An economic order quantity lot sizing model with random supplier capacity

This paper presents a general formulation of the inventory lot sizing model with random supplier capacity under the EOQ framework. For a general capacity distribution, we show that the expected cost per unit of time is a unimodal function and pseudo-convex in the ordering quantity. Moreover, we derive some simple data-dependent bounds for both optimal lot size and expected cost per unit of time. In order to illustrate the general model, three types of distributions for the random capacity are analyzed as special cases. These are the uniform, exponential, and truncated normal distributions. For each of these distributions, we find that the maximum cost penalty of using the EOQ lot size instead of the optimal one is almost negligible (not greater than 0.52%, 1.81%, and 0.91% for the uniform, exponential, and truncated normal distributions, repectively). In addition, we extend the general model to allow for the presence of defective units in the quantity received from the supplier. It is shown that this extra randomness does not affect the optimal ordering policy for the original model.