An inventory model with controllable lead time and ordering cost, log-normal-distributed demand, and gamma-distributed available capacity

Abstract

Studying the inventory management literature regarding the models with controllable lead time, many researchers have assumed the random demand follows the normal distribution. However, in practice, it is observed that an accurate demand distribution is often skewed to the right for many items and fitting the normal distribution to the random demand may cause a great financial loss for an inventory/production system. Hence, the motivation of this study is to design a mathematical model where the demand follows the log-normal distribution. Also in order to expand upon previous research concerning the random available capacity, we assume that the random capacity follows a gamma-type distribution to cover a wide range of distribution shapes. Moreover, we consider the ordering cost is a deterministic variable and it is reduced by an extra investment. Also, to find an optimal policy of the proposed probabilistic mathematical model, a solution algorithm is established and a numerical example is proposed showing that utilizing the proposed model rather than the standard continuous-review model with the normal demand may reduce the total expected cost more than 20%.

Keywords

• inventory management
• log-normal distribution
• gamma/erlang distribution
• lead time
• ordering cost
• capacity