ways on an increased demand uncertainty during lead time, which gives practitioners important examples of how lead time-dependent risks may be controlled in practical situations.
One important aspect that has not been addressed in this paper is that varying the production rate or crashing setup time may impact the quality of the product under consideration. Thus, with an increasing or a decreasing production rate, the production process may produce a higher or a lower percentage of defective products that need to be reworked or scrapped. Although the production cost function used in this paper may reflect this relation in part, more complex interdependencies between the production rate of a production facility and the quality of the products produced on this facility may prevail in practice. Consequently, it would be necessary to consider a separate quality cost function to account for scrap, rework or shortages as a result of a variation in the production rate. One approach could be to use an exponentially distributed random variable, which describes the point in time at which a production process goes out of control, and to establish a connection between the production rate of the production facility and the mean of the variable (see for example Lee and Rosenblatt, 1987 and Zhu et al., 2007). Thus, with an increase or a decrease of the production rate, the mean of the random variable would be changed, resulting in a lower or higher probability of the production process going out of control. The same holds true for reductions in setup time, which may also influence product quality.
To increase the scope of our analysis, the model presented in this article could be extended to consider further measures for reducing lead time. For example, a queuing factor, which takes account of waiting times of the lots (see Kim and Benton, 1995), could be introduced in the model and subjected to control as well. In our point of view, a logarithmic investment function, as proposed by Portheus (1985), could be appropriate to describe the interdependencies between an investment and the reduction of the queuing factor. Further measures for reducing lead time, which may be incorporated in our model, can be found in the relevant literature (see for example Heard and Plossl, 1984 and Hopp et al., 1990). Finally, developing alternative solution procedures for finding the global minimum of the function proposed in this paper would be interesting.
