Solutions to the <Q,r> inventory model for gamma lead‐time demand

Studies have shown (1) that a company that ignores lead‐time demand variability may suffer great financial damage, (2) that the gamma distribution provides the most common best fit to lead‐time demand for a variety of inventory items, and (3) that a fixed lead‐time demand assumption or a normal approximation to it will often yield significant errors because the true distribution is usually very much skewed to the right. Unfortunately, all of the methods for solving the <Q,r> inventory model with gamma lead‐time demand call for tabulated values and perhaps interpolation between them in every iteration. This paper developed an efficient and accurate algorithm for solving the <Q,r> model with gamma lead‐time demand. The suggested algorithm eliminates the need for tabulated values completely and converges to the optimal solution quadratically. Solutions for two special cases of gamma lead‐time demand were also discussed.